Google Research details TurboQuant, a quantization algorithm to enable massive compression of LLMs and vector search engines without sacrificing accuracy (Google Research)
https://research.google/blog/turboquant-redefining-ai-efficiency-with-extreme…
I won’t lose any sleep over it, but for some reason YouTube’s algorithm is showing me way too many (any is too many) ads for women’s deodorants lately.
China's Cyberspace Administration requires firms to file their AI tools in a public algorithm registry, creating a detailed map of the country's AI ecosystem (Yi-Ling Liu/Wired)
https://www.wired.com/story/china-ai-boom-algorithm-registry/
Ski Rental with Distributional Predictions of Unknown Quality
Qiming Cui, Michael Dinitz
https://arxiv.org/abs/2602.21104 https://arxiv.org/pdf/2602.21104 https://arxiv.org/html/2602.21104
arXiv:2602.21104v1 Announce Type: new
Abstract: We revisit the central online problem of ski rental in the "algorithms with predictions" framework from the point of view of distributional predictions. Ski rental was one of the first problems to be studied with predictions, where a natural prediction is simply the number of ski days. But it is both more natural and potentially more powerful to think of a prediction as a distribution p-hat over the ski days. If the true number of ski days is drawn from some true (but unknown) distribution p, then we show as our main result that there is an algorithm with expected cost at most OPT O(min(max({eta}, 1) * sqrt(b), b log b)), where OPT is the expected cost of the optimal policy for the true distribution p, b is the cost of buying, and {eta} is the Earth Mover's (Wasserstein-1) distance between p and p-hat. Note that when {eta} < o(sqrt(b)) this gives additive loss less than b (the trivial bound), and when {eta} is arbitrarily large (corresponding to an extremely inaccurate prediction) we still do not pay more than O(b log b) additive loss. An implication of these bounds is that our algorithm has consistency O(sqrt(b)) (additive loss when the prediction error is 0) and robustness O(b log b) (additive loss when the prediction error is arbitrarily large). Moreover, we do not need to assume that we know (or have any bound on) the prediction error {eta}, in contrast with previous work in robust optimization which assumes that we know this error.
We complement this upper bound with a variety of lower bounds showing that it is essentially tight: not only can the consistency/robustness tradeoff not be improved, but our particular loss function cannot be meaningfully improved.
toXiv_bot_toot
All this to say that it's absurd on its face to try to achieve "AGI" with some algorithm.
I love taking the train, but the weaponized incompetence of VIA Rail makes wish I'd taken another type of transportation, nearly every time.
Current status: “I, like the other two agents you spoke to, can't actually help you in any way, but I assure you that once you're on the train, the staff will be able to help. It's *the algorithm* not us!”
An experiment finds X's feed algorithm favored conservative content, and switching to the "For you" feed shifted users' views toward more conservative positions (Ece Yildirim/Gizmodo)
https://gizmodo.com/researchers-find-t
X says it has open sourced its "core recommendation system" on GitHub and that the system "ranks everything using a Grok-based transformer model" (Lucas Ropek/TechCrunch)
https://techcrunch.com/2026/01/20/x-op
I am starting first concept drafts for a book about "the algorithm" and it is fascinating how "my ChatGPT" is really basically "my FYP" on steroids. So maybe labeling a person's chatbot also just as "algorithm" might help starting to show people a path out of psychosis.
Not that the "my algorithm" narrative is any good for us. It's probably the best illustration of the things we fucked up with computers/computing
@… When I started at Google in 2016 I had to sign a bunch of export control paperwork because I *might* be able to find some encryption algorithm somewhere in the VCS I guess.
Statistical Query Lower Bounds for Smoothed Agnostic Learning
Ilias Diakonikolas, Daniel M. Kane
https://arxiv.org/abs/2602.21191 https://arxiv.org/pdf/2602.21191 https://arxiv.org/html/2602.21191
arXiv:2602.21191v1 Announce Type: new
Abstract: We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus on the prototypical task of agnostically learning halfspaces under subgaussian distributions in the smoothed model. The best known upper bound for this problem relies on $L_1$-polynomial regression and has complexity $d^{\tilde{O}(1/\sigma^2) \log(1/\epsilon)}$, where $\sigma$ is the smoothing parameter and $\epsilon$ is the excess error. Our main result is a Statistical Query (SQ) lower bound providing formal evidence that this upper bound is close to best possible. In more detail, we show that (even for Gaussian marginals) any SQ algorithm for smoothed agnostic learning of halfspaces requires complexity $d^{\Omega(1/\sigma^{2} \log(1/\epsilon))}$. This is the first non-trivial lower bound on the complexity of this task and nearly matches the known upper bound. Roughly speaking, we show that applying $L_1$-polynomial regression to a smoothed version of the function is essentially best possible. Our techniques involve finding a moment-matching hard distribution by way of linear programming duality. This dual program corresponds exactly to finding a low-degree approximating polynomial to the smoothed version of the target function (which turns out to be the same condition required for the $L_1$-polynomial regression to work). Our explicit SQ lower bound then comes from proving lower bounds on this approximation degree for the class of halfspaces.
toXiv_bot_toot
Some _very_ early algorithm concept/pre-viz sketches/explorations for the Tron Legacy (2010) intro sequence. They informed another concept/approach in which we applied a similar algorithm to progressively trace out edges of an initially invisible and super detailed 3D city mesh. This required a lot of effort to retopologize the (huge) geometry supplied and creating a multi-res navigation graph to prioritize long/major edges over shorter ones, filter out undesired edges/directions, thereby cr…
The US' TikTok deal is a win for ByteDance: it will keep and license the algorithm instead of selling it, and continue to run TikTok's commercial activities (Jim Secreto/Financial Times)
https://www.ft.com/content/59b91fc8-03a1-48df-9821-e2fdff24bd33
<…
How to survive Instagram's algorithm as a creative
- "Instagram is wrecking my head. I have a fairly decent number of followers. But hardly anyone sees my work"
- "I have a completely organic audience, yet my posts don't reach most of my followers"
- "Instagram hides your posts unless you post a selfie or anything personal"
- "You have something new? Post it, leave and focus on more important things."
- "Do o…
I’m sorry that your precious little token based markov algorithm that you think of as human isn’t useful, but it’s not useful.
Tony Hoare,
the Turing Award-winning pioneer who created the Quicksort algorithm,
developed Hoare logic,
and advanced theories of concurrency and structured programming,
has died at age 92.
https://m.slashdot.org/story/453208
Submodular Maximization over a Matroid $k$-Intersection: Multiplicative Improvement over Greedy
Moran Feldman, Justin Ward
https://arxiv.org/abs/2602.08473 https://arxiv.org/pdf/2602.08473 https://arxiv.org/html/2602.08473
arXiv:2602.08473v1 Announce Type: new
Abstract: We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k 1)$-approximation for this problem, and the state-of-the-art algorithm only improves this approximation ratio to $k$. We give a $\frac{2k\ln2}{1 \ln2} O(\sqrt{k})<0.819k O(\sqrt{k})$ approximation for this problem. Our result is the first multiplicative improvement over the approximation ratio of the greedy algorithm for general $k$. We further show that our algorithm can be used to obtain roughly the same approximation ratio also for the more general problem in which the objective is not guaranteed to be monotone (the sublinear term in the approximation ratio becomes $O(k^{2/3})$ rather than $O(\sqrt{k})$ in this case).
All of our results hold also when the $k$-matroid intersection constraint is replaced with a more general matroid $k$-parity constraint. Furthermore, unlike the case in many of the previous works, our algorithms run in time that is independent of $k$ and polynomial in the size of the ground set. Our algorithms are based on a hybrid greedy local search approach recently introduced by Singer and Thiery (STOC 2025) for the weighted matroid $k$-intersection problem, which is a special case of the problem we consider. Leveraging their approach in the submodular setting requires several non-trivial insights and algorithmic modifications since the marginals of a submodular function $f$, which correspond to the weights in the weighted case, are not independent of the algorithm's internal randomness. In the special weighted case studied by Singer and Thiery, our algorithms reduce to a variant of their algorithm with an improved approximation ratio of $k\ln2 1-\ln2<0.694k 0.307$, compared to an approximation ratio of $\frac{k 1}{2\ln2}\approx0.722k 0.722$ guaranteed by Singer and Thiery.
toXiv_bot_toot
Someone asked me, “Have you read the latest Dan Brown?” There’s actually a mention of MISP in The Secret of Secrets. And yes, it fits surprisingly well within the story. Alex Conan (who assists Jonas Faukman in the investigation) mentions that he detected the activity using FTK, and that the indicators were later reused by the threat actor (having a hit on a MISP instance).
“But before I could build the algorithm, my FTK scan returned a hit. One of
the IoCs from th…
I went to see the Claude Desktop announcement, and they embed a YouTube Video, and this is what the algorithm thinks I should watch next:
A year since I cautioned about using APCA and calling it WCAG3’s next contrast algorithm:
https://toot.cafe/@aardrian/113801092971854851
As recent as last week, it seems WCAG3 contrast is still an open item:
Crosslisted article(s) found for cond-mat.dis-nn. https://arxiv.org/list/cond-mat.dis-nn/new
[1/1]:
- Partitioning networks into clusters of synchronized nodes via the message-passing algorithm: an u...
Massimo Ostilli
Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[5/6]:
- Watermarking Degrades Alignment in Language Models: Analysis and Mitigation
Apurv Verma, NhatHai Phan, Shubhendu Trivedi
https://arxiv.org/abs/2506.04462 https://mastoxiv.page/@arXiv_csCL_bot/114635190037336859
- Sensory-Motor Control with Large Language Models via Iterative Policy Refinement
J\^onata Tyska Carvalho, Stefano Nolfi
https://arxiv.org/abs/2506.04867 https://mastoxiv.page/@arXiv_csAI_bot/114635187854195641
- ICE-ID: A Novel Historical Census Dataset for Longitudinal Identity Resolution
de Carvalho, Popov, Kaatee, Correia, Th\'orisson, Li, Bj\"ornsson, Sigur{\dh}arson, Dibangoye
https://arxiv.org/abs/2506.13792 https://mastoxiv.page/@arXiv_csAI_bot/114703312162525342
- Feedback-driven recurrent quantum neural network universality
Lukas Gonon, Rodrigo Mart\'inez-Pe\~na, Juan-Pablo Ortega
https://arxiv.org/abs/2506.16332 https://mastoxiv.page/@arXiv_quantph_bot/114732532383196043
- Programming by Backprop: An Instruction is Worth 100 Examples When Finetuning LLMs
Cook, Sapora, Ahmadian, Khan, Rocktaschel, Foerster, Ruis
https://arxiv.org/abs/2506.18777 https://mastoxiv.page/@arXiv_csAI_bot/114738213040759661
- Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning
Jiechen Chen, Bipin Rajendran, Osvaldo Simeone
https://arxiv.org/abs/2506.21324 https://mastoxiv.page/@arXiv_csNE_bot/114754367612728319
- Enjoying Non-linearity in Multinomial Logistic Bandits: A Minimax-Optimal Algorithm
Pierre Boudart (SIERRA), Pierre Gaillard (Thoth), Alessandro Rudi (PSL, DI-ENS, Inria)
https://arxiv.org/abs/2507.05306 https://mastoxiv.page/@arXiv_statML_bot/114822374525501660
- Characterizing State Space Model and Hybrid Language Model Performance with Long Context
Saptarshi Mitra, Rachid Karami, Haocheng Xu, Sitao Huang, Hyoukjun Kwon
https://arxiv.org/abs/2507.12442 https://mastoxiv.page/@arXiv_csAR_bot/114867589638074984
- Is Exchangeability better than I.I.D to handle Data Distribution Shifts while Pooling Data for Da...
Ayush Roy, Samin Enam, Jun Xia, Won Hwa Kim, Vishnu Suresh Lokhande
https://arxiv.org/abs/2507.19575 https://mastoxiv.page/@arXiv_csCV_bot/114935399825741861
- TASER: Table Agents for Schema-guided Extraction and Recommendation
Nicole Cho, Kirsty Fielding, William Watson, Sumitra Ganesh, Manuela Veloso
https://arxiv.org/abs/2508.13404 https://mastoxiv.page/@arXiv_csAI_bot/115060386723032051
- Morphology-Aware Peptide Discovery via Masked Conditional Generative Modeling
Nuno Costa, Julija Zavadlav
https://arxiv.org/abs/2509.02060 https://mastoxiv.page/@arXiv_qbioBM_bot/115139546511384706
- PCPO: Proportionate Credit Policy Optimization for Aligning Image Generation Models
Jeongjae Lee, Jong Chul Ye
https://arxiv.org/abs/2509.25774 https://mastoxiv.page/@arXiv_csCV_bot/115298580419859537
- Multi-hop Deep Joint Source-Channel Coding with Deep Hash Distillation for Semantically Aligned I...
Didrik Bergstr\"om, Deniz G\"und\"uz, Onur G\"unl\"u
https://arxiv.org/abs/2510.06868 https://mastoxiv.page/@arXiv_csIT_bot/115343320768797486
- MoMaGen: Generating Demonstrations under Soft and Hard Constraints for Multi-Step Bimanual Mobile...
Chengshu Li, et al.
https://arxiv.org/abs/2510.18316 https://mastoxiv.page/@arXiv_csRO_bot/115416889485910123
- A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs
Roxanne Holden, Luana Ruiz
https://arxiv.org/abs/2510.20954 https://mastoxiv.page/@arXiv_statML_bot/115445273121677005
- Breaking Agent Backbones: Evaluating the Security of Backbone LLMs in AI Agents
Bazinska, Mathys, Casucci, Rojas-Carulla, Davies, Souly, Pfister
https://arxiv.org/abs/2510.22620 https://mastoxiv.page/@arXiv_csCR_bot/115451397563132982
- Uncertainty Calibration of Multi-Label Bird Sound Classifiers
Raphael Schwinger, Ben McEwen, Vincent S. Kather, Ren\'e Heinrich, Lukas Rauch, Sven Tomforde
https://arxiv.org/abs/2511.08261 https://mastoxiv.page/@arXiv_csSD_bot/115535982708483824
- Two-dimensional RMSD projections for reaction path visualization and validation
Rohit Goswami (Institute IMX and Lab-COSMO, \'Ecole polytechnique f\'ed\'erale de Lausanne)
https://arxiv.org/abs/2512.07329 https://mastoxiv.page/@arXiv_physicschemph_bot/115688910885717951
- Distribution-informed Online Conformal Prediction
Dongjian Hu, Junxi Wu, Shu-Tao Xia, Changliang Zou
https://arxiv.org/abs/2512.07770 https://mastoxiv.page/@arXiv_statML_bot/115689281155541568
- Coupling Experts and Routers in Mixture-of-Experts via an Auxiliary Loss
Ang Lv, Jin Ma, Yiyuan Ma, Siyuan Qiao
https://arxiv.org/abs/2512.23447 https://mastoxiv.page/@arXiv_csCL_bot/115808311310246601
toXiv_bot_toot
I read, When AI is Fluent in Data but Illiterate in Context:
'We are building evidence infrastructure at speed, and we are not asking, systematically enough, what the tools assume when they read human realities they were never designed to understand.'
https://reamby.substac…
@… @… For sure. Definitely a 30 second back of the napkin suggestion, not the one I think anyone should actually implement.
Hard to know *what* that algorithm should be without incentivizing *some* sort of gamification.
Possible identification of the Luna 9 Moon landing site using a novel machine learning algorithm: #Luna9 Spacecraft, 60 Years After It Vanished: https://www.iflscience.com/nasas-lunar-orbiter-may-have-spotted-long-lost-luna-9-spacecraft-60-years-after-it-vanished-82507
Why we devs don't "just do ___":
https://loadbearingtomato.com/p/why-chasing-twitters-approval-doesnt
> “what people say” is data, not truth. It is a story they are telling you. That story has value, but only if you don’t blindly interpre…
That kind of coverage achieves something even individual posts on social media cannot: it was not just the people with lots of followers, not just the people favored by the recommender algorithm or the tides of popularity, but instead a broad cross section of whoever was out there.
I don’t know who’s offering coverage like that in Iran like that right now. It may not exist. But even the BBC article at the top — filtered, edited, formatted, and tidied to sound like a BBC article, but still individual voices of people who are living through it — even that is welcome.
/end
algorithm, n.:
Trendy dance for hip programmers.
Incremental (k, z)-Clustering on Graphs
Emilio Cruciani, Sebastian Forster, Antonis Skarlatos
https://arxiv.org/abs/2602.08542 https://arxiv.org/pdf/2602.08542 https://arxiv.org/html/2602.08542
arXiv:2602.08542v1 Announce Type: new
Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric.
While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\tilde O(k m^{1 o(1)} k^{1 \frac{1}{\lambda}} m)$, where $\lambda \geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\tilde{O}(k)$ with a total update time of $m^{1 o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest.
In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.
toXiv_bot_toot
Clearly the military needs AI in order to have an algorithm to blame when everything goes sideways.
Damned robots.
Reading through Anthropic's official repo for giving agents various "super skills"[1]... There's an "algorithmic art" skill and the instructions are explicitly encouraging pure deception as one of the key "critical guidelines":
"The philosophy MUST stress multiple times that the final algorithm should appear as though it took countless hours to develop, was refined with care, and comes from someone at the absolute top of their field. This fram…
Meta launches an AI feature that lets Threads users temporarily personalize their feed by specifying topics in a public post that begins with "Dear Algo" (Jonathan Vanian/CNBC)
https://www.cnbc.com/2026/02/11/meta-threads-dear-algo-ai-algori…
Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
Behrooz Zarebavami, Ahmed H. Mahmoud, Ana Dodik, Changcheng Yuan, Serban D. Porumbescu, John D. Owens, Maryam Mehri Dehnavi, Justin Solomon
https://arxiv.org/abs/2602.00898 https://arxiv.org/pdf/2602.00898 https://arxiv.org/html/2602.00898
arXiv:2602.00898v1 Announce Type: new
Abstract: We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations, repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x.
toXiv_bot_toot
“Instead of wanting to learn and improve as humans, and build better software, we’ve outsourced our mistakes to an unthinking algorithm.”
https://localghost.dev/blog/stop-generating-start-thinking/
Partial fraction decompositions on hyperplane arrangements
Claire de Korte, Teresa Yu
https://arxiv.org/abs/2602.06531 https://arxiv.org/pdf/2602.06531 https://arxiv.org/html/2602.06531
arXiv:2602.06531v1 Announce Type: new
Abstract: We initiate the study of partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained by examining the primary decomposition of ideals coming from hyperplane arrangements. We then present an algorithm for finding a PFD that satisfies properties desired by physicists, and demonstrate the effectiveness of this algorithm for computing large examples coming from Feynman integrals.
toXiv_bot_toot
Design of Robust Raman Pulses for Cold Atom Interferometers Based on the Krotov Algorithm
Ziwen Song
https://arxiv.org/abs/2602.14494 https://arxiv.org/pdf…
Took a look at the ngscopeclient "fall time" filter since it's the next in line alphabetically for some refactoring and decided hey, the inner loop is pretty simple let's try GPUing it.
But first I wanted to get a baseline run time for 50M points (790 ms).
Aaand found numerical stability issues. So I need to fix the algorithm before I optimize it.
This is why we use int64's for time values in all new code, not float32 or even (as done here) float64.
Online Algorithm for Fractional Matchings with Edge Arrivals in Graphs of Maximum Degree Three
Kanstantsin Pashkovich, Thomas Snow
https://arxiv.org/abs/2602.07355 https://arxiv.org/pdf/2602.07355 https://arxiv.org/html/2602.07355
arXiv:2602.07355v1 Announce Type: new
Abstract: We study online algorithms for maximum cardinality matchings with edge arrivals in graphs of low degree. Buchbinder, Segev, and Tkach showed that no online algorithm for maximum cardinality fractional matchings can achieve a competitive ratio larger than $4/(9-\sqrt 5)\approx 0.5914$ even for graphs of maximum degree three. The negative result of Buchbinder et al. holds even when the graph is bipartite and edges are revealed according to vertex arrivals, i.e. once a vertex arrives, all edges are revealed that include the newly arrived vertex and one of the previously arrived vertices. In this work, we complement the negative result of Buchbinder et al. by providing an online algorithm for maximum cardinality fractional matchings with a competitive ratio at least $4/(9-\sqrt 5)\approx 0.5914$ for graphs of maximum degree three. We also demonstrate that no online algorithm for maximum cardinality integral matchings can have the competitive guarantee $0.5807$, establishing a gap between integral and fractional matchings for graphs of maximum degree three. Note that the work of Buchbinder et al. shows that for graphs of maximum degree two, there is no such gap between fractional and integral matchings, because for both of them the best achievable competitive ratio is $2/3$. Also, our results demonstrate that for graphs of maximum degree three best possible competitive ratios for fractional matchings are the same in the vertex arrival and in the edge arrival models.
toXiv_bot_toot
from my link log —
Four ways to improve a perfect SQL join algorithm.
https://remy.wang/blog/ya-fast.html
saved 2026-01-04 https://dotat.at/:/QZ8MM.…
Maybe in 2026 we can start to agree that "a complex algorithm selects content" is an editorial stance and platforms should be responsible to a certain degree.
I’m mildly curious why YouTube’s algorithm is showing me so many ads for women’s deodorants. Is my iPad telling me I stink now? Maybe TMI but never in all my 76 years have I ever bothered to use any kind of deodorant.
HALO: A Fine-Grained Resource Sharing Quantum Operating System
John Zhuoyang Ye, Jiyuan Wang, Yifan Qiao, Jens Palsberg
https://arxiv.org/abs/2602.07191 https://arxiv.org/pdf/2602.07191 https://arxiv.org/html/2602.07191
arXiv:2602.07191v1 Announce Type: new
Abstract: As quantum computing enters the cloud era, thousands of users must share access to a small number of quantum processors. Users need to wait minutes to days to start their jobs, which only takes a few seconds for execution. Current quantum cloud platforms employ a fair-share scheduler, as there is no way to multiplex a quantum computer among multiple programs at the same time, leaving many qubits idle and significantly under-utilizing the hardware. This imbalance between high user demand and scarce quantum resources has become a key barrier to scalable and cost-effective quantum computing.
We present HALO, the first quantum operating system design that supports fine-grained resource-sharing. HALO introduces two complementary mechanisms. First, a hardware-aware qubit-sharing algorithm that places shared helper qubits on regions of the quantum computer that minimize routing overhead and avoid cross-talk noise between different users' processes. Second, a shot-adaptive scheduler that allocates execution windows according to each job's sampling requirements, improving throughput and reducing latency. Together, these mechanisms transform the way quantum hardware is scheduled and achieve more fine-grained parallelism.
We evaluate HALO on the IBM Torino quantum computer on helper qubit intense benchmarks. Compared to state-of-the-art systems such as HyperQ, HALO improves overall hardware utilization by up to 2.44x, increasing throughput by 4.44x, and maintains fidelity loss within 33%, demonstrating the practicality of resource-sharing in quantum computing.
toXiv_bot_toot
Spotify announces Taste Profile editing in beta, the first time it lets users fine-tune the recommendation algorithm, starting with Premium users in New Zealand (Sarah Perez/TechCrunch)
https://techcrunch.com/2026/03/13/spotify-…
More than 20% of the videos that YouTube’s algorithm shows to new users are “AI slop”
– low-quality AI-generated content designed to farm views, research has found.
The video-editing company Kapwing surveyed 15,000 of the world’s most popular YouTube channels
– the top 100 in every country
– and found that 278 of them contain only AI slop.
Together, these AI slop channels have amassed more than 63 billion views and 221 million subscribers,
-- generating ab…
Space Complexity Dichotomies for Subgraph Finding Problems in the Streaming Model
Yu-Sheng Shih, Meng-Tsung Tsai, Yen-Chu Tsai, Ying-Sian Wu
https://arxiv.org/abs/2602.08002 https://arxiv.org/pdf/2602.08002 https://arxiv.org/html/2602.08002
arXiv:2602.08002v1 Announce Type: new
Abstract: We study the space complexity of four variants of the standard subgraph finding problem in the streaming model. Specifically, given an $n$-vertex input graph and a fixed-size pattern graph, we consider two settings: undirected simple graphs, denoted by $G$ and $H$, and oriented graphs, denoted by $\vec{G}$ and $\vec{H}$. Depending on the setting, the task is to decide whether $G$ contains $H$ as a subgraph or as an induced subgraph, or whether $\vec{G}$ contains $\vec{H}$ as a subgraph or as an induced subgraph. Let Sub$(H)$, IndSub$(H)$, Sub$(\vec{H})$, and IndSub$(\vec{H})$ denote these four variants, respectively.
An oriented graph is well-oriented if it admits a bipartition in which every arc is oriented from one part to the other, and a vertex is non-well-oriented if both its in-degree and out-degree are non-zero. For each variant, we obtain a complete dichotomy theorem, briefly summarized as follows.
(1) Sub$(H)$ can be solved by an $\tilde{O}(1)$-pass $n^{2-\Omega(1)}$-space algorithm if and only if $H$ is bipartite.
(2) IndSub$(H)$ can be solved by an $\tilde{O}(1)$-pass $n^{2-\Omega(1)}$-space algorithm if and only if $H \in \{P_3, P_4, co\mbox{-}P_3\}$.
(3) Sub$(\vec{H})$ can be solved by a single-pass $n^{2-\Omega(1)}$-space algorithm if and only if every connected component of $\vec H$ is either a well-oriented bipartite graph or a tree containing at most one non-well-oriented vertex.
(4) IndSub$(\vec{H})$ can be solved by an $\tilde{O}(1)$-pass $n^{2-\Omega(1)}$-space algorithm if and only if the underlying undirected simple graph $H$ is a $co\mbox{-}P_3$.
toXiv_bot_toot
So how do I know which TikTok I’m on when I’m opening the app in Germany— oracle TikTok or bytedance TikTok? Because it feels to me like their algorithm has changed somehow, it’s trying to show me a lot more „controversial“ posts.
VoroUDF: Meshing Unsigned Distance Fields with Voronoi Optimization
Ningna Wang, Zilong Wang, Xiana Carrera, Xiaohu Guo, Silvia Sell\'an
https://arxiv.org/abs/2602.02907 https://arxiv.org/pdf/2602.02907 https://arxiv.org/html/2602.02907
arXiv:2602.02907v1 Announce Type: new
Abstract: We present VoroUDF, an algorithm for reconstructing high-quality triangle meshes from Unsigned Distance Fields (UDFs). Our algorithm supports non-manifold geometry, sharp features, and open boundaries, without relying on error-prone inside/outside estimation, restrictive look-up tables nor topologically noisy optimization. Our Voronoi-based formulation combines a L_1 tangent minimization with feature-aware repulsion to robustly recover complex surface topology. It achieves significantly improved topological consistency and geometric fidelity compared to existing methods, while producing lightweight meshes suitable for downstream real-time and interactive applications.
toXiv_bot_toot
on my blog!
a hybrid quota-linear rate limiter
https://dotat.at/@/2026-01-12-hqlr.html
i was wondering if there's a "best of both worlds" algorithm, but on balance i think not
a pure linear rate limiter is better, if you can persuade your product managers to let yo…
A Faster Directed Single-Source Shortest Path Algorithm
Ran Duan, Xiao Mao, Xinkai Shu, Longhui Yin
https://arxiv.org/abs/2602.07868 https://arxiv.org/pdf/2602.07868 https://arxiv.org/html/2602.07868
arXiv:2602.07868v1 Announce Type: new
Abstract: This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n} \sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log \log n})$ for sparse graphs. This improves the recent breakthrough result of $O(m\log^{2/3} n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].
toXiv_bot_toot
They told the poor white man:
"You may be starving,
you may be broke,
but at least you aren't one of Them."
It worked.
The poor whites stopped fighting the rich.
They started guarding the rich.
They accepted their poverty -- because they had been given a false sense of superiority.
The "Divide and Rule" algorithm was born.
350 years later, the campaign is still running.
The Elite are still terrified of Unity…
An interview with Hinge CEO Jackie Jantos, promoted from CMO in December 2025, as the dating app hits 1.8M paying users, gaining ground while others struggle (Kieran Smith/Financial Times)
https://www.ft.com/content/32af07ca-213c-422b-a7a4-a1ae04e023d0
Robust Multiagent Collaboration Through Weighted Max-Min T-Joins
Sharareh Alipour
https://arxiv.org/abs/2602.07720 https://arxiv.org/pdf/2602.07720 https://arxiv.org/html/2602.07720
arXiv:2602.07720v1 Announce Type: new
Abstract: Many multiagent tasks -- such as reviewer assignment, coalition formation, or fair resource allocation -- require selecting a group of agents such that collaboration remains effective even in the worst case. The \emph{weighted max-min $T$-join problem} formalizes this challenge by seeking a subset of vertices whose minimum-weight matching is maximized, thereby ensuring robust outcomes against unfavorable pairings.
We advance the study of this problem in several directions. First, we design an algorithm that computes an upper bound for the \emph{weighted max-min $2k$-matching problem}, where the chosen set must contain exactly $2k$ vertices. Building on this bound, we develop a general algorithm with a \emph{$2 \ln n$-approximation guarantee} that runs in $O(n^4)$ time. Second, using ear decompositions, we propose another upper bound for the weighted max-min $T$-join cost. We also show that the problem can be solved exactly when edge weights belong to $\{1,2\}$.
Finally, we evaluate our methods on real collaboration datasets. Experiments show that the lower bounds from our approximation algorithm and the upper bounds from the ear decomposition method are consistently close, yielding empirically small constant-factor approximations. Overall, our results highlight both the theoretical significance and practical value of weighted max-min $T$-joins as a framework for fair and robust group formation in multiagent systems.
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Approximate Cartesian Tree Matching with Substitutions
Panagiotis Charalampopoulos, Jonas Ellert, Manal Mohamed
https://arxiv.org/abs/2602.08570 https://arxiv.org/pdf/2602.08570 https://arxiv.org/html/2602.08570
arXiv:2602.08570v1 Announce Type: new
Abstract: The Cartesian tree of a sequence captures the relative order of the sequence's elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a text $T$ of length $n$ and a pattern $P$ of length $m$. In the exact Cartesian tree matching problem, the task is to find all length-$m$ fragments of $T$ whose Cartesian tree coincides with the Cartesian tree $CT(P)$ of the pattern. Although the exact version of the problem can be solved in linear time [Park et al., TCS 2020], it remains rather restrictive; for example, it is not robust to outliers in the pattern.
To overcome this limitation, we consider the approximate setting, where the goal is to identify all fragments of $T$ that are close to some string whose Cartesian tree matches $CT(P)$. In this work, we quantify closeness via the widely used Hamming distance metric. For a given integer parameter $k>0$, we present an algorithm that computes all fragments of $T$ that are at Hamming distance at most $k$ from a string whose Cartesian tree matches $CT(P)$. Our algorithm runs in time $\mathcal O(n \sqrt{m} \cdot k^{2.5})$ for $k \leq m^{1/5}$ and in time $\mathcal O(nk^5)$ for $k \geq m^{1/5}$, thereby improving upon the state-of-the-art $\mathcal O(nmk)$-time algorithm of Kim and Han [TCS 2025] in the regime $k = o(m^{1/4})$.
On the way to our solution, we develop a toolbox of independent interest. First, we introduce a new notion of periodicity in Cartesian trees. Then, we lift multiple well-known combinatorial and algorithmic results for string matching and periodicity in strings to Cartesian tree matching and periodicity in Cartesian trees.
toXiv_bot_toot
The EU says that TikTok's "addictive design" is illegal under the DSA, citing the app's infinite scroll and recommendation algorithm, in preliminary findings (Adam Satariano/New York Times)
https://www.nytimes.com/2026/02/06/business/tiktok-a…
Perfect Network Resilience in Polynomial Time
Matthias Bentert, Stefan Schmid
https://arxiv.org/abs/2602.03827 https://arxiv.org/pdf/2602.03827 https://arxiv.org/html/2602.03827
arXiv:2602.03827v1 Announce Type: new
Abstract: Modern communication networks support local fast rerouting mechanisms to quickly react to link failures: nodes store a set of conditional rerouting rules which define how to forward an incoming packet in case of incident link failures. The rerouting decisions at any node $v$ must rely solely on local information available at $v$: the link from which a packet arrived at $v$, the target of the packet, and the incident link failures at $v$. Ideally, such rerouting mechanisms provide perfect resilience: any packet is routed from its source to its target as long as the two are connected in the underlying graph after the link failures. Already in their seminal paper at ACM PODC '12, Feigenbaum, Godfrey, Panda, Schapira, Shenker, and Singla showed that perfect resilience cannot always be achieved. While the design of local rerouting algorithms has received much attention since then, we still lack a detailed understanding of when perfect resilience is achievable.
This paper closes this gap and presents a complete characterization of when perfect resilience can be achieved. This characterization also allows us to design an $O(n)$-time algorithm to decide whether a given instance is perfectly resilient and an $O(nm)$-time algorithm to compute perfectly resilient rerouting rules whenever it is. Our algorithm is also attractive for the simple structure of the rerouting rules it uses, known as skipping in the literature: alternative links are chosen according to an ordered priority list (per in-port), where failed links are simply skipped. Intriguingly, our result also implies that in the context of perfect resilience, skipping rerouting rules are as powerful as more general rerouting rules. This partially answers a long-standing open question by Chiesa, Nikolaevskiy, Mitrovic, Gurtov, Madry, Schapira, and Shenker [IEEE/ACM Transactions on Networking, 2017] in the affirmative.
toXiv_bot_toot
Replaced article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Optimal Hardness of Online Algorithms for Large Independent Sets
David Gamarnik, Eren C. K{\i}z{\i}lda\u{g}, Lutz Warnke
https://arxiv.org/abs/2504.11450 https://mastoxiv.page/@arXiv_csDS_bot/114346418465357434
- An Approximation Algorithm for Monotone Submodular Cost Allocation
Ryuhei Mizutani
https://arxiv.org/abs/2511.00470 https://mastoxiv.page/@arXiv_csDS_bot/115490466535056736
- Expected Cost of Greedy Online Facility Assignment on Regular Polygons (v3)
Md. Rawha Siddiqi Riad, Md. Tanzeem Rahat, Md. Manzurul Hasan
https://arxiv.org/abs/2512.00506 https://mastoxiv.page/@arXiv_csDS_bot/115648910775471187
- Nested and outlier embeddings into trees
Shuchi Chawla, Kristin Sheridan
https://arxiv.org/abs/2601.15470 https://mastoxiv.page/@arXiv_csDS_bot/115943420904659985
- Bankrupting DoS Attackers
Trisha Chakraborty, Abir Islam, Valerie King, Daniel Rayborn, Jared Saia, Maxwell Young
https://arxiv.org/abs/2205.08287
- An Algorithm for Fast and Correct Computation of Reeb Spaces for PL Bivariate Fields
Amit Chattopadhyay, Yashwanth Ramamurthi, Osamu Saeki
https://arxiv.org/abs/2403.06564 https://mastoxiv.page/@arXiv_csCG_bot/112081476174323525
- On Densest $k$-Subgraph Mining and Diagonal Loading: Optimization Landscape and Finite-Step Exact...
Qiheng Lu, Nicholas D. Sidiropoulos, Aritra Konar
https://arxiv.org/abs/2410.07388 https://mastoxiv.page/@arXiv_csSI_bot/113287589348257824
- A New Quantum Linear System Algorithm Beyond the Condition Number and Its Application to Solving ...
Jianqiang Li
https://arxiv.org/abs/2510.05588 https://mastoxiv.page/@arXiv_quantph_bot/115337999786748703
- On Purely Private Covariance Estimation
Tommaso d'Orsi, Gleb Novikov
https://arxiv.org/abs/2510.26717 https://mastoxiv.page/@arXiv_csLG_bot/115468358153466988
- The Query Complexity of Local Search in Rounds on General Graphs
Simina Br\^anzei, Ioannis Panageas, Dimitris Paparas
https://arxiv.org/abs/2601.13266 https://mastoxiv.page/@arXiv_csCC_bot/115932039505257286
toXiv_bot_toot
on my blog!
doubly dual shuffles
https://dotat.at/@/2025-12-25-shuffle.html
polishing a classic algorithm to a pearlescent sheen as a gift to you this winter holiday
i wrote three lines of code in four different ways, but i tried to highlight how similar the four vari…
A $5$-Approximation Analysis for the Cover Small Cuts Problem
Miles Simmons, Ishan Bansal, Joe Cheriyan
https://arxiv.org/abs/2602.01462 https://arxiv.org/pdf/2602.01462 https://arxiv.org/html/2602.01462
arXiv:2602.01462v1 Announce Type: new
Abstract: In the Cover Small Cuts problem, we are given a capacitated (undirected) graph $G=(V,E,u)$ and a threshold value $\lambda$, as well as a set of links $L$ with end-nodes in $V$ and a non-negative cost for each link $\ell\in L$; the goal is to find a minimum-cost set of links such that each non-trivial cut of capacity less than $\lambda$ is covered by a link. Bansal, Cheriyan, Grout, and Ibrahimpur (arXiv:2209.11209, Algorithmica 2024) showed that the WGMV primal-dual algorithm, due to Williamson, Goemans, Mihail, and Vazirani (Combinatorica, 1995), achieves approximation ratio $16$ for the Cover Small Cuts problem; their analysis uses the notion of a pliable family of sets that satisfies a combinatorial property. Later, Bansal (arXiv:2308.15714v2, IPCO 2025) and then Nutov (arXiv:2504.03910, MFCS 2025) proved that the same algorithm achieves approximation ratio $6$. We show that the same algorithm achieves approximation ratio $5$, by using a stronger notion, namely, a pliable family of sets that satisfies symmetry and structural submodularity.
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TikTok US says it is working to restore services after a power outage at a data center and any algorithm changes users noticed were likely due to the outage (Dan Whateley/Business Insider)
https://www.businessinsider.com/tiktok-outage-data-cent…
A polynomial-time algorithm for recognizing high-bandwidth graphs
Luis M. B. Varona
https://arxiv.org/abs/2602.01755 https://arxiv.org/pdf/2602.01755 https://arxiv.org/html/2602.01755
arXiv:2602.01755v1 Announce Type: new
Abstract: An unweighted, undirected graph $G$ on $n$ nodes is said to have \emph{bandwidth} at most $k$ if its nodes can be labelled from $0$ to $n - 1$ such that no two adjacent nodes have labels that differ by more than $k$. It is known that one can decide whether the bandwidth of $G$ is at most $k$ in $O(n^k)$ time and $O(n^k)$ space using dynamic programming techniques. For small $k$ close to $0$, this approach is effectively polynomial, but as $k$ scales with $n$, it becomes superexponential, requiring up to $O(n^{n - 1})$ time (where $n - 1$ is the maximum possible bandwidth). In this paper, we reformulate the problem in terms of bipartite matching for sufficiently large $k \ge \lfloor (n - 1)/2 \rfloor$, allowing us to use Hall's marriage theorem to develop an algorithm that runs in $O(n^{n - k 1})$ time and $O(n)$ auxiliary space (beyond storage of the input graph). This yields polynomial complexity for large $k$ close to $n - 1$, demonstrating that the bandwidth recognition problem is solvable in polynomial time whenever either $k$ or $n - k$ remains small.
toXiv_bot_toot
Crosslisted article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- A Fault-Tolerant Version of Safra's Termination Detection Algorithm
Wan Fokkink, Georgios Karlos, Andy Tatman
https://arxiv.org/abs/2602.00272 https://mastoxiv.page/@arXiv_csDC_bot/116005743114928343
- Non-Clashing Teaching in Graphs: Algorithms, Complexity, and Bounds
Sujoy Bhore, Liana Khazaliya, Fionn Mc Inerney
https://arxiv.org/abs/2602.00657 https://mastoxiv.page/@arXiv_csCC_bot/116005533092908045
- Sublinear Time Quantum Algorithm for Attention Approximation
Zhao Song, Jianfei Xue, Jiahao Zhang, Lichen Zhang
https://arxiv.org/abs/2602.00874 https://mastoxiv.page/@arXiv_quantph_bot/116006587128552159
- Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing
Anxin Guo, Jingwei Li
https://arxiv.org/abs/2602.00906 https://mastoxiv.page/@arXiv_csLG_bot/116006973804501595
- Counting Unit Circular Arc Intersections
Haitao Wang
https://arxiv.org/abs/2602.01074 https://mastoxiv.page/@arXiv_csCG_bot/116005535191670040
- Profit Maximization in Closed Social Networks
Poonam Sharma, Suman Banerjee
https://arxiv.org/abs/2602.01232 https://mastoxiv.page/@arXiv_csSI_bot/116005691056225955
- Totally $\Delta$-Modular Tree Decompositions of Graphic Matrices for Integer Programming
Caleb McFarland
https://arxiv.org/abs/2602.01499 https://mastoxiv.page/@arXiv_mathCO_bot/116006381339684193
- Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex A...
Taihei Oki, Shinsaku Sakaue
https://arxiv.org/abs/2602.01682 https://mastoxiv.page/@arXiv_csLG_bot/116007186801693076
- Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences
Samuel McCauley, Benjamin Moseley, Helia Niaparast, Shikha Singh
https://arxiv.org/abs/2602.02254 https://mastoxiv.page/@arXiv_csGT_bot/116005915605630934
- Deciding Reachability and the Covering Problem with Diagnostics for Sound Acyclic Free-Choice Wor...
Thomas M. Prinz, Christopher T. Schwanen, Wil M. P. van der Aalst
https://arxiv.org/abs/2602.02447 https://mastoxiv.page/@arXiv_csFL_bot/116005733006023408
toXiv_bot_toot
End Cover for Initial Value Problem: Complete Validated Algorithms with Complexity Analysis
Bingwei Zhang, Chee Yap
https://arxiv.org/abs/2602.00162 https://arxiv.org/pdf/2602.00162 https://arxiv.org/html/2602.00162
arXiv:2602.00162v1 Announce Type: new
Abstract: We consider the first-order autonomous ordinary differential equation \[ \mathbf{x}' = \mathbf{f}(\mathbf{x}), \] where $\mathbf{f} : \mathbb{R}^n \to \mathbb{R}^n$ is locally Lipschitz. For a box $B_0 \subseteq \mathbb{R}^n$ and $h > 0$, we denote by $\mathrm{IVP}_{\mathbf{f}}(B_0,h)$ the set of solutions $\mathbf{x} : [0,h] \to \mathbb{R}^n$ satisfying \[ \mathbf{x}'(t) = \mathbf{f}(\mathbf{x}(t)), \qquad \mathbf{x}(0) \in B_0 . \]
We present a complete validated algorithm for the following \emph{End Cover Problem}: given $(\mathbf{f}, B_0, \varepsilon, h)$, compute a finite set $\mathcal{C}$ of boxes such that \[ \mathrm{End}_{\mathbf{f}}(B_0,h) \;\subseteq\; \bigcup_{B \in \mathcal{C}} B \;\subseteq\; \mathrm{End}_{\mathbf{f}}(B_0,h) \oplus [-\varepsilon,\varepsilon]^n , \] where \[ \mathrm{End}_{\mathbf{f}}(B_0,h) = \left\{ \mathbf{x}(h) : \mathbf{x} \in \mathrm{IVP}_{\mathbf{f}}(B_0,h) \right\}. \]
Moreover, we provide a complexity analysis of our algorithm and introduce a novel technique for computing the end cover $\mathcal{C}$ based on covering the boundary of $\mathrm{End}_{\mathbf{f}}(B_0,h)$. Finally, we present experimental results demonstrating the practicality of our approach.
toXiv_bot_toot
Crosslisted article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Algebraic Reduction to Improve an Optimally Bounded Quantum State Preparation Algorithm
Giacomo Belli, Michele Amoretti
https://arxiv.org/abs/2602.06535 https://mastoxiv.page/@arXiv_quantph_bot/116040046858615026
- Induced Cycles of Many Lengths
Maria Chudnovsky, Ilya Maier
https://arxiv.org/abs/2602.06874 https://mastoxiv.page/@arXiv_mathCO_bot/116039905295882594
- Circuit Diameter of Polyhedra is Strongly Polynomial
Bento Natura
https://arxiv.org/abs/2602.06958 https://mastoxiv.page/@arXiv_mathOC_bot/116040016711065918
toXiv_bot_toot
Local Computation Algorithms for (Minimum) Spanning Trees on Expander Graphs
Pan Peng, Yuyang Wang
https://arxiv.org/abs/2602.07394 https://arxiv.org/pdf/2602.07394 https://arxiv.org/html/2602.07394
arXiv:2602.07394v1 Announce Type: new
Abstract: We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $ T $ is defined implicitly by $ G $ and the randomness of the algorithm. It is known that LCAs for spanning trees do not exist in general graphs, even for simple graph families. We identify a natural and well-studied class of graphs -- \emph{expander graphs} -- that do admit \emph{sublinear-time} LCAs for spanning trees. This is perhaps surprising, as previous work on expanders only succeeded in designing LCAs for \emph{sparse spanning subgraphs}, rather than full spanning trees. We design an LCA with probe complexity $ O\left(\sqrt{n}\left(\frac{\log^2 n}{\phi^2} d\right)\right)$ for graphs with conductance at least $ \phi $ and maximum degree at most $ d $ (not necessarily constant), which is nearly optimal when $\phi$ and $d$ are constants, since $\Omega(\sqrt{n})$ probes are necessary even for expanders. Next, we show that for the natural class of \emph{\ER graphs} $ G(n, p) $ with $ np = n^{\delta} $ for any constant $ \delta > 0 $ (which are expanders with high probability), the $ \sqrt{n} $ lower bound can be bypassed. Specifically, we give an \emph{average-case} LCA for such graphs with probe complexity $ \tilde{O}(\sqrt{n^{1 - \delta}})$.
Finally, we extend our techniques to design LCAs for the \emph{minimum spanning tree (MST)} problem on weighted expander graphs. Specifically, given a $d$-regular unweighted graph $\bar{G}$ with sufficiently strong expansion, we consider the weighted graph $G$ obtained by assigning to each edge an independent and uniform random weight from $\{1,\ldots,W\}$, where $W = O(d)$. We show that there exists an LCA that is consistent with an exact MST of $G$, with probe complexity $\tilde{O}(\sqrt{n}d^2)$.
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Neighborhood-Aware Graph Labeling Problem
Mohammad Shahverdikondori, Sepehr Elahi, Patrick Thiran, Negar Kiyavash
https://arxiv.org/abs/2602.08098 https://arxiv.org/pdf/2602.08098 https://arxiv.org/html/2602.08098
arXiv:2602.08098v1 Announce Type: new
Abstract: Motivated by optimization oracles in bandits with network interference, we study the Neighborhood-Aware Graph Labeling (NAGL) problem. Given a graph $G = (V,E)$, a label set of size $L$, and local reward functions $f_v$ accessed via evaluation oracles, the objective is to assign labels to maximize $\sum_{v \in V} f_v(x_{N[v]})$, where each term depends on the closed neighborhood of $v$. Two vertices co-occur in some neighborhood term exactly when their distance in $G$ is at most $2$, so the dependency graph is the squared graph $G^2$ and $\mathrm{tw}(G^2)$ governs exact algorithms and matching fine-grained lower bounds. Accordingly, we show that this dependence is inherent: NAGL is NP-hard even on star graphs with binary labels and, assuming SETH, admits no $(L-\varepsilon)^{\mathrm{tw}(G^2)}\cdot n^{O(1)}$-time algorithm for any $\varepsilon>0$. We match this with an exact dynamic program on a tree decomposition of $G^2$ running in $O\!\left(n\cdot \mathrm{tw}(G^2)\cdot L^{\mathrm{tw}(G^2) 1}\right)$ time. For approximation, unless $\mathsf{P}=\mathsf{NP}$, for every $\varepsilon>0$ there is no polynomial-time $n^{1-\varepsilon}$-approximation on general graphs even under the promise $\mathrm{OPT}>0$; without the promise $\mathrm{OPT}>0$, no finite multiplicative approximation ratio is possible. In the nonnegative-reward regime, we give polynomial-time approximation algorithms for NAGL in two settings: (i) given a proper $q$-coloring of $G^2$, we obtain a $1/q$-approximation; and (ii) on planar graphs of bounded maximum degree, we develop a Baker-type polynomial-time approximation scheme (PTAS), which becomes an efficient PTAS (EPTAS) when $L$ is constant.
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