2026-02-06 21:45:56
Spotify rolls out About the Song, swipeable stories in English, summarized from third-party sources to highlight song details, in beta for Premium users (Aisha Malik/TechCrunch)
https://techcrunch.com/2026/02/06/spotifys-n…
Spotify rolls out About the Song, swipeable stories in English, summarized from third-party sources to highlight song details, in beta for Premium users (Aisha Malik/TechCrunch)
https://techcrunch.com/2026/02/06/spotifys-n…
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
The pressure is
'at a fever pitch'
as the US pursues
a third oil tanker
near Venezuela
https://sg.news.yahoo.com/trump-summarized-washingtons-multi-pronged-072945336.html
Metacurity is the only independent daily cybersecurity newsletter that is written outside the usual cyber press echosphere and is a refreshing alternative to vendor-driven content and PR-flavored threat intelligence.
Every day, Metacurity publishes critical infosec developments that CISOs, security engineers, IT decision-makers, and infosec practitioners should know, scanned from thousands of sources and expertly summarized.
I've never asked on social media before, but if yo…
Iskander missile collapse and 1.26 million occupiers eliminated: Russia's 4-year losses summarized!: https://benborges.xyz/2026/02/25/iskander-missile-collapse-and-million.html
It's better not to let me ponder on things too much, because I reach worrying conclusions. Like the one that my social life recently could be summarized as attending a funeral in December.
Don't miss today's Metacurity which is jam-packed with a host of intense cybersecurity developments, including
--Texas AG sues TP-Link, saying it allowed the CCP to hack routers,
--A hacker gained access to a French national bank database with 1.2m accounts,
--Microsoft 365 Copilot bug summarized confidential emails,
--DEF CON bans Epstein's hacking associates,
--Deutsche Bahn operations disrupted by cyberattack,
--Polish army bans Chinese cars,…
NFL wild-card round by the numbers: What to know about thrilling weekend of playoff games https://www.nytimes.com/athletic/6965133/2026/01/13/nfl-wild-card-round-numbers-interesting-facts/