Tootfinder

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
Logan Nye
https://arxiv.org/abs/2508.14831 https://arxiv.org/pdf/2508.14831

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
We prove a square-root space simulation for deterministic multitape Turing machines, showing $\TIME[t] \subseteq \SPACE[O(\sqrt{t})]$. The key step is a Height Compression Theorem that uniformly (and in logspace) reshapes the canonical left-deep succinct computation tree for a block-respecting run into a binary tree whose evaluation-stack depth along any DFS path is $O(\log T)$ for $T = \lceil t/b \rceil$, while preserving $O(b)$ work at leaves, $O(1)$ at internal nodes, and edges that are logs…

Barycentric subspace analysis of network-valued data
Elodie Maignant (UniCA, EPIONE, CB, ZIB), Xavier Pennec (UniCA, EPIONE), Alain Trouv\'e (CB), Anna Calissano (UniCA, EPIONE, UCL)
https://arxiv.org/abs/2507.23559

Barycentric subspace analysis of network-valued data
Certain data are naturally modeled by networks or weighted graphs, be they arterial networks or mobility networks. When there is no canonical labeling of the nodes across the dataset, we talk about unlabeled networks. In this paper, we focus on the question of dimensionality reduction for this type of data. More specifically, we address the issue of interpreting the feature subspace constructed by dimensionality reduction methods. Most existing methods for network-valued data are derived from p…