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arXiv:2610.20079v1 Announce Type: new Abstract: Network coding allows intermediate nodes to combine messages, whereas routing only forwards them. The Li-Li conjecture asserts that network coding and fractional routing…
arXiv:2010.05779v5 Announce Type: replace-cross Abstract: We show that for every integer $n\geq 1$ there exists a graph $G_n$ with $(1+o(1))n$ vertices and $n^{1 + o(1)}$ edges such that every $n$-vertex planar graph is…
arXiv:2610.19710v1 Announce Type: new Abstract: We give a dynamic graph algorithm which maintains a 3-coloring in bipartite graphs under edge insertions such that the coloring only changes within a radius of $O(\log n)$…
arXiv:2610.10596v2 Announce Type: replace Abstract: Dijkstra's algorithm is traditionally classified as a greedy algorithm. We argue that this classification misrepresents the mechanism by which the algorithm determines…
arXiv:2610.19733v1 Announce Type: cross Abstract: We study proportional cake cutting under an equal-length constraint, where each of $n$ agents must receive a bundle of length exactly $1/n$ that is worth at least $1/n$…
arXiv:2610.19139v1 Announce Type: new Abstract: Tokenization is an essential preprocessing step in almost all large language models (LLMs). One of the most popular frameworks is BPE tokenization, which consists of…
arXiv:2610.19093v1 Announce Type: cross Abstract: A $u\hbox{-}v$ separator in $G$ is a set $S\subseteq V(G)\setminus\{u,v\}$ such that there is no $u\hbox{-}v$ path in $G\setminus S$. A minimal separator in $G$ is a set…
arXiv:2610.18884v1 Announce Type: cross Abstract: Let $n=2^d$. We prove that the worst-start total-variation mixing time of the full labelled Thorp shuffle satisfies, for every fixed $0<\varepsilon<1$, \[…
arXiv:2610.15801v2 Announce Type: replace-cross Abstract: We study the problem of fair allocation when agents have dichotomous submodular preferences over groups of, rather than individual, items. These preferences…
arXiv:2609.25292v2 Announce Type: replace Abstract: In the online metric matching problem, we have $n$ servers with known locations in some metric space. Requests arrive one-by-one at certain locations, and upon arrival…
arXiv:2610.20250v1 Announce Type: new Abstract: Clustering is a basic tool for grouping data into meaningful classes, but in many applications the resulting clusters must also respect the fairness conditions among…
arXiv:2607.08997v3 Announce Type: replace Abstract: In this paper we develop the framework of using a parametrized mapping $[\sigma(1), \sigma(2), \cdots, \sigma(n)] \mapsto \sigma(1)z + \sigma(2)z^2 + \cdots…
arXiv:2601.21660v2 Announce Type: replace Abstract: The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Given a depot and a set of customers with…
arXiv:2610.17406v2 Announce Type: replace Abstract: On the Internet, we use the Base64 format to represent binary data (e.g., images or cryptographic keys) as text. The ES2026 JavaScript standard, following the WHATWG…
arXiv:2610.19239v1 Announce Type: new Abstract: In this note we explore the following simple question: How does the classic \emph{gambler's ruin} phenomenon change if we allow the gambler \emph{financial leverage}? We…
arXiv:2610.20375v1 Announce Type: new Abstract: Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection seeks a distribution…
arXiv:2610.20510v1 Announce Type: new Abstract: Edge deletion problems ask for the fewest edges whose deletion gives a graph with a specified property. We study two such problems on block graphs. First making the graph…
arXiv:2605.12461v2 Announce Type: replace-cross Abstract: We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.e., densities of the form $\pi\propto e^{-f-g}$, assuming…
arXiv:2604.22699v3 Announce Type: replace Abstract: Given a matrix $A$, the goal of the entrywise low-rank approximation problem is to find $\operatorname{argmin} \|A-B\|_p$ over all rank-$k$ matrices $B$, where $\|…
arXiv:2610.20244v1 Announce Type: cross Abstract: We study multi-robot motion planning in a polygonal environment with polygonal robots. The setting of the problem consists of a polygonal domain $\mathcal{W}$ with $n$…