Daily edition · Algorithms
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27 articles · 1 source · 27 papers ·
Top topics: Algorithms
arXiv:2609.02234v2 Announce Type: replace-cross Abstract: Cycles $C_1,\ldots,C_k$ in a graph are called nested without geometric crossings if they are pairwise edge-disjoint, $V(C_k)\subseteq\cdots\subseteq V(C_1)$, and…
arXiv:2502.11961v4 Announce Type: replace-cross Abstract: Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration…
arXiv:2609.07253v1 Announce Type: cross Abstract: Given a graph $G=(V,E)$, let $S$ ($\subseteq V$) be a set of vertices. Two vertices are \emph{mutually visible} if there exists a shortest path in $G$ between them that…
arXiv:2609.05780v1 Announce Type: cross Abstract: Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors $(0,0,\ldots, 0, 1, 0, \ldots, 0)$? We prove…
arXiv:2609.08937v1 Announce Type: cross Abstract: We construct an explicit infinite family of simple two-dimensional Cayley complexes over $\mathbb{F}_2^n$ whose degree is polynomial in $n$ and whose nontrivial…
arXiv:2607.20269v2 Announce Type: replace-cross Abstract: Prophet inequalities are a fundamental model for online decision-making under uncertainty. For matroid constraints, Kleinberg and Weinberg gave a tight…
arXiv:2512.13058v2 Announce Type: replace-cross Abstract: Two graphs $G$ and $H$ are homomorphism indistinguishable over a graph class $\mathcal{F}$ if they admit the same number of homomorphisms from every graph $F \in…
arXiv:2407.05827v4 Announce Type: replace-cross Abstract: Reed in 1998 conjectured that every graph $G$ satisfies $\chi(G) \leq \lceil \frac{\Delta(G)+1+\omega(G)}{2} \rceil$. As a partial result, he proved the…
arXiv:2607.04141v3 Announce Type: replace-cross Abstract: We introduce split-free cable expressions and their sequential restriction. Live cables are vertex blocks that future operations cannot split. The main result…
arXiv:2412.03540v2 Announce Type: replace-cross Abstract: We prove a sharp version of Talagrand's selector process conjecture. Roughly speaking, given any collection of nonnegative weight vectors whose support form a…
arXiv:2609.07304v1 Announce Type: new Abstract: The independent set polytope, or stable set polytope, of a graph $G$ is the 0/1-polytope defined by the convex hull of the characteristic vectors of all independent sets…
arXiv:2609.04122v2 Announce Type: replace-cross Abstract: Synchronization strings provide deterministic position labels for recovering coordinates after insertions and deletions. Haeupler and Shahrasbi introduced these…
arXiv:2606.18048v2 Announce Type: replace-cross Abstract: Improving an earlier bound of Frieze and Mubayi, Iliopoulos showed that any $k$-uniform uncrowded hypergraph of maximum degree $\Delta$ has list chromatic number…
arXiv:2609.05771v1 Announce Type: cross Abstract: Families of sequences with low mutual aperiodic crosscorrelation assist the design of systems for multi-user asynchronous communications and multiple-input…
arXiv:2609.09146v1 Announce Type: new Abstract: Let $X$ be a finite set with $|X|=n$ and let $\mathrm{Jac}(a,b)=|a\,\triangle\, b|/|a\cup b|$ be the Jaccard distance on the power set $2^X$. Lladser and Paradise recently…
arXiv:2609.05750v1 Announce Type: cross Abstract: We study the mixing time of the systematic scan dynamics for high-dimensional discrete distributions. This Markov chain updates coordinates sequentially according to a…
arXiv:2609.06570v1 Announce Type: cross Abstract: Let $C \le \mathbb{F}_q^n$ be a uniformly random $\mathbb{F}_q$-linear code of rate $1 - h_q(\rho) - \varepsilon$, and let $L^*(C,\rho)$ be the least $L$ such that every…
arXiv:2609.08847v1 Announce Type: cross Abstract: Let $P_t$ denote the induced path on $t$ vertices. Let $\omega(G)$ denote the maximum number of vertices in a clique of a graph $G$. Previously Gy\'arf\'as (1987) proved…
arXiv:2609.08662v1 Announce Type: cross Abstract: For $q\in\set{2,3}$, we show that a $k$-dimensional linear code over the finite field $\F_q$ of order $q$ is linear complementary dual (LCD) exactly when one…
arXiv:2605.20434v2 Announce Type: replace-cross Abstract: We study the contradiction graphs associated with a binary concept class. For a class $H\subseteq\{0,1\}^X$, the order-$m$ contradiction graph $G_m(H)$ has as…
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