Related papers: VEST is W[2]-hard

We initiate a program of parameterized proof complexity that aims to provide evidence that FPT is different from W[1]. A similar program already exists for the classes W[2] and W[SAT]. We contrast these programs and prove upper and lower…

We recall a group-theoretic description of the first non-vanishing homotopy group of a certain (n+1)-ad of spaces and show how it yields several formulae for homotopy and homology groups of specific spaces. In particular we obtain an…

$ \newcommand{\eps}{\varepsilon} \newcommand{\problem}[1]{\ensuremath{\mathrm{#1}} } \newcommand{\CVP}{\problem{CVP}} \newcommand{\SVP}{\problem{SVP}} \newcommand{\CVPP}{\problem{CVPP}} \newcommand{\ensuremath}[1]{#1} $For odd integers $p…

We study the witness-counting problem: given a set of vectors $V$ in the $d$-dimensional vector space over $\mathbb{F}_2$, a target vector $t$, and an integer $k$, count all ways to sum-up exactly $k$ different vectors from $V$ to reach…

We show that if we suppose n>3 and the (2n-1)-stem in the stable homotopy groups of spheres has no 2-torsion, then the Whitehead squares of the identity maps of (2n+1) and (4n+3)-spheres are divisible by 2. Applying the result of G. Wang…

The necessary conditions to derive the quantum VdW EoS with hard-core repulsion from the quantum partition are discussed. On a plausible example it is shown that an alternative way to account correctly for the 3-rd virial coefficient of…

Recent work [BGS17,ABGS19] has shown SETH hardness of CVP in the $\ell_p$ norm for any $p$ that is not an even integer. This result was shown by giving a Karp reduction from $k$-SAT on $n$ variables to CVP on a lattice of rank $n$. In this…

A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…

VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by considering the complex of cochains which are k-homogeneous…

We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…

Two vertices $u, v \in V$ of an undirected connected graph $G=(V,E)$ are resolved by a vertex $w$ if the distance between $u$ and $w$ and the distance between $v$ and $w$ are different. A set $R \subseteq V$ of vertices is a $k$-resolving…

We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known hypertopology…

A map $f\colon K\to \mathbb R^d$ of a simplicial complex is an almost embedding if $f(\sigma)\cap f(\tau)=\emptyset$ whenever $\sigma,\tau$ are disjoint simplices of $K$. Theorem. Fix integers $d,k\ge2$ such that $d=\frac{3k}2+1$. (a)…

Given a set of leaf-labeled trees with identical leaf sets, the well-known "Maximum Agreement SubTree" problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its…

Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…

The NP-hard 2-Club problem is, given an undirected graph G=(V,E) and l\in N, to decide whether there is a vertex set S\subseteq V of size at least l such that the induced subgraph G[S] has diameter at most two. We make progress towards a…

In this paper, we investigate bounds for the following judicious $k$-partitioning problem: Given an edge-weighted graph $G$, find a $k$-partition $(V_1,V_2,\dots ,V_k)$ of $V(G)$ such that the total weight of edges in the heaviest induced…

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces,…

In this paper, we study the parameterized complexity and inapproximability of the {\sc Induced Matching} problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is…

The Weighted Vertex Integrity (wVI) problem takes as input an $n$-vertex graph $G$, a weight function $w:V(G)\to\mathbb{N}$, and an integer $p$. The task is to decide if there exists a set $X\subseteq V(G)$ such that the weight of $X$ plus…