Related papers: Deterministic polynomial-time approximation algori…
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…
We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a…
In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…
We study polynomial-time approximation algorithms for two closely-related problems, namely computing shortcuts and transitive-closure spanners (TC spanners). For a directed unweighted graph $G=(V, E)$ and an integer $d$, a set of edges…
In 2015, Guth proved that for any set of $k$-dimensional bounded complexity varieties in $\mathbb{R}^d$ and for any positive integer $D$, there exists a polynomial of degree at most $D$ whose zero set divides $\mathbb{R}^d$ into open…
Robin Thomas asked whether for every proper minor-closed class C, there exists a polynomial-time algorithm approximating the chromatic number of graphs from C up to a constant additive error independent on the class C. We show this is not…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Coordination graph is a promising approach to model agent collaboration in multi-agent reinforcement learning. It conducts a graph-based value factorization and induces explicit coordination among agents to complete complicated tasks.…
A subset of vertices $S$ of a graph $G$ is a dominating set if every vertex in $V \setminus S$ has at least one neighbor in $S$. A domatic partition is a partition of the vertices of a graph $G$ into disjoint dominating sets. The domatic…
Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In \cite{carmeli2020} (\textsc{Pods 2017}) Carmeli \emph{et al.}…
We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds. This answers one of the…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
We determine the computational complexity of approximately counting and sampling independent sets of a given size in bounded-degree graphs. That is, we identify a critical density $\alpha_c(\Delta)$ and provide (i) for $\alpha <…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph…