Related papers: A Fixed-Parameter Perspective on #BIS
The complexity of classical computational problems in graph classes defined by forbidding induced subgraphs is one of the central topics of algorithmic graph theory. Recently, there has been a growing interest in the complexity of such…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
We study the Maximum Bipartite Subgraph (MBS) problem, which is defined as follows. Given a set $S$ of $n$ geometric objects in the plane, we want to compute a maximum-size subset $S'\subseteq S$ such that the intersection graph of the…
For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$…
It is shown in this note that approximating the number of independent sets in a $k$-uniform linear hypergraph with maximum degree at most $\Delta$ is NP-hard if $\Delta\geq 5\cdot 2^{k-1}+1$. This confirms that for the relevant sampling and…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
In this paper we consider the Maximum Independent Set problem (MIS) on $B_1$-EPG graphs. EPG (for Edge intersection graphs of Paths on a Grid) was introduced in ~\cite{edgeintersinglebend} as the class of graphs whose vertices can be…
We study a natural extension of the Maximum Weight Independent Set Problem (MWIS), one of the most studied optimization problems in Graph algorithms. We are given a graph $G=(V,E)$, a weight function $w: V \rightarrow \mathbb{R^+}$, a…
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…
In an undirected graph $G=(V,E)$, we say $(A,B)$ is a pair of perfectly matched sets if $A$ and $B$ are disjoint subsets of $V$ and every vertex in $A$ (resp. $B$) has exactly one neighbor in $B$ (resp. $A$). The size of a pair of perfectly…
The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We present a polynomial-time solution in a subclass of subcubic graphs generalizing several previously known…
We introduce a class of parameterised counting problems on graphs, p-#Induced Subgraph With Property(\Phi), which generalises a number of problems which have previously been studied. This paper focusses on the case in which \Phi defines a…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
We prove that, unless P=NP, there is no polynomial-time algorithm to approximate within some multiplicative constant the average size of an independent set in graphs of maximum degree 6. This is a special case of a more general result for…
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…