Related papers: Fast algorithms for min independent dominating set
In a graph $G = (V,E)$, a k-ruling set $S$ is one in which all vertices $V$ \ $S$ are at most $k$ distance from $S$. Finding a minimum k-ruling set is intrinsically linked to the minimum dominating set problem and maximal independent set…
In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph $G$, each pair of vertices are joined by an edge with a probability $p$, where $p$ is a…
In this paper we provide algorithms faster than O*(2^n) for several NP-complete domination-type problems. More precisely, we provide: an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89^n), a branch-and-reduce algorithm…
A dominating set $D$ of a graph $G$ is a set of vertices such that any vertex in $G$ is in $D$ or its neighbor is in $D$. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of…
We provide an algorithm requiring only $O(N^2)$ time to compute the maximum weight independent set of interval filament graphs. This also implies an $O(N^4)$ algorithm to compute the maximum weight induced matching of interval filament…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
Fix a positive integer $n$ and consider the bipartite graph whose vertices are the $3$-element subsets and the $2$-element subsets of $[n]=\{1,2,\dots,n\}$, and there is an edge between $A$ and $B$ if $A\subset B$. We prove that the…
We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a…
We present a polynomial-space algorithm that computes the number independent sets of any input graph in time $O(1.1387^n)$ for graphs with maximum degree 3 and in time $O(1.2355^n)$ for general graphs, where n is the number of vertices.…
We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published…
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 greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
Recently it was shown that many classic graph problems -- Independent Set, Dominating Set, Hamiltonian Cycle, and more -- can be solved in subexponential time on unit-ball graphs. More precisely, these problems can be solved in…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
Maximum independent set from a given set $D$ of unit disks intersecting a horizontal line can be solved in $O(n^2)$ time and $O(n^2)$ space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set…