New parameterized algorithms for edge dominating set

TL;DR

This paper introduces new parameterized algorithms for the edge dominating set problem, achieving faster exponential time solutions and polynomial kernelization, advancing the efficiency of solving this graph problem.

Contribution

The paper presents an improved fixed-parameter algorithm with runtime O^*(2.3147^k) and a quadratic kernel with O(k^3) edges for the edge dominating set problem.

Findings

Algorithm runs in O^*(2.3147^k) time

Achieves polynomial space complexity

Provides a quadratic kernel with O(k^3) edges

Abstract

An edge dominating set of a graph G=(V,E) is a subset M of edges in the graph such that each edge in E-M is incident with at least one edge in M. In an instance of the parameterized edge dominating set problem we are given a graph G=(V,E) and an integer k and we are asked to decide whether G has an edge dominating set of size at most k. In this paper we show that the parameterized edge dominating set problem can be solved in O^*(2.3147^k) time and polynomial space. We show that this problem can be reduced to a quadratic kernel with O(k^3) edges.