Fast algorithms for min independent dominating set

TL;DR

This paper introduces faster algorithms for finding minimum independent dominating sets in graphs, improving previous bounds and providing approximation solutions with specific time complexities.

Contribution

It presents a new branching algorithm with improved exponential time complexity and extends to approximation algorithms for various r values.

Findings

New branching algorithm with O*(2^0.424n) time

Approximation algorithms for r-((r-1)/r)log_2(r) with O*(2^(nlog_2(r)/r)) time

Improved bounds over previous methods

Abstract

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r)).