# Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

## TL;DR

This paper introduces a novel local search algorithm for the Minimum Weight Dominating Set problem, combining two-level configuration checking and a frequency-based scoring function, significantly improving solution quality.

## Contribution

It proposes CC2FS, a new local search method that integrates two-level configuration checking and frequency-based scoring for MWDS, outperforming existing algorithms.

## Key findings

- CC2FS outperforms state-of-the-art algorithms on MWDS benchmarks.
- The two-level configuration checking effectively avoids recent search paths.
- Frequency-based scoring improves the quality of solutions.

## Abstract

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.