On combinatorial optimization for dominating sets (literature survey, new models)

TL;DR

This paper surveys connected dominating set problems, reviews existing methods, and introduces new integer programming models with multiset estimates to improve problem-solving approaches.

Contribution

It provides a comprehensive literature review and proposes novel integer programming formulations for connected dominating set problems.

Findings

Surveyed various problem formulations and solution approaches.

Introduced new integer programming models with multiset estimates.

Illustrated models with simplified numerical examples.

Abstract

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set problems are illustrated by simplifyed numerical examples. New integer programming formulations of dominating set problems (with multiset estimates) are suggested.