Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem

Abstract

We present exact algorithms for solving the minimum connected dominating set problem in an undirected graph. The algorithms are based on two approaches: a Benders decomposition algorithm and a branch-and-cut method. We also develop a hybrid algorithm that combines these two approaches. Two variants of each of the three resulting algorithms are considered: a stand-alone version and an iterative probing variant. The latter variant is based on a simple property of the problem, which states that if no connected dominating set of a given cardinality exists, then there are no connected dominating sets of lower cardinality. We present computational results on a large set of instances from the literature.

Regenerator Location Problem and survivable extensions: A hub covering location perspective

“…Lucena et al (2010) provide branch and cut solution methodologies for the MLSTP and MCDSP and ultimately for the RLP. In a recent study, Gendron et al (2014) propose efficient exact solution methodologies built on Benders decomposition and branch and cut techniques. Our experimental results prove that none of these exact solution methodologies can compete with the branch and cut algorithm developed in this study which has the advantage of working only in the hub network due to the hub location perspective we adopt.…”

Matheuristics for Variants of the Dominating Set Problem

“…Exact methods and formulations have been proposed mainly for the MCDS problem. These approaches are unable to solve most instances in a reasonable time (van Rooij & Bodlaender, 2011;Lucena et al, 2010;Gendron et al, 2014).…”

“…Some exact approaches have been developed for the MCDS problem, such as those of Fujie (2003), Lucena et al (2010), Fernau et al (2011), and Gendron et al (2014. In more details, Lucena et al (2010) introduced two integer programming formulations: the first one is based on a Steiner reformulation of the problem, and the second considers the problem in a directed graph, seeking later a spanning arborescence with as many leaves as possible.…”

A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application

“…(informal) Intuitively, by direct reduction to the 'Minimum Dominating Set' (MDS) [19] (note, not MCDS [20], since the relays do not, themselves, have to form a connected core) and demonstration of polynomial certification (the full version follows).…”

“…Conventional linear and integer programming [21], 'branch-and-cut' [20], 'branch-and-price-and-cut' [22] methods, metaheuristics [14], or exhaustive search approaches [23] will be inappropriate. Not only is speed of the essence, but Future Internet 2017, 9, 18 4 of 11 optimisation may also have to be performed on network devices with limited processing power.…”