A node covering algorithm

Abstract

This paper describes a node covering algorithm, i.e., a procedure for finding :I smallest set of nodes covering all edges of an arbitrary graph. The algorithm i.; based on the concept of a dual node-clique set, which allows us to identify partial covers associated with int.egw dual feasible solutions to the linear progr:utlminp equivalent of the node covering problem. An initial partid cover with the above property is first found by a labeling procedure. Another labeling procedure then successively modifies the dual node-clique set, so that more and more cdgrs : r c covered, i.e., the (primal) infeasibility of the solution i.; gradually rcdured, whilr, integrality and dual feasihilitp are preserved. When this cannot he continued, thc problem is partitioned and the procedure applied to the resulting aut)liroblrms. While the steps of the algorithm correspond to sequences of dual simples i)ivot.<, these are carried out implicitly, by labeling. The procedure is ilhist raited by c w mples, and some early computational experience is reported. We cnnclude \vit,h :I discussion of potential improvements and extensions.

Molecular Structure Disassembly Program (MOSDAP): A Chemical Information Model To Automate Structure-Based Physical Property Estimation

“…The exact cover complication, although well-known among general practitioners, has not been directly addressed in the literature. Several exact cover algorithms have been published − for arbitrary graphs, but the algorithm selected for use with MOSDAP is due to Frenz and Kreher . A straightforward description of the updated procedure, pseudocode illustration of the algorithm, and example are presented by Kreher .…”

A branch and bound algorithm for the maximum clique problem

“…For some previous efforts in finding a clique of maximal cardinality or enumerating all cliques concerning the general case see Bron, Kerbosch [4], Nemhauser, Trotter [18], Balas, Samuelsson [2], Tarjan, Trojanowski [20], Gerhards, Lindenberg [10], Loukakis, Tsouros [15]. Recently, Friden, Hertz and de Werra [5] developed an algorithm called TABARIS which produces a maximum independent set using tabu search techniques.…”

A Branch-And-Price Approach for Graph Multi-Coloring

“…Since a clique is an independent set in the complement of a graph, the literature on the maximum weighted clique is equally relevant. Various solution approaches have been tried, including implicit enumeration [6], integer programming with branch and bound [3,4], and integer programming with cutting planes [2,15]. In addition, a number of heuristics have been developed [16] and combined with general heuristic methods such as simulated annealing [8].…”