A flow based pruning scheme for enumerative equitable coloring algorithms

Collection Location Koleksi E-book & E-Journal Perpustakaan Pusat Unila
Edition vol.272,issue 1-2
Call Number
ISBN/ISSN 1572-9338
Author(s) Koster, A. M. C. A.
Scheidweiler, R.
Tieves, · M.
Subject(s) Business and Management
Classification NONE
Series Title
GMD E-Journal
Language English
Publisher Springer
Publishing Year 2019
Publishing Place Switzerland
Abstract/Notes Abstract An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number, denoted by χeq(G), is the smallest number k such that G admits such equitable k-coloring. We focus on enumerative algorithms for the computation of χeq(G) and propose a general scheme to derive pruning rules for them: We show how the extendability of a partial coloring into an equitable coloring can be modeled via network flows. Thus, we obtain pruning rules which can be checked via flow algorithms. Computational experiments show that the search tree of enumerative algorithms can be significantly reduced in size by these rules and, in most instances, such naive approach even yields a faster algorithm. Moreover, the stability, i.e., the number of solved instances within a given time limit, is greatly improved. Since the execution of flow algorithms at each node of a search tree is time consuming, we derive arithmeticpruningrules(generalizedHall-conditions)fromthenetworkmodel.Addingthese rules to an enumerative algorithm yields an even larger runtime improvement.
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