An Existential Problem of a Weightcontrolled Subset and its Application to School Timetable Construction

Kitagawa, Fumio; Ikeda, Hideto

doi:10.1016/s0167-5060(08)70787-8

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…is can be proved by a straightforward reduction from graph coloring to equitable coloring by adding sufficiently many isolated vertices to a graph and testing whether the graph has an equitable coloring with a given number of colors [8]. e ECP model has a number of practical applications related to garbage collection [25], load balancing [3], timetabling [16], scheduling [7,15,24] and so on.…”

Section: Introductionmentioning

confidence: 99%

On feasible and infeasible search for equitable graph coloring

Sun

Hao

Lai

et al. 2017

Proceedings of the Genetic and Evolutionary Computation Conference

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An equitable legal k-coloring of an undirected graph G = (V , E) is a partition of the vertex set V into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one (this is called the equity constraint). As a variant of the popular graph coloring problem (GCP), the equitable coloring problem (ECP) involves finding a minimum k for which an equitable legal k-coloring exists. In this paper, we present a study of searching both feasible and infeasible solutions with respect to the equity constraint. e resulting algorithm relies on a mixed search strategy exploring both equitable and inequitable colorings unlike existing algorithms where the search is limited to equitable colorings only. We present experimental results on 73 DIMACS and COLOR benchmark graphs and demonstrate the competitiveness of this search strategy by showing 9 improved best-known results (new upper bounds).

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