Group for Research in Decision Analysis

G-2016-111

Online algorithms for the maximum k-colorable subgraph problem

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The maximum \(k\)-colorable subgraph problem (\(k\)-MCSP) is to color as many vertices as possible with at most \(k\) colors, such that no two adjacent vertices share the same color. We consider online algorithms for this \(\mathcal{NP}\)-hard problem, and give bounds on their competitive ratio. We then consider a large family \(\cal{A}\) of online sequential coloring algorithms and determine the smallest graphs for which no algorithm in \(\cal{A}\) can produce an optimal solution to the \(k\)-MCSP. We then compare the performance of several online sequential coloring algorithms, using DIMACS benchmark instances. We finally consider the case where vertices colored at an early stage can receive a new color later on, as long as they remain colored.

, 23 pages