G-2016-111
Online algorithms for the maximum k-colorable subgraph problem
, , and BibTeX reference
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.
Published November 2016 , 23 pages