"Rent-or-Buy" Scheduling and Cost Coloring Problems

We study several cost coloring problems, where we are given a graph and a cost function on the independent sets and are to find a coloring that minimizes the function costs of the color classes. The “Rent-or-Buy” scheduling/coloring problem (RBC) is one that captures e.g., job scheduling situations involving resource constraints where one can either pay a full fixed price for a color class (representing e.g., a server), or a small per-item charge for each vertex in the class (corresponding to jobs that are either not served, or are farmed out to an outside agency). We give exact and approximation algorithms for RBC and three other cost coloring problems (including the previously studied Probabilistic coloring problem), both on interval and on perfect graphs. The techniques rely heavily on the computation of maximum weight induced k-colorable subgraphs (k-MCS). We give a novel bicriteria approximation for k-MCS in perfect graphs, and extend the known exact algorithm for interval graphs to some problem extensions.