Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Restrictions of graph partition problems. Part I
Theoretical Computer Science
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
Approximating minimum cocolorings
Information Processing Letters
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
Weighted Coloring: further complexity and approximability results
Information Processing Letters
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Weighted sum coloring in batch scheduling of conflicting jobs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Probabilistic coloring of bipartite and split graphs
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Entropy Combinatorial Optimization Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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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 costs of the color classes. The "Rent-or-Buy" scheduling/coloring problem (RBC) is one that, e.g., captures 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.