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
SIAM Journal on Discrete Mathematics
All-norm approximation algorithms
Journal of Algorithms
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
Convex programming for scheduling unrelated parallel machines
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
How to Pay, Come What May: Approximation Algorithms for Demand-Robust Covering Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Weighted coloring: further complexity and approximability results
Information Processing Letters
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
"Rent-or-buy" scheduling and cost coloring problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
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
Source coding and graph entropies
IEEE Transactions on Information Theory
Minimum Entropy Combinatorial Optimization Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
"Rent-or-buy" scheduling and cost coloring problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
Return of the boss problem: competing online against a non-adaptive adversary
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Robust matchings and matroid intersections
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Computing knapsack solutions with cardinality robustness
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Operations Research Letters
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We consider graph coloring problems where the cost of a coloring is the sum of the costs of the colors, and the cost of a color is a monotone concave function of the total weight of the class. This models resource allocation problems where the cost of a resource depends on the use of the resource. The specific case of interval graphs is of special interest as multi-criteria interval scheduling. We give an algorithm for all perfect graphs that yields a robust coloring: a particular solution that simultaneously approximates all concave functions. For graphs with uniform weights, we show how to modify the solution to approximate any monotone cost function. We complement these results with a number of hardness results and some exact algorithms on restricted classes of graphs.