Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
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
Efficient labeling procedures for image partition encoding
Signal Processing - Special issue on fuzzy logic in signal processing
Feasible edge colorings of trees with cardinality constraints
Discrete Mathematics
Low Complexity Code Design for Lossless and Near-Lossless Side Information Source Codes
DCC '03 Proceedings of the Conference on Data Compression
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Source coding and graph entropies
IEEE Transactions on Information Theory
A short proof of the NP-completeness of minimum sum interval coloring
Operations Research Letters
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
"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
Distributed joint source-channel coding for functions over a multiple access channel
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Tight results on minimum entropy set cover
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
Operations Research Letters
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We study an information-theoretic variant of the graph coloring problem in which the objective function to minimize is the entropy of the coloring. The minimum entropy of a coloring is called the chromatic entropy and was shown by Alon and Orlitsky to play a fundamental role in the problem of coding with side information. In this paper, we consider the minimum entropy coloring problem from a computational point of view. We first prove that this problem is NP-hard on interval graphs. We then show that it is NP-hard to find a coloring whose entropy is within $({1 \over 7} - \epsilon){\rm log} n$ of the chromatic entropy for any ε 0, where n is the number of vertices of the graph. A simple polynomial case is also identified. It is known that the traditional graph entropy is a lower bound for the chromatic entropy. We prove that this bound can be arbitrarily bad, even for chordal graphs. Finally, we consider the minimum number of colors required to achieve minimum entropy and prove a Brooks-type theorem.