Abstract
We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy coloring problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agarwal, S., Belongie, S.: On the non-optimality of four color coding of image partitions. In: ICIP 2002: Proceedings of the IEEE International Conference on Image Processing (2002)
Alon, N., Orlitsky, A.: Source coding and graph entropies. IEEE Trans. Inform. Theory 42(5), 1329–1339 (1996)
Bonizzoni, P., Della Vedova, G., Dondi, R., Mariani, L.: Experimental analysis of a new algorithm for partial haplotype completion. Int. J. Bioinformatics Res. Appl. 1(4), 461–473 (2005)
Cardinal, J., Fiorini, S., Joret, G.: Minimum entropy coloring. J. Comb. Opt. 16(4), 361–377 (2008)
Cardinal, J., Fiorini, S., Joret, G.: Minimum entropy orientations. Op. Res. Lett. 36, 680–683 (2008)
Cardinal, J., Fiorini, S., Joret, G.: Tight results on minimum entropy set cover. Algorithmica 51(1), 49–60 (2008)
Cardinal, J., Fiorini, S., Joret, G., Jungers, R., Munro, J.I.: An efficient algorithm for partial order production. In: STOC 2009: 41st ACM Symposium on Theory of Computing (2009) (to appear)
Csiszár, I., Körner, J., Lovász, L., Marton, K., Simonyi, G.: Entropy splitting for antiblocking corners and perfect graphs. Combinatorica 10(1), 27–40 (1990)
Doshi, V., Shah, D., Médard, M.: Source coding with distortion through graph coloring. In: ISIT 2007: Proceedings of the IEEE International Symposium on Information Theory, pp. 1501–1505 (2007)
Doshi, V., Shah, D., Médard, M., Jaggi, S.: Graph coloring and conditional graph entropy. In: ACSSC 2006: Proceedings of the Fortieth Asilomar Conference on Signals, Systems and Computers, pp. 2137–2141 (2006)
Doshi, V., Shah, D., Médard, M., Jaggi, S.: Distributed functional compression through graph coloring. In: DCC 2007: Proceedings of the IEEE Data Compression Conference, pp. 93–102 (2007)
Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–652 (1998)
Feige, U., Lovász, L., Tetali, P.: Approximating min sum set cover. Algorithmica 40(4), 219–234 (2004)
Fukunaga, T., Halldórsson, M.M., Nagamochi, H.: Rent-or-buy scheduling and cost coloring problems. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 84–95. Springer, Heidelberg (2007)
Fukunaga, T., Halldórsson, M.M., Nagamochi, H.: Robust cost colorings. In: SODA 2008: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 1204–1212 (2008)
Gijswijt, D., Jost, V., Queyranne, M.: Clique partitioning of interval graphs with submodular costs on the cliques. RAIRO – Operations Research 41(3), 275–287 (2007)
Gusev, A., Măndoiu, I.I., Paşaniuc, B.: Highly scalable genotype phasing by entropy minimization. IEEE/ACM Trans. Comput. Biol. Bioinformatics 5(2), 252–261 (2008)
Halldórsson, M.M., Radhakrishnan, J.: Greed is good: approximating independent sets in sparse and bounded-degree graphs. In: STOC 1994: Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, pp. 439–448 (1994)
Halperin, E., Karp, R.M.: The minimum-entropy set cover problem. Theoret. Comput. Sci. 348(2-3), 240–250 (2005)
Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999)
Kierstead, H.A., Trotter, W.A.: An extremal problem in recursive combinatorics. Congr. Numer. 33, 143–153 (1981)
Körner, J.: Coding of an information source having ambiguous alphabet and the entropy of graphs. In: Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Tech. Univ., Prague, 1971; dedicated to the memory of Antonín Špaček), pp. 411–425. Academia, Prague (1973)
Körner, J., Orlitsky, A.: Zero-error information theory. IEEE Trans. Inform. Theory 44(6), 2207–2229 (1998)
Koulgi, P., Tuncel, E., Regunathan, S., Rose, K.: On zero-error source coding with decoder side information. IEEE Trans. Inform. Theory 49(1), 99–111 (2003)
Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21(1), 193–201 (1992)
Nicoloso, S., Sarrafzadeh, M., Song, X.: On the sum coloring problem on interval graphs. Algorithmica 23(2), 109–126 (1999)
Parnas, M., Ron, D.: Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms. Theoret. Comput. Sci. 381(1-3), 183–196 (2007)
Pemmaraju, S.V., Raman, R., Varadarajan, K.: Buffer minimization using max-coloring. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 562–571 (2004)
Shannon, C.E.: A mathematical theory of communication. Bell. System Technical Journal 27, 379–423, 623–656 (1948)
Simonyi, G.: Graph entropy: a survey. In: Combinatorial Optimization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 20, pp. 399–441 (1995)
Yannakakis, M., Gavril, F.: The maximum k-colorable subgraph problem for chordal graphs. Inf. Process. Lett. 24(2), 133–137 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cardinal, J., Fiorini, S., Joret, G. (2009). Minimum Entropy Combinatorial Optimization Problems. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-03073-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03072-7
Online ISBN: 978-3-642-03073-4
eBook Packages: Computer ScienceComputer Science (R0)