On the approximability of maximum and minimum edge clique partition problems
Authors: 
Anders Dessmark, Jesper Jansson, Andrzej Lingas, Eva-Marta Lundell, Mia PerssonAuthors Info & Claims
Anders Dessmark, Jesper Jansson, Andrzej Lingas, Eva-Marta Lundell, Mia PerssonAuthors Info & ClaimsPages 101 - 105
Abstract
We consider the following clustering problems: given a general undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone classification. We investigate the hardness of finding such partitions and provide approximation algorithms. Further, we show that greedy strategies yield constant factor approximations for graph classes for which maximum cliques can be found efficiently.
References
[1]
Ailon, N., Charikar, M. & Newman, A. (2005), Aggregating inconsistent information: Ranking and Clustering, in 'Proc. 37th Annual ACM Symposium on Theory of Computing (STOC 2005)', pp. 684--693.
[2]
Bansal, N., Blum, A. & Chawla, S. (2004), 'Correlation Clustering', Machine Learning 56(1--3), 89--113.
[3]
Charikar, M., Guruswami, V. & Wirth, A. (2003), Clustering with Qualitative Information, in 'Proc. 44th Annual Symposium on Foundations of Computer Science (FOCS 2003)', pp. 524--533.
[4]
Dahlhaus, E., Johnson, D. S., Papadimitriou, C. H., Seymour, P. D. & Yannakakis, M. (1994), 'The Complexity of Multiterminal Cuts', SIAM J. Comput. 23, 864--894.
[5]
Demaine, E. & Immorlica, N. (2003)Correlation Clustering with Partial Information, in 'Proc. 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2003)', pp. 1--13.
[6]
Drmanac, S., Stavropoulos, N. A., Labat, I., Vonau, J., Hauser, B., Soares, M. B. & Drmanac, R. (1996), 'Gene-representing cDNA clusters defined by hybridization of 57,419 clones from infant brain libraries with short oligonucleotide probes', Genomics 37, 29--40.
[7]
Emanuel, D. & Fiat, A. (2003)Correlation Clustering --- Minimizing Disagreements on Arbitrary Weighted Graphs, in 'Proc. 11th Annual European Symposium on Algorithms (ESA 2003)', pp. 208--220.
[8]
Figueroa, A., Borneman, J. & Jiang, T. (2004), 'Clustering binary fingerprint vectors with missing values for DNA array data analysis', Journal of Computational Biology 11(5), 887--901.
[9]
Figueroa, A., Goldstein, A., Jiang, T., Kurowski, M., Lingas, A. & Persson, M. (2005)Approximate Clustering of Fingerprint Vectors with Missing Values, in 'Proc. 11th Computing: The Australasian Theory Symposium (CATS 2005)', pp. 57--60.
[10]
Herwig, R., Poustka, A. J., Müller, C., Bull, C., Lehrach, H. & O'Brien, J. (1999), 'Large-scale clustering of cDNA-fingerprinting data', Genome research 9, 1093--1105.
[11]
Håstad, J. (2001), 'Some optimal inapproximability results', Journal of the ACM 48(4), 798--859.
[12]
Khot, S. (2001), Improved inapproximability results for MaxClique, chromatic number, and approximate graph coloring, in 'Proc. 42th Annual Symposium on Foundations of Computer Science (FOCS 2001)', pp. 600--609.
[13]
Shamir, R., Sharan, R. & Tsur, D. (2002)Cluster Graph Modification Problems, in 'Proc. 28th International Workshop on Graph Theoretic Concepts in Computer Science (WG 2002)', pp. 379--390.
[14]
Swamy, C. (2004)Correlation Clustering: maximizing agreements via semidefinite programming, in 'Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004)', pp. 526--527.
[15]
Valinsky, L., Della Vedova, G., Jiang, T. & Borneman, J. (2002), 'Oligonucleotide fingerprinting of ribosomal RNA genes for analysis of fungal community composition', Applied and Environmental Microbiology 68, 5999--6004.
[16]
Valinsky, L., Della Vedova, G., Scupham, A., Alvey, S., Figueroa, A., Yin, B., Hartin, R., Chrobak, M., Crowley, D., Jiang, T. & Borneman, J. (2002), 'Analysis of bacterial community composition by oligonucleotide fingerprinting of rRNA genes', Applied and Environmental Microbiology 68, 3243--3250.
- On the approximability of maximum and minimum edge clique partition problems
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Australian Computer Society, Inc.
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Published: 16 January 2006
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CATS '06 Paper Acceptance Rate 17 of 32 submissions, 53%;
Overall Acceptance Rate 118 of 228 submissions, 52%
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