TY - GEN

T1 - Dense subgraph problems with output-density conditions

AU - Suzuki, Akiko

AU - Tokuyama, Takeshi

PY - 2005

Y1 - 2005

N2 - We consider the dense subgraph problem that extracts a subgraph with a prescribed number of vertices that has the maximum number of edges (total edge weight in the weighted case) in a given graph. We give approximation algorithms with improved theoretical approximation ratios-assuming that the density of the optimal output subgraph is high, where density is the ratio of number of edges (or sum of edge weights) to the number of edges in the clique on the same number of vertices. Moreover, we investigate the case where the input graph is bipartite, and design a pseudo-polynomial time approximation scheme that can become a PTAS even if the size of the optimal output graph is comparatively small. This is a significant improvement in a theoretical sense, since no constant-ratio approximation algorithm was known previously if the output graph has o(n) vertices.

AB - We consider the dense subgraph problem that extracts a subgraph with a prescribed number of vertices that has the maximum number of edges (total edge weight in the weighted case) in a given graph. We give approximation algorithms with improved theoretical approximation ratios-assuming that the density of the optimal output subgraph is high, where density is the ratio of number of edges (or sum of edge weights) to the number of edges in the clique on the same number of vertices. Moreover, we investigate the case where the input graph is bipartite, and design a pseudo-polynomial time approximation scheme that can become a PTAS even if the size of the optimal output graph is comparatively small. This is a significant improvement in a theoretical sense, since no constant-ratio approximation algorithm was known previously if the output graph has o(n) vertices.

UR - http://www.scopus.com/inward/record.url?scp=33744955394&partnerID=8YFLogxK

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U2 - 10.1007/11602613_28

DO - 10.1007/11602613_28

M3 - Conference contribution

AN - SCOPUS:33744955394

SN - 3540309357

SN - 9783540309352

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 266

EP - 276

BT - Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings

PB - Springer Verlag

T2 - 16th International Symposium on Algorithms and Computation, ISAAC 2005

Y2 - 19 December 2005 through 21 December 2005

ER -