TY - GEN

T1 - Finding dense subgraphs of sparse graphs

AU - Komusiewicz, Christian

AU - Sorge, Manuel

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We investigate the computational complexity of the Densest-k-Subgraph (D k S) problem, where the input is an undirected graph G = (V,E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on D k S by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density μ of the sought subgraph, D k S becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixed-parameter algorithm for D k S with respect to the combined parameter "degeneracy of G and |V| - k". On the negative side, we find that D k S is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for D k S [Cai, Comput. J., 2008] by showing that for every fixed μ, 0 < μ < 1, the problem of deciding whether G contains a subgraph of density at least μ is W[1]-hard with respect to the parameter |V| - k.

AB - We investigate the computational complexity of the Densest-k-Subgraph (D k S) problem, where the input is an undirected graph G = (V,E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on D k S by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density μ of the sought subgraph, D k S becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixed-parameter algorithm for D k S with respect to the combined parameter "degeneracy of G and |V| - k". On the negative side, we find that D k S is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for D k S [Cai, Comput. J., 2008] by showing that for every fixed μ, 0 < μ < 1, the problem of deciding whether G contains a subgraph of density at least μ is W[1]-hard with respect to the parameter |V| - k.

UR - http://www.scopus.com/inward/record.url?scp=84887299736&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33293-7_23

DO - 10.1007/978-3-642-33293-7_23

M3 - Conference contribution

AN - SCOPUS:84887299736

SN - 9783642332920

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

SP - 242

EP - 251

BT - Parameterized and Exact Computation - 7th International Symposium, IPEC 2012, Proceedings

T2 - 7th International Symposium on Parameterized and Exact Computation, IPEC 2012

Y2 - 12 September 2013 through 14 September 2013

ER -