TY - GEN

T1 - The parameterized complexity of the Minimum Shared Edges problem

AU - Fluschnik, Till

AU - Kratsch, Stefan

AU - Niedermeier, Rolf

AU - Sorge, Manuel

N1 - Funding Information:
Due to space constraints numerous details are deferred to a full version. Till Fluschnik, Stefan Kratsch, and Manuel Sorge gratefully acknowledge support by the DFG, projects DAMM (NI 369/13-2), PREMOD (KR 4286/2-1), and DAPA (NI 369/12-2), respectively.
Publisher Copyright:
© Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP ⊆ coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].

AB - We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP ⊆ coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].

KW - Kernelization

KW - Parameterized complexity

KW - Treewidth

KW - Treewidth reduction

UR - http://www.scopus.com/inward/record.url?scp=84958768153&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2015.448

DO - 10.4230/LIPIcs.FSTTCS.2015.448

M3 - Conference contribution

AN - SCOPUS:84958768153

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 448

EP - 462

BT - 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015

A2 - Harsha, Prahladh

A2 - Ramalingam, G.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015

Y2 - 16 December 2015 through 18 December 2015

ER -