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 - 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 -