TY - GEN
T1 - Fixed-parameter tractability of multicut parameterized by the size of the cutset
AU - Marx, Dániel
AU - Razgon, Igor
PY - 2011/1/1
Y1 - 2011/1/1
N2 - Given an undirected graph G, a collection {(s1,t1), ..., (sl,tl)} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding t i. Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) · nO(1), i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p) · n O(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.
AB - Given an undirected graph G, a collection {(s1,t1), ..., (sl,tl)} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding t i. Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) · nO(1), i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p) · n O(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.
KW - fixed-parameter tractability
KW - multicut
UR - http://www.scopus.com/inward/record.url?scp=79959760912&partnerID=8YFLogxK
U2 - 10.1145/1993636.1993699
DO - 10.1145/1993636.1993699
M3 - Conference contribution
AN - SCOPUS:79959760912
SN - 9781450306911
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 469
EP - 478
BT - STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing
PB - Association for Computing Machinery
T2 - 43rd ACM Symposium on Theory of Computing, STOC 2011
Y2 - 6 June 2011 through 8 June 2011
ER -