TY - GEN

T1 - Finding the minimum-weight k-path

AU - Hassidim, Avinatan

AU - Keller, Orgad

AU - Lewenstein, Moshe

AU - Roditty, Liam

N1 - Place of conference:Canada

PY - 2013

Y1 - 2013

N2 - Given a weighted n-vertex graph G with integer edge-weights taken from a range [-M,M], we show that the minimum-weight simple path visiting k vertices can be found in time Õ(2kpoly(k)Mnω) = O*(2kM). If the weights are reals in [1,M], we provide a (1 + ε)-approximation which has a running time of Õ(2kpoly(k) nω (log log M + 1/ε)). For the more general problem of k-tree, in which we wish to find a minimum-weight copy of a k-node tree T in a given weighted graph G, under the same restrictions on edge weights respectively, we give an exact solution of running time Õ(2 kpoly(k)Mn3) and a (1 + ε)-approximate solution of running time Õ(2kpoly(k)n3(log log M + 1/ε)). All of the above algorithms are randomized with a polynomially-small error probability.

AB - Given a weighted n-vertex graph G with integer edge-weights taken from a range [-M,M], we show that the minimum-weight simple path visiting k vertices can be found in time Õ(2kpoly(k)Mnω) = O*(2kM). If the weights are reals in [1,M], we provide a (1 + ε)-approximation which has a running time of Õ(2kpoly(k) nω (log log M + 1/ε)). For the more general problem of k-tree, in which we wish to find a minimum-weight copy of a k-node tree T in a given weighted graph G, under the same restrictions on edge weights respectively, we give an exact solution of running time Õ(2 kpoly(k)Mn3) and a (1 + ε)-approximate solution of running time Õ(2kpoly(k)n3(log log M + 1/ε)). All of the above algorithms are randomized with a polynomially-small error probability.

UR - http://www.scopus.com/inward/record.url?scp=84881145020&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40104-6_34

DO - 10.1007/978-3-642-40104-6_34

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AN - SCOPUS:84881145020

SN - 9783642401039

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

SP - 390

EP - 401

BT - Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings

T2 - 13th International Symposium on Algorithms and Data Structures, WADS 2013

Y2 - 12 August 2013 through 14 August 2013

ER -