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 - https://doi.org/10.1007/978-3-642-40104-6_34
DO - https://doi.org/10.1007/978-3-642-40104-6_34
M3 - منشور من مؤتمر
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 -