TY - GEN
T1 - Computing maximum flows in undirected planar networks with both edge and vertex capacities
AU - Zhang, Xianchao
AU - Liang, Weifa
AU - Chen, Guoliang
N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].
PY - 2008
Y1 - 2008
N2 - We study the maximum flow problem in an undirected planar network with both edge and vertex capacities (EVC-network). A previous study reduces the minimum cut problem in an undirected planar EVC-network to the minimum edge-cut problem in another planar network with edge capacity only (EC-network), thus the minimum-cut or the maximum flow value can be computed in O(nlogn) time. Based on this reduction, in this paper we devise an O(nlogn) time algorithm for computing the maximum flow in an undirected general planar EVC-network and an O(n) time algorithm for computing the maximum flow in an undirected (s,t)-planar EVC-network. As a result, the maximum flow problem in undirected planar EVC-networks is as easy as the problem in undirected planar EC-networks in terms of computational complexity. © 2008 Springer-Verlag Berlin Heidelberg.
AB - We study the maximum flow problem in an undirected planar network with both edge and vertex capacities (EVC-network). A previous study reduces the minimum cut problem in an undirected planar EVC-network to the minimum edge-cut problem in another planar network with edge capacity only (EC-network), thus the minimum-cut or the maximum flow value can be computed in O(nlogn) time. Based on this reduction, in this paper we devise an O(nlogn) time algorithm for computing the maximum flow in an undirected general planar EVC-network and an O(n) time algorithm for computing the maximum flow in an undirected (s,t)-planar EVC-network. As a result, the maximum flow problem in undirected planar EVC-networks is as easy as the problem in undirected planar EC-networks in terms of computational complexity. © 2008 Springer-Verlag Berlin Heidelberg.
UR - https://www.scopus.com/pages/publications/48249099630
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-48249099630&origin=recordpage
U2 - 10.1007/978-3-540-69733-6_57
DO - 10.1007/978-3-540-69733-6_57
M3 - RGC 32 - Refereed conference paper (with host publication)
SN - 3540697322
SN - 9783540697329
VL - 5092 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 577
EP - 586
BT - Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
T2 - 14th Annual International Conference on Computing and Combinatorics, COCOON 2008
Y2 - 27 June 2008 through 29 June 2008
ER -