TY - JOUR

T1 - Improved algorithms for the multicut and multiflow problems in rooted trees

AU - Tamir, A.

PY - 2008/7

Y1 - 2008/7

N2 - Costa et al. (Oper. Res. Lett. 31:21-27, 2003) presented a quadratic O (min(Kn, n2)) greedy algorithm to solve the integer multicut and multiflow problems in a rooted tree. (n is the number of nodes of the tree, and K is the number of commodities). Their algorithm is a special case of the greedy type algorithm of Kolen (Location problems on trees and in the rectilinear plane. Ph.D. dissertation, 1982) to solve weighted covering and packing problems defined by general totally balanced (greedy) matrices. In this communication we improve the complexity bound in Costa et al. (Oper. Res. Lett. 31:21-27, 2003) and show that in the case of the integer multicut and multiflow problems in a rooted tree the greedy algorithm of Kolen can be implemented in subquadratic O(K+n+min(K, n)log n) time. The improvement is obtained by identifying additional properties of this model which lead to a subquadratic transformation to greedy form and using more sophisticated data structures.

AB - Costa et al. (Oper. Res. Lett. 31:21-27, 2003) presented a quadratic O (min(Kn, n2)) greedy algorithm to solve the integer multicut and multiflow problems in a rooted tree. (n is the number of nodes of the tree, and K is the number of commodities). Their algorithm is a special case of the greedy type algorithm of Kolen (Location problems on trees and in the rectilinear plane. Ph.D. dissertation, 1982) to solve weighted covering and packing problems defined by general totally balanced (greedy) matrices. In this communication we improve the complexity bound in Costa et al. (Oper. Res. Lett. 31:21-27, 2003) and show that in the case of the integer multicut and multiflow problems in a rooted tree the greedy algorithm of Kolen can be implemented in subquadratic O(K+n+min(K, n)log n) time. The improvement is obtained by identifying additional properties of this model which lead to a subquadratic transformation to greedy form and using more sophisticated data structures.

KW - Greedy matrices

KW - Maximum integral multiflows

KW - Minimum multicuts

KW - Rooted trees

KW - Totally balanced matrices

UR - http://www.scopus.com/inward/record.url?scp=44649089951&partnerID=8YFLogxK

U2 - 10.1007/s11750-007-0037-9

DO - 10.1007/s11750-007-0037-9

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AN - SCOPUS:44649089951

VL - 16

SP - 114

EP - 125

JO - TOP

JF - TOP

SN - 1134-5764

IS - 1

ER -