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
SN - 1134-5764
VL - 16
SP - 114
EP - 125
JO - TOP
JF - TOP
IS - 1
ER -