Improved algorithms for the multicut and multiflow problems in rooted trees

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)114-125
Number of pages12
JournalTOP
Volume16
Issue number1
DOIs
StatePublished - Jul 2008

Keywords

  • Greedy matrices
  • Maximum integral multiflows
  • Minimum multicuts
  • Rooted trees
  • Totally balanced matrices

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