Increasing the rooted-connectivity of a digraph by one

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

D.R. Fulkerson [7] described a two-phase greedy algorithm to find a minimum cost spanning arborescence and to solve the dual linear program. This was extended by the present author for "kernel systems", a model including the rooted edge-connectivity augmentation problem, as well. A similar type of method was developed by D. Komblum [9] for "lattice polyhedra", a notion introduced by A. Hoffman and D.E. Schwanz [8]. In order to unify these approaches, here we describe a two-phase greedy algorithm working on a slight extension of lattice polyhedra. This framework includes the rooted node-connectivity augmentation problem, as well, and hence the resulting algorithm, when appropriately specialized, finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity by one. The only known algorithm for this problem used submodular flows. Actually, the specialized algorithm solves an extension of the rooted edge-connectivity and node-connectivity augmentation problem.

Original languageEnglish
Pages (from-to)565-576
Number of pages12
JournalMathematical Programming, Series B
Volume84
Issue number3
DOIs
Publication statusPublished - 1999

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Digraph
Connectivity
Augmentation
Edge-connectivity
Greedy Algorithm
Polyhedron
Costs
Vertex of a graph
Linear Program
kernel
Model
Greedy algorithm
Node

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

Cite this

Increasing the rooted-connectivity of a digraph by one. / Frank, A.

In: Mathematical Programming, Series B, Vol. 84, No. 3, 1999, p. 565-576.

Research output: Contribution to journalArticle

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