article

Maximizing the minimum source-sink path subject to a budget constraint

Authors:

D. R. Fulkerson,

Gary C. HardingAuthors Info & Claims

Mathematical Programming: Series A and B, Volume 13, Issue 1

Pages 116 - 118

https://doi.org/10.1007/BF01584329

Published: 01 December 1977 Publication History

Abstract

Given a linear cost function for lengthening arcs, a technique is shown for maximizing, within a budget, the shortest source--sink path length in a graph. The computation is equivalent to the parametric solution of a minimum cost flow problem.

References

[1]

C. Berge, Graphs and hypergraphs (North-Holland, Amsterdam, 1973).

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[2]

R.G. Bland,"Complementary orthogonal subspaces of Rⁿ and orientability of matroids," Department of Operations Research, Cornell University, Tech. Rept. No. 219.

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[3]

L.R. Ford, Jr. and D.R. Fulkerson. Flows in networks (Princeton Press, 1962).

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[4]

D.R. Fulkerson, "Increasing the capacity of a network: the parametric budget problem", Management Science 5 (1959) 472-483.

Crossref

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[5]

D.R. Fulkerson, "Networks, frames and blocking systems", in: G.B. Dantzig and A.F. Veinott, Jr., Eds., Mathematics of the decision sciences, Lecture in applied mathematics, Vol. II (Am. Math. Soc., 1968) pp. 303-334.

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[6]

G.C. Harding, "Some budgeted optimization problems and the edge disjoint branchings problem," Dissertation, Cornell University (1977).

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Index Terms

Maximizing the minimum source-sink path subject to a budget constraint
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Mathematical Programming: Series A and B

Mathematical Programming: Series A and B Volume 13, Issue 1

December 1977

368 pages

ISSN:0025-5610

Issue’s Table of Contents

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1977

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Abstract

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Finding a contra-risk path between two nodes in undirected graphs

Disjoint path covers joining prescribed source and sink sets in interval graphs

Solving all-pairs shortest path by single-source computations

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