Computing disjoint paths with length constraints

  • Spyros Tragoudas
  • Yaakov L. Varol
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)


We show that the problem of computing a pair of disjoint paths between nodes s and t of an undirected graph, each having at most K, K ε Z+, edges is NP-complete. A heuristic for its optimization version is given whose performance is within a constant factor from the optimal. It can be generalized to compute any constant number of disjoint paths. We also generalize an algorithm in [1] to compute the maximum number of edge disjoint paths of the shortest possible length between s and t. We show that it is NP-complete to decide whether there exist at least K, K ε Z+, disjoint paths that may have at most S+1 edges, where S is the minimum number of edges on any path between s and t. In addition, we examine a generalized version of the problem where disjoint paths are routed either between a node pair (s1, t1) or a node pair (s2, t2). We show that it is NP-hard to find the maximum number of disjoint paths that either connect pair (s1, t1) the shortest way or (s2, t2) the shortest way.


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  1. 1.
    Itai A., Perl Y., Shiloach Y.: The Complexity of Finding Maximum Disjoint Paths with Length Constraints. Networks 12 (1982) 277–286Google Scholar
  2. 2.
    Garey M.R., Johnson D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, NY, 1979Google Scholar
  3. 3.
    Shiloach Y.: The Two Paths Problem is Polynomially Solvable. Report STAN-CS-78-654. Computer Science Department, Stanford University, Stanford, CAGoogle Scholar
  4. 4.
    Suurballe, J.W.: Disjoint Paths in a Network. Networks 4 (1974) 125–145Google Scholar
  5. 5.
    Suurballe, J.W., Tarjan, R.E.: A Quick Method for Finding Shortest Pairs of Disjoint Paths. Networks 14 (1984) 325–336Google Scholar
  6. 6.
    Tragoudas, S., Varol Y.L.: On the Computation of Disjoint Paths with Length Constraints. Technical Report 96-6. Computer Science Department, Southern Illinois Univerity, Carbondale, IL 62901Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Spyros Tragoudas
    • 1
  • Yaakov L. Varol
    • 2
  1. 1.Computer Science Dept.Southern Illinois UniversityCarbondaleUSA
  2. 2.Computer Science Dept.University of NevadaRenoUSA

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