The complexity of finding maximum disjoint paths with length constraints

A. Itai, Y. Perl, Y. Shiloach

Research output: Contribution to journalArticlepeer-review

134 Scopus citations


The following problem is considered: Given an integer K, a graph G with two distinct vertices s and t, find the maximum number of disjoint paths of length K from s to t. The problem has several variants: the paths may be vertex‐disjoint or edge‐disjoint, the lengths of the paths may be equal to K or bounded by K, the graph may be undirected or directed. It is shown that except for small values of K all the problems are NP‐complete. Assuming P ≠ NP, for each problem, the largest value of K for which the problem is not NP‐complete is found. Whenever a polynomial algorithm exists, an efficient algorithm is described.

Original languageEnglish (US)
Pages (from-to)277-286
Number of pages10
Issue number3
StatePublished - 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Networks and Communications


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