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The complexity of finding maximum disjoint paths with length constraints
Author(s) -
Itai A.,
Perl Y.,
Shiloach Y.
Publication year - 1982
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230120306
Subject(s) - combinatorics , disjoint sets , mathematics , bounded function , undirected graph , vertex (graph theory) , time complexity , discrete mathematics , graph , integer (computer science) , computer science , programming language , mathematical analysis
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.