The Complexity of Rerouting Shortest Paths

  • Paul Bonsma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and ends with Q, such that subsequent paths differ in only one vertex. This is called a rerouting sequence.

This problem is shown to be PSPACE-complete. For claw-free graphs and chordal graphs, it is shown that the problem can be solved in polynomial time, and that shortest rerouting sequences have linear length. For these classes, it is also shown that deciding whether a rerouting sequence exists between all pairs of shortest st-paths can be done in polynomial time.


Short Path Polynomial Time Chordal Graph Color Assignment Graph Class 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paul Bonsma
    • 1
  1. 1.Computer Science DepartmentHumboldt University BerlinGermany

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