On the complexity of local search
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Theoretical Computer Science - Game theory meets theoretical computer science
On the Complexity of Reconfiguration Problems
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Mixing 3-colourings in bipartite graphs
European Journal of Combinatorics
Reconfiguration of List Edge-Colorings in a Graph
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Finding Paths between graph colourings: PSPACE-completeness and superpolynomial distances
Theoretical Computer Science
The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
SIAM Journal on Computing
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
On the complexity of reconfiguration problems
Theoretical Computer Science
Shortest paths between shortest paths and independent sets
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Finding paths between 3-colorings
Journal of Graph Theory
Complexity of independent set reconfigurability problems
Theoretical Computer Science
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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.