Reconfigurations in Graphs and Grids

  • Gruia Calinescu
  • Adrian Dumitrescu
  • János Pach
Conference paper

DOI: 10.1007/11682462_27

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3887)
Cite this paper as:
Calinescu G., Dumitrescu A., Pach J. (2006) Reconfigurations in Graphs and Grids. In: Correa J.R., Hevia A., Kiwi M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg


Let G be a connected graph, and let V and V ′ two n-element subsets of its vertex set V(G). Imagine that we place a chip at each element of V and we want to move them into the positions of V ′ (V and V ′ may have common elements). A move is defined as shifting a chip from v1 to v2 (v1,v2V(G)) on a path formed by edges of G so that no intermediate vertices are occupied. We give upper and lower bounds on the number of moves that are necessary, and analyze the computational complexity of this problem under various assumptions: labeled versus unlabeled chips, arbitrary graphs versus the case when the graph is the rectangular (infinite) planar grid, etc. We provide hardness and inapproximability results for several variants of the problem. We also give a linear-time algorithm which performs an optimal (minimum) number of moves for the unlabeled version in a tree, and a constant-ratio approximation algorithm for the unlabeled version in a graph. The graph algorithm uses the tree algorithm as a subroutine.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gruia Calinescu
    • 1
  • Adrian Dumitrescu
    • 2
  • János Pach
    • 3
  1. 1.Department of Computer ScienceIllinois Institute of TechnologyChicagoUSA
  2. 2.Department of Computer ScienceUniversity of Wisconsin–MilwaukeeMilwaukeeUSA
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA

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