The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The lifting model for reconfiguration
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Coordinating Pebble Motion On Graphs, The Diameter Of Permutation Groups, And Applications
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Colored pebble motion on graphs
European Journal of Combinatorics
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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,v2 ∈ V(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.