O(1)-Approximations for maximum movement problems

Authors:
Piotr Berman;Erik D. Demaine;Morteza Zadimoghaddam
Affiliations:
Department of Computer Science and Engineering, Pennsylvania State University, PA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

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Abstract

We develop constant-factor approximation algorithms for minimizing the maximum movement made by pebbles on a graph to reach a configuration in which the pebbles form a connected subgraph (connectivity), or interconnect a constant number of stationary nodes (Steiner tree). These problems model the minimization of the total time required to reconfigure a robot swarm to achieve a proximity (e.g., radio) network with these connectivity properties. Our approximation factors are tight up to constant factors, as none of these problems admit a (2 - ε)-approximation assuming P ≠ NP.