Minimizing movement

Authors:
Erik D. Demaine;MohammadTaghi Hajiaghayi;Hamid Mahini;Amin S. Sayedi-Roshkhar;Shayan Oveisgharan;Morteza Zadimoghaddam
Affiliations:
MIT;MIT and Carnegie Mellon University and Institute for Theoretical Physics and Mathematics (IPM);Sharif University of Technology and Institute for Theoretical Physics and Mathematics (IPM);Sharif University of Technology;Sharif University of Technology;Sharif University of Technology
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompass an intriguing range of graph and geometric algorithms, with several real-world applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P ≠ NP.