Exact and Approximate Algorithms for Movement Problems on (Special Classes of) Graphs
When a large collection of objects (e.g., robots, sensors, etc.) has to be deployed in a given environment, it is often required to plan a coordinated motion of the objects from their initial position to a final configuration enjoying some global property. In such a scenario, the problem of minimizing the distance travelled, and therefore energy consumption, is of vital importance. In this paper we study several motion planning problems that arise when the objects must be moved on a network, in order to reach certain goals which are of interest for several network applications. Among the others, these goals include broadcasting messages and forming connected or interference-free networks. We study these problems with the aim to minimize a number of natural measures such as the average/overall distance travelled, the maximum distance travelled, or the number of objects that need to be moved. To this respect, we provide approximability and inapproximability results, most of which are tight.
KeywordsApproximation Algorithm Polynomial Time Bipartite Graph Vertex Cover Approximate Algorithm
Unable to display preview. Download preview PDF.
- 1.Ahmadian, S., Friggstad, Z., Swamy, C.: Local-search based approximation algorithms for mobile facility location problems. arXiv preprint arXiv:1301.4478 (2013)Google Scholar
- 3.Bollobás, B.: Modern graph theory, vol. 184. Springer (1998)Google Scholar
- 4.Demaine, E.D., Hajiaghayi, M., Mahini, H., Sayedi-Roshkhar, A.S., Oveisgharan, S., Zadimoghaddam, M.: Minimizing movement. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 258–267. Society for Industrial and Applied Mathematics (2007)Google Scholar
- 6.Dinur, I., Safra, S.: On the hardness of approximating minimum vertex cover. Annals of Mathematics pp. 439–485 (2005)Google Scholar
- 10.Khot, S.: On the power of unique 2-prover 1-round games. In: Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing, pp. 767–775. ACM (2002)Google Scholar
- 12.Prencipe, G., Santoro, N.: Distributed algorithms for autonomous mobile robots. In: Navarro, G., Bertossi, L., Kohayakwa, Y. (eds.) IFIP TCS 2006. IFIP, vol. 209, pp. 47–62. Springer, Bostan (2006)Google Scholar