Harry Buhrman
Juan A. Garay
Abstract
We introduce a search problem called “mutual search” where k agents, arbitrarily distributed over n sites, are required to locate one another by posing queries of the form “Anybody at site i?”. We ask for the least number of queries that is necessary and sufficient. For the case of two agents using deterministic protocols, we obtain the following worst-case results: In an oblivious setting (where all pre-planned queries are executed), there is no savings: n-1 queries are required and are sufficient. In a nonoblivious setting, we can exploit the paradigm of “no news is also news” to obtain significant savings: in the synchronous case 0.586n queries are required; in the asynchronous case 0.896n queries suffice and a fortiori 0.536n queries are required; for o(√n) agents using a synchronous deterministic protocol less than n queries suffice; there is a simple randomized protocol for two agents with worst-case expected 0.5n queries and all radomized protocols require at least 0.25n worst-case expected queries. The graph-theoretic framework we formulate for expressing and analyzing algorithms for this problem may be of independent interest.
- AWERBUCH, B., AND PELEG, D. 1989. On-line tracking of mobile users. Tech. Memo TM-410. MIT, Lab. for Computer Science, Cambridge, Mass.Google Scholar
- AWERBUCH, B., AND PELEG, D. 1990. Sparse partitions. In Proceedings of the 31st IEEE Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 503-513.Google Scholar
- AXELROD, R., AND HAMILTON, W. 1988. The evolution of cooperation. Science 211 (Mar.), 1390-1396.Google Scholar
- BEN-OR, M., GOLDWASSER, S., AND WIGDERSON, A. 1988. Completeness theorems for noncryptographic fault-tolerant distributed computation. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing (Chicago, Ill., May 2-4). ACM, New York, pp. 1-10. Google Scholar
- BILLARD, E., AND PASQUALE, J. 1995. Probabilistic coalition formation in distributed knowledge environments. IEEE Trans. Syst., Man, and Cybern 25, 2 (Feb.), 277-286.Google Scholar
- CHOR, B., GOLDWASSER, S., MICALI, S., AND AWERBUCH, B. 1985. Verifiable secret sharing and achieving simultaneity in the presence of faults. In Proceedings of the 26th Annual IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, Calif., pp. 383-395.Google Scholar
- GALLAGER, R., HUMBLET, P., AND SPIRA, P. 1983. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Prog. Lang. Syst. 5, 1 (Jan.), 66-77. Google Scholar
- FISCHER, M. J., LYNCH, N. A., AND PATERSON, M.S. 1985. Impossibility of distributed consensus with one faulty processor. J. ACM. 32, 2 (Apr.), 374-382. Google Scholar
- HAKIMI, S.L. 1971. Steiner's problem in graphs and its implications. Networks 1, 113-133.Google Scholar
- HUBERMAN, B., AND HOGG, f. 1988. The behavior of computational ecologies. In The Ecology of Computation, B. Huberman, ed. North Holland, Elsevier Science Publishers, Amsterdam, The Netherlands, pp. 77-115.Google Scholar
- KNUTH, D. E. 1998. The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed. Addison-Wesley, Reading, Mass. Google Scholar
- KOOPMAN, B. 0. 1956a. The theory of search, Part I. Oper. Res. 4, 324-346.Google Scholar
- KOOPMAN, B. 0. 1956b. The theory of search, Part II. Oper. Res. 4, 503-531.Google Scholar
- KOOPMAN, B. 0. 1957. The theory of search, Part III. Oper. Res. 5, 613-626.Google Scholar
- KRANAKIS, E., AND VITANYI, P. M.B. 1992. A note on weighted distributed match-making. Math. Syst. Theory 25, 123-140.Google Scholar
- LAMPORT, L., SHOSTAK, R., AND PEASE, M. 1982. The Byzantine generals problem. ACM Trans. Prog. Lang. Systems, 4, 3 (July), 382-401. Google Scholar
- MAEKAWA, M. 1985. A # algorithm for mutual exclusion in decentralized systems. ACM Trans. Comput. Syst. 3, 2 (May), 145-159. Google Scholar
- MAYNARD-SMITH, J. 1982. Evolution and the Theory of Games. Cambridge University Press, Cambridge, Mass.Google Scholar
- MULLENDER, S. J., AND VITANYI, P. M. B. 1988. Distributed match-making. Algorithmica 3, 367-391.Google Scholar
- ZHU, Q., AND OOMMEN, J. 1997. Optimal search with unknown target distributions. In Proceedings of the XVII International Conference of the Chilean Computer Science Society. IEEE Computer Society Press, Los Alamitos, Calif., pp. 268-277. Google Scholar
Index Terms
- Mutual search
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