{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:03:21Z","timestamp":1787385801969,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1994,4]]},"abstract":"<jats:p>In this paper, the authors prove lower bounds on the competitive ratio of randomized algorithms for two on-line problems: the k-server problem, suggested by Manasse, McGeoch, and Sleator [Competitive lgorithms for on-line problems, J. Algorithms, 11 (1990), pp. 208\u2013230], and an on-line motion-planning problem due to Papadimitriou and Yannakakis [Shortest paths without a map, Lecture Notes in Comput. Sci. 372, Springer-Verlag, New York, 1989, pp. 610\u2013620]. The authors prove, against an oblivious adversary, 1. an $\\Omega \\log k$ lower bound on the competitive ratio of any randomized on-line k-server algorithm in any sufficiently large metric space, 2. an $\\Omega (\\log \\log k)$ lower bound on the competitive ratio of any randomized on-line k-server algorithm in any metric space with at least $k + 1$ points, and 3. an $\\Omega (\\log \\log n)$ lower bound on the competitive ratio of any on-line motion-planning algorithm for a scene with n obstacles.<\/jats:p>\n                  <jats:p>Previously, no superconstant lower bound on the competitive ratio of randomized on-line algorithms was known for any of these problems.<\/jats:p>","DOI":"10.1137\/s0097539792224838","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:39:46Z","timestamp":1109227186000},"page":"293-312","source":"Crossref","is-referenced-by-count":23,"title":["Lower Bounds for Randomized\n                    <i>k<\/i>\n                    -Server and Motion-Planning Algorithms"],"prefix":"10.1137","volume":"23","author":[{"given":"Howard","family":"Karloff","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuval","family":"Rabani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiftach","family":"Ravid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, A. Wigderson,  On the power of randomization in online algorithms,  Proc. 22nd Annual ACM Symposium on Theory of Computing,  1990,  379\u2013386","DOI":"10.1145\/100216.100268"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"R. A. Baeza-Yates, J. C. Culberson, G. J. E. Rawlins,  Searching with Uncertainty, Tech. Report, University of Waterloo,  1987","DOI":"10.1007\/3-540-19487-8_20"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Borodin, N. Linial, M. Saks,  An optimal on-line algorithm for metrical task systems,  Proc. 19th Annual ACM Symposium on Theory of Computing,  1987,  373\u2013382","DOI":"10.1145\/28395.28435"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"A. Blum, P. Raghavan, B. Schieber,  Navigating in unfamiliar geometric terrain,  Proc. 23rd Annual ACM Symposium on Theory of Computing,  1991","DOI":"10.1145\/103418.103419"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0404017"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0220008"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1991.185381"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(91)90041-V"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(05)80060-1"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"E. Grove,  The harmonic\n                      k\n                      -server algorithm is competitive,  Proc. 23rd Annual ACM Symposium on Theory of Computing,  1991,  260\u2013266","DOI":"10.1145\/103418.103448"},{"key":"R11","unstructured":"A. R. Karlin, M. S. Manasse, L. A. McGeoch, S. Owicki,  Competitive randomized algorithms for non-uniform problems,  Proc. 1st Annual ACM-SIAM Symposium on Discrete Algorithms,  1990,  301\u2013309 0800.68456"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90096-4"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90003-W"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01759073"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0035787"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0035792"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1145\/2786.2793"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(92)90061-G"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539792224838","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:51:09Z","timestamp":1787338269000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539792224838"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,4]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,4]]}},"alternative-id":["10.1137\/S0097539792224838"],"URL":"https:\/\/doi.org\/10.1137\/s0097539792224838","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,4]]}}}