{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:13:24Z","timestamp":1787386404611,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>A lower bound of $\\Omega(\\sqrt{\\log k \/ \\log \\log k})$ is proved for the competitive ratio of randomized algorithms for the k-server problem against an oblivious adversary. The bound holds for arbitrary metric spaces (having at least k+1 points) and provides a new lower bound for the metrical task system problem as well. This improves the previous best lower bound of $\\Omega(\\log \\log k)$ for arbitrary metric spaces [H.J. Karloff, Y. Rabani, and Y. Ravid, SIAM J. Comput., 23 (1994), pp. 293--312] and more closely approaches the conjectured lower bound of $\\Omega(\\log k)$. For the server problem on k+1 equally spaced points on a line, which corresponds to a natural motion-planning problem, a lower bound of $\\Omega(\\frac{\\log k}{\\log \\log k})$ is obtained.<\/jats:p>\n                  <jats:p>The results are deduced from a general decomposition theorem for a simpler version of both the k-server and the metrical task system problems, called the \"pursuit-evasion game.\" It is shown that if a metric space $\\cal M$ can be decomposed into two spaces $\\cal M_L$ and $\\cal M_R$ such that the distance between them is sufficiently large compared to their diameter, then the competitive ratio for this game on $\\cal M$ can be expressed nearly exactly in terms of the ratios on each of the two subspaces. This yields a divide-and-conquer approach to bounding the competitive ratio of a space.<\/jats:p>","DOI":"10.1137\/s0097539799351882","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1624-1661","source":"Crossref","is-referenced-by-count":17,"title":["A Decomposition Theorem for Task Systems and Bounds for Randomized Server Problems"],"prefix":"10.1137","volume":"30","author":[{"given":"Avrim","family":"Blum","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Howard","family":"Karloff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuval","family":"Rabani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Saks","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01294260"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Y. 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Grove,\n                      The harmonic k\u2010server algorithm is competitive\n                      , in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, ACM, New York, 1991, pp. 260\u2013266.","DOI":"10.1145\/103418.103448"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01762111"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792224838"},{"key":"R11","unstructured":"J. L. Kelley,\n                      General Topology\n                      , American Book Company, New York, 1955."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1145\/210118.210128"},{"key":"R13","unstructured":"Carsten Lund, Nick Reingold, Linear programs for randomized on\u2010line algorithms, ACM, New York, 1994, 382\u20133911285182"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90003-W"},{"key":"R15","first-page":"451","volume":"33","author":"Matou\u0161ek Ji\u0159\u00ed","year":"1992","journal-title":"Comment. Math. Univ. Carolin."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01759073"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Prabhakar Raghavan, Marc Snir, Memory versus randomization in on\u2010line algorithms (extended abstract), Lecture Notes in Comput. Sci., Vol. 372, Springer, Berlin, 1989, 687\u20137031037084","DOI":"10.1007\/BFb0035792"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1145\/2786.2793"},{"key":"R19","unstructured":"J. von Neumann and O. Morgenstern,\n                      Theory of Games and Economic Behavior\n                      , 2nd ed., Princeton University Press, Princeton, NJ, 1947."}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539799351882","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:19:49Z","timestamp":1787336389000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539799351882"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S0097539799351882"],"URL":"https:\/\/doi.org\/10.1137\/s0097539799351882","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}