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A deterministicO(k 3)-competitivek-server algorithm for the circle

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Abstract

Suppose thatk mobile servers are located on a circle. Repeatedly, a request at a pointx on the circle appears. To serve this request one of the servers has to be moved tox. The cost of moving a server tox is the distance on the circle between the server's previous location andx. The decision which server to move has to be doneon-line; that is, without the knowledge of future requests. We give a deterministic on-line algorithm for making these decisions. Our algorithm isO(k 3)-competitive: for any sequence of requests, the cost incurred by our algorithm in serving this sequence is bounded (up to an additive constant) byO(k 3) times the cost of serving this sequence using the bestoff-line algorithm; i.e., an algorithm that hasa priori knowledge of the whole sequence. Our algorithm is the best deterministic constructive algorithm fork>2.

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Communicated by Prabhakar Raghavan.

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Fiat, A., Rabani, Y., Ravid, Y. et al. A deterministicO(k 3)-competitivek-server algorithm for the circle. Algorithmica 11, 572–578 (1994). https://doi.org/10.1007/BF01189994

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  • DOI: https://doi.org/10.1007/BF01189994

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