A Note on the Server Problem
نویسنده
چکیده
We consider the k-server problem, with the additional assumptions that (1) the adversary makes only lazy moves (if it has a free server, not matched with our server, then it puts a request on such a server without moving it), and (2) whenever all our servers are matched with his servers, then he announces it to our algorithm. We show a k-competitive algorithm against such an adversary. As with the original server problem, no better than a k-competitive on-line algorithm is possible in this model. 1 The Server Problem The k-server problem is deened as follows: Let M be a metric space, in which we have k servers that occupy points of M. At each time step we are given a request point r 2 M, and we have to move one of our servers to r. Note that the decision of which server to move has to be made on-line, without the knowledge about the future requests. Our goal is to minimize the total distance traveled by our servers. Since it is known that no on-line algorithm can guarantee an optimal schedule, it is natural to look for algorithms that only approximate the optimal schedule as close as possible. Let A be an on-line server algorithm. For a given initial connguration K 0 2 k M of k servers ((k X = the collection of all multisets of cardinality k drawn from X) and a sequence of requests % 2 M (X = the set of nite sequences drawn from X), let cost A (K 0 ; %) be the total cost of A on % when starting from K 0 , and cost opt (K 0 ; %) the cost of the corresponding optimal schedule. (For simplicity, we will often omit the parameters K 0 and %.) Then, for a given constant c, A is called 1
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