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Following Mettu and Plaxton [22, 21], we study oblivious algorithms for the k-medians problem. Such an algorithm produces an incremental sequence of facility sets. We give improved algorithms, including a (24 + ǫ)-competitive deterministic polynomial algorithm and a 2e ≈ 5.44-competitive, randomized, non-polynomial algorithm. Our approach is similar to that(More)
In the paging problem we have to manage a two-level memory system, in which the rst level has short access time but can hold only up to k pages, while the second level is very large but slow. We use competitive analysis to study the relative performance of the two best known algorithms for paging, LRU and FIFO. Sleator and Tarjan proved that the competitive(More)
We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs. We give an(More)
We study the problem of online scheduling on two uniform machines with speeds 1 and s 1. For this problem, a 1:61803 competitive de-terministic algorithm was already known. We present the rst randomized results for this problem: We show that randomization does not help for speeds s 2, but does help for all s < 2. We present a simple memoryless randomized(More)
In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following the work of Mettu(More)