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The paging problem is deened as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p, a miss occurs if p is not present in the fast memory. In(More)
In the paging problem we have to manage a two-level memory system, in which the first 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(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)
We study the problem of online scheduling on two uniform machines with speeds 1 and s 1. A 1:61803 competitive deterministic 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 algorithm with(More)
The randomized k-paging algorithm Equitable given by Achlioptas et al. is Hk-competitive and uses O(k 2 log k) memory. This competitive ratio is best possible. The randomized algorithm RMark given by Fiat et al. is (2Hk − 1)-competitive, but only uses O(k) memory. Borodin and El Yaniv [6] list as an open question whether there exists an Hk-competitive(More)
The knapsack problem can and has been used to model many resource sharing problems. The allocation of a portion of a resource to a particular agent provides a benefit to the system, but also blocks other agents from utilizing that portion of the resource. For a problem where the number of agents as well as each agent's demand and potential benefit are known(More)
We introduce the novel concept of knowledge states. The knowledge state approach can be used to construct competitive randomized online algorithms and study the trade-off between competitiveness and memory. Many well-known algorithms can be viewed as knowledge state algorithms. A knowledge state consists of a distribution of states for the algorithm,(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)