We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for on-line data tracking (a generalization of mobile user tracking [AP1...

This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file re-allocation strategy that adapts on-line to a sequence of read and write requests whose location and relative frequencies are completely unpredictable. This is achieved by replicating the file in response to read requests and migrating the file in response to write requests while paying the associated communications costs, so as to be closer to processors that access it frequently. We develop first explicit deterministic on-line strategy assuming existence of global information about the state of the network; previous (deterministic) solutions were complicated and more expensive. Our solution has (optimal) logarithmic competitive ratio. The paper also contains the first explicit deterministic data migration [BS89] algorithm achieving the best known competitive ratio for this problem. Using somewhat ...

In this paper, we formulate and provide optimal solutions for a broad class of problems in which a decision-maker is required to select from among numerous competing options. The goal of the decision-maker is to select the option that will have the best future performance. This task is made difficult by the constraint that the decision-maker has no way to predict the future performance of any of the options. Somewhat surprisingly, we find that the decision-maker can still (at least in several important scenarios) pick a winner with high probability. Our result has several applications. For example, consider the problem of scheduling background jobs on a network of workstations (NOW) when very little is known about the future speed or availability of each workstation. In this problem, the goal is to schedule each job on a workstation which will have enough idle capacity to complete the job within a reasonable or ...

Distributed paging [BFR92, ABF93b, AK95] deals with the dynamic allocation of copies of files in a distributed network as to minimize the total communication cost over a sequence of read and write requests. Most previous work deals with the file allocation problem [BS89, West91, CLRW93, ABF93a, WY93, Koga93, AK94, LRWY94] where infinite nodal memory capacity is assumed. In contrast the distributed paging problem makes the more realistic assumption that nodal memory capacity is limited. Former work on distributed paging deals with the problem only in the case of a uniform network topology. This paper gives the first distributed paging algorithm for general networks. The algorithm is competitive in storage and communication. The competitive ratios are poly-logarithmic in the total number of network nodes and the diameter of the network. Johns Hopkins University and Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86-K-0171, NSF contract 9114440-CCR, DARPA contract N00014J -92-1799, and a special grant from IBM. E-Mail: baruch@theory.lcs.mit.edu. y Department of Computer Science, School of Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel. Supported by a grant from the Israeli Academy of Sciences. E-mail: yairb@math.tau.ac.il, fiat@math.tau.ac.il 0 1

This paper considers an on-line optimization version of the set cover problem. We present a optimally competitive on-line randomized algorithm which is O(logn log m) competitive where n is the maximum number of sets and m is maximum the number of elements. Moreover, we provide a matching lower bound for the problem. We also give several applications of the results. Randomization is crucial for our result since a deterministic algorithm may cover only one element with each accepted set and thus, cannot achieve any non-trivial bound. 1 Introduction 1.1 The Problem In this paper we consider an on-line version of the following variant of the set cover problem, parameterized by k: Given a family of sets F = fS 1 ; S 2 ; : : : ; S n g, where S i ae fv 1 ; v 2 ; : : : ; v m g, for all i, choose some subset F 0 ae F , where F 0 is of size k, such that the size of the union of all S 2 F 0 is maximized. This paper introduces and optimally solves an on-line version of this problem: Base ...