On Page Migration and Other Related Task Systems

This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of on-line problems. The page migration problem deals with the management of pages residing in a network of processors. In the classical problem there is only one copy of each page which is accessed by different processors over time. The page is allowed to be migrated between processors. However a migration incurs higher communication cost than an access (proportionally to the page size). The problem is that of deciding when and where to migrate the page in order to lower access costs. A more general setting is the k-page migration where we wish to maintain k copies of the page. The page migration problems are concerned with a dilemma common to many on-line problems: determining when is it beneficial to make configuration changes. We deal with the relaxed task systems model which captures a large class of problems of this type, that can be described as the generalization of some original task system problem [BLS87]. Given a c-competitive algorithm for a task system we show how to obtain a deterministic O(c2) and randomized O(c) competitive algorithms for the corresponding relaxed task system. The result implies first deterministic algorithms for k-page migration by using k-server [MMS88] algorithms, and for network leasing by using generalized Steiner tree algorithms [AAB96], as well as providing solutions for natural generalizations of other problems (e.g. storage rearrangement [FMRW95]). We further study some special cases of the k-page migration problem and get optimal deterministic algorithms. For the classical page migration problem we present a deterministic algorithm that achieves a competitive ratio of 4:086, improving upon the previously best competitive ratio of 7 [ABF93a]. (The current lower bound on the problem is 3:148 [CLRW93].) International Computer Science Institute, Berkeley. Research supported in part by the Rothschild Postdoctoral fellowship and by the National Science Foundation operating grants CCR-9304722 and NCR-9416101. e-mail: [email protected] yDepartment of Computer Science, Stanford University. Research supported in part by Stanford School of Engineering Groswith Fellowship, and by NSF Award CCR-9357849,with matching funds from IBM, Mitsubishi, SchlumbergerFoundation, Shell Foundation, and Xerox Corporation. e-mail: [email protected] zDepartment of Computer Science, Stanford University. Research supported by NSF Award CCR-9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. e-mail: [email protected]