Direct - Mapped Constrained Migration Problem

The constrained migration problem arises in the memory management of large multiprocessor systems. Given a network of processors, each of which has its own local memory, the purpose of this problem is to nd an e cient migration strategy which locates each writable page at an appropriate processor by migration to reduce the total access cost, while considering the actual capacity of each local memory. Although this problem is focused recently in the competitive analysis area for on-line algorithms, only a few results are known so far about this problem. This paper examines the on-line constrained migration problem deeper by attacking some special case of the problem which we named the direct-mapped constrained migration problem, where all processors are assumed to manage pages in their local memory using the same hash function. For the direct-mapped constrained migration problem we present an optimal 3-competitive deterministic on-line algorithm when the network consists of only 2 nodes. Furthermore we develop two O(1)-competitive on-line algorithms for uniform graphs which are either deterministic or memoryless. Interestingly this competitive ratio breaks the previous best upper bound obtained by applying known algorithms for the constrained migration problem to this problem. Observing this fact, we also give an important conjecture on the constrained migration problem. ANY OTHER IDENTIFYING INFORMATION OF THIS REPORT DISTRIBUTION STATEMENT First issue 35 copies. SUPPLEMENTARY NOTES Part of this work was done when the second author visited Max-Planck-Institut f ur Informatik, Saarbr ucken, Germany. REPORT DATE November 2, 1994 TOTAL NO. OF PAGES 19 WRITTEN LANGUAGE English NO. OF REFERENCES 14 DEPARTMENT OF INFORMATION SCIENCE Faculty of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Direct-Mapped Constrained Migration Problem Susanne Albers Max-Planck-Institut f ur Informatik Saarbr ucken, Germany [email protected] Hisashi Koga The University of Tokyo Tokyo, Japan [email protected]