The page migration problem occurs in managing a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors are charged a cost equal to the network distance. At times the page may migrate between processors, at a cost equal to the distance times a page size factor, D. The problem is to schedule movements on-line so as to minimize the total cost of memory references. Page migration can also be viewed as a restriction of the 1-server with excursions problem. This paper presents a collection of algorithms and lower bounds for the page migration problem in various settings. Competitive analysis is used. The competitiveness of an on-line algorithm is the worst-case ratio of its cost to the optimum cost on any sequence of requests. Randomized (2 + 1 2D )-competitive on-line algorithms are given for trees and products of trees, including the mesh and the hypercube, and for uniform spaces when D = 1; 2. These algorithms are shown to be optimal. A lower bound of 85 27 on the competitiveness of any deterministic algorithm (in arbitrary spaces) with D = 1 is shown, disproving a conjecture by Black and Sleator. Deterministic (2 + 1 2D )-competitive algorithms are given for products of continuous trees under the L 1 metric, such as IR n with the \Manhattan" metric. A deterministic algorithm for IR n under any norm is presented, and shown to have competitive ratio tending to 1 + = 2:618 : : : The paper makes extensive use of the concept of a work function, a tool which provides a systematic approach to many competitive analysis problems. Marek : Thu Aug
On the other hand, REF shows a lower bound of roughly 3.148.
Page Migration Algorithms Using Work Functions
In Proc. of the 4th Int. Symp. on Algorithms and Computation (ISAAC
Computer Science