Abstract
The page migration problem in Euclidean space is revisited. In this problem, online requests occur at any location to access a single page located at a server. Every request must be served, and the server has the choice to migrate from its current location to a new location in space. Each service costs the Euclidean distance between the server and request. A migration costs the distance between the former and the new server location, multiplied by the page size. We study the problem in the uniform model, in which the page has size D = 1 . All request locations are not known in advance; however, they are sequentially presented in an online fashion. We design a 2.75 -competitive online algorithm that improves the current best upper bound for the problem with the unit page size. We also provide a lower bound of 2.732 for our algorithm. It was already known that 2.5 is a lower bound for this problem.
Highlights
The page migration problem is a classical formulation of efficient memory management in a shared memory multiprocessor system comprising a network of processors having their own local memories
The objective of the page migration problem is to minimize the total costs of services and migrations
We proposed a deterministic algorithm for the page migration problem in
Summary
The page migration problem is a classical formulation of efficient memory management in a shared memory multiprocessor system comprising a network of processors having their own local memories. Larmore, Reingold, and Westbrook [3] studied this problem on continuous metric spaces as well as networks They proposed a (2 + 1/2D )-competitive randomized algorithm on trees against oblivious adversaries, together with the same lower bound as this competitiveness even at two points, where. Westbrook [4] proposed a ( )-competitive randomized algorithm against oblivious adversaries, where ( ) is a function defined in [4] that tends toward 2.618 as grows large. One commonly used technique for proving the competitiveness of an online algorithm A is to utilize a potential function Φ, which typically maps the situation at a point of time, such as the page locations of A and OPT, to a real value. Summing the inequality over all events for an initial server s0 and a request sequence σ, we have cost A (s0 , σ ) ≤ c·costOPT (s0 , σ) + β + γ, which means that A is c-competitive
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