On algorithm design for metrical task systems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On page migration and other relaxed task systems
Theoretical Computer Science
Invited Lecture: Online Algorithms: A Study of Graph-Theoretic Concepts
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
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The page migration problem is to manage 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 incur a cost proportional to the network distance. At times the page may migrate between processors at cost proportional to the distance times $D$, a page size factor. The problem is to schedule movements on-line so that the total cost of memory references is within a constant factor $c$ of the best off-line schedule. An algorithm that does so is called c-competitive. Black and Sleator gave 3-competitive deterministic on-line algorithms for uniform networks (complete graphs with unit edge lengths) and for trees with arbitrary edge lengths. No good deterministic algorithm is known for general networks with arbitrary edge lengths. Randomized algorithms are presented for the migration problem that are both simple and better than 3-competitive against an oblivious adversary. An algorithm for uniform graphs is given. It is approximately 2.28-competitive as $D$ grows large. A second, more powerful algorithm that works on graphs with arbitrary edge distances is also given. This algorithm is approximately 2.62-competitive (or, 1 plus the golden ratio) for large $D$. Both these algorithms use random bits only during an initialization phase, and from then on run deterministically. The competitiveness of a very simple coin-flipping algorithm is also examined.