On Broadcast Disk Paging
Broadcast disks are an emerging paradigm for massive data dissemination. In a broadcast disk, data is divided into n equal-sized pages, and pages are broadcast in a round-robin fashion by a server. Broadcast disks are effective because many clients can simultaneously retrieve any transmitted data. Paging is used by the clients to improve performance, much as in virtual memory systems. However, paging on broadcast disks differs from virtual memory paging in at least two fundamental aspects: - A page fault in the broadcast disk model has a variable cost that depends on the requested page as well as the current state of the broadcast. - Prefetching is both natural and a provably essential mechanism for achieving significantly better competitive ratios in broadcast disk paging. In this paper, we design a deterministic algorithm that uses prefetching to achieve an O(n log k) competitive ratio for the broadcast disk paging problem, where k denotes the size of the client's cache. We also show a matching lower bound of Ω(n log k) that applies even when the adversary is not allowed to use prefetching. In contrast, we show that when prefetching is not allowed, no deterministic online algorithm can achieve a competitive ratio better than Ω(nk). Moreover, we show a lower bound of Ω(n log k) on the competitive ratio achievable by any nonprefetching randomized algorithm against an oblivious adversary. These lower bounds are trivially matched from above by known results about deterministic and randomized marking algorithms for paging. An interpretation of our results is that in the broadcast disk paging, prefetching is a perfect substitute for randomization.
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Postprint version. Copyright ACM, 2000. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Siam Journal on Computing, Volume 29, Number 5, March 1999, pages 1683-1702. Publisher URL: http://epubs.siam.org/sam-bin/dbq/article/34139 NOTE: At the time of publication, author Sanjeev Khanna was affiliated with Bell Labs. Currently (July 2005), he is a faculty member in the Department of Computer and Information Science at the University of Pennsylvania.