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40th ACM SiGPLAN-SiGACT Symposium on Principles of Programming Languages

作者： Blelloch, Guy E. Harper, Robert Carnegie Mellon Univ Pittsburgh PA 15213 USA

The widely studied i/o and ideal-cache models were developed to account for the large difference in costs to access memory at different levels of the memory hierarchy. Both models are based on a two level memory hierarchy with a fixed size primary memory (cache) of size M, an unbounded secondary memory organized in blocks of size B. The cost measure is based purely on the number of block transfers between the primary and secondary memory. All other operations are free. Many algorithms have been analyzed in these models and indeed these models predict the relative performance of algorithms much more accurately than the standard RAM model. The models, however, require specifying algorithms at a very low level requiring the user to carefully lay out their data in arrays in memory and manage their own memory allocation. in this paper we present a cost model for analyzing the memory efficiency of algorithms expressed in a simple functional language. We show how some algorithms written in standard forms using just lists and trees (no arrays) and requiring no explicit memory layout or memory management are efficient in the model. We then describe an implementation of the language and show provable bounds for mapping the cost in our model to the cost in the ideal-cache model. These bound imply that purely functional programs based on lists and trees with no special attention to any details of memory layout can be as asymptotically as efficient as the carefully designed imperative i/o efficient algorithms. For example we describe an o (n/B log(M)/(B) n/B) cost sorting algorithm, which is optimal in the ideal cache and i/o models.

关键词： algorithms Design Languages Performance Theory cost semantics i/o algorithms

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RAM-Efficient External Memory Sorting

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ALGoRiTHMiCA 2015年第4期73卷 623-636页

作者： Arge, Lars Thorup, Mikkel Aarhus Univ Dept Comp Sci Ctr Mass Data Algorithm MADALGO DK-8000 Aarhus Denmark Univ Copenhagen Dept Comp Sci Copenhagen Denmark

in recent years a large number of problems have been considered in external memory models of computation, where the complexity measure is the number of blocks of data that are moved between slow external memory and fast internal memory (also called i/os). in practice, however, internal memory time often dominates the total running time once i/o-efficiency has been obtained. in this paper we initiate a study of algorithms for fundamental problems that are simultaneously i/o-efficient and internal memory efficient in the RAM model of computation. For sorting the conventional wisdom is to use merging base algorithms in external memory but we describe how this leads to suboptimal RAM performance. However, by using a splitting based algorithm in combination with existing RAM sorting techniques we obtain a sorting algorithm that is both i/o and RAM model efficient. Furthermore, we design an i/o- and RAM-efficient priority queue. Finally, we prove a sorting lower bound that shows that in most cases our results are optimal both in terms of i/o and internal computation.

关键词： i/o algorithms RAM algorithms External memory algorithms Sorting Priority queue

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RAM-Efficient External Memory Sorting

RAM-Efficient External Memory Sorting

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24th international Symposium on algorithms and Computation

作者： Arge, Lars Thorup, Mikkel Aarhus Univ Dept Comp Sci Ctr Mass Data Algorithm MADALGO DK-8000 Aarhus Denmark Univ Copenhagen Dept Comp Sci Copenhagen Denmark

ISBN: (纸本)9783642450297

关键词： i/o algorithms RAM algorithms External memory algorithms Sorting Priority queue

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BUiLDiNG VERY LARGE NEiGHBoUR-JoiNiNG TREES

BUILDING VERY LARGE NEIGHBOUR-JOINING TREES

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1st international Conference on Bioinformatics (BioiNFoRMATiCS 2010)

作者： Simonsen, Martin Mailund, Thomas Pedersen, Christian N. S. Aarhus Univ Bioinformat Res Ctr BIRC CF Mollers Alle 8 DK-8000 Aarhus C Denmark

ISBN: (纸本)9789896740191

The neighbour-joining method by Saitou and Nei is a widely used method for phylogenetic reconstruction, made popular by a combination of computational efficiency and reasonable accuracy. With its cubic running time by Studier and Kepler, the method scales to hundreds of species, and while it is usually possible to infer phylogenies with thousands of species, tens or hundreds of thousands of species is infeasible. Recently we developed a simple branch and bound heuristic, RapidNJ, which significantly reduces the average running time. However, the o(n(2)) space consumption of the RapidNJ method, and the NJ method in general, becomes a problem when inferring phylogenies with 10000+ taxa. in this paper we present two extentions of RapidNJ which reduce memory requirements and enable RapidNJ to infer very large phylogenetic trees efficiently. We also present an improved search heuristic for RapidNJ which improves RapidNJ's performance on many data sets of all sizes.

关键词： Neighbour-joining Distance based phylogenetic inference i/o algorithms RapidNJ Evolution

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