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We have designed a radix sort algorithm for vector multiprocessors and have implemented the algorithm on the CRAY Y-MP. On one processor of the Y-MP, our sort is over 5 times faster on large sorting problems than the optimized library sort provided by CRAY Research. On eight processors we achieve an additional speedup of almost 5, yielding a routine over 25 times faster than the library sort. Using this multiprocessor version, we can sort at a rate of 15 million 64-bit keys per second. Our sorting algorithm is adapted from a data-parallel algorithm previously designed for a highly parallel Single Instruction Multiple Data (SIMD) computer, the Connection Machine CM-2. To develop our version we introduce three general techniques for mapping data-parallel algorithms ontovector multiprocessors. These techniques allow us to fully vectorize and parallelize the algorithm. The paper also derives equations that model the performance of our algorithm on the Y-MP. These equations are then used t...

We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through low-level implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present the results from a study in which we used: multiple languages, compilers, and machines; all the major variants of the comparison-based algorithms; and eight varieties of graphs in five families, with sizes of up to 0.5 million vertices (in sparse graphs) or 1.3 million edges (in dense graphs).

We compare algorithms for the construction of a minimum spanning tree through large-scale experimentation on randomly generated graphs of different structures and different densities. In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense). Algorithms included in our experiments are Prim's algorithm (implemented with a variety of priority queues), Kruskal's algorithm (using presorting or demand sorting), Cheriton and Tarjan's algorithm, and Fredman and Tarjan 's algorithm. We also ran a large variety of tests to investigate low-level implementation decisions for the data structures, as well as to enable us to eliminate the effect of compilers and architectures. Within the range of sizes used, Prim's algorithm, using pairing heaps or sometimes binary heaps, is clearly preferable. While versions of Prim's algorithm using efficient implementations of Fibonacci heaps or rankrelaxed heaps often approach and (on the densest graphs) so...

A phylogeny is the evolutionary history of a group of organisms; systematists (and other biologists) attempt to reconstruct this history from various forms of data about contemporary organisms. Phylogeny reconstruction is a crucial step in the understanding of evolution as well as an important tool in biological, pharmaceutical, and medical research. Phylogeny reconstruction from molecular data is very difficult: almost all optimization models give rise to NP-hard (and thus computationally intractable) problems. Yet approximations must be of very high quality in order to avoid outright biological nonsense. Thus many biologists have been willing to run farms of processors for many months in order to analyze just one dataset. High-performance algorithm engineering offers a battery of tools that can reduce, sometimes spectacularly, the running time of existing phylogenetic algorithms, as well as help designers produce better algorithms. We present an overview of algorithm engineering techniques, illustrating them with an application to the "breakpoint analysis" method of Sankoff et al., which resulted in the GRAPPA software suite. GRAPPA demonstrated a speedup in running time by over eight orders of magnitude over the original implementation on a variety of real and simulated datasets. We show how these algorithmic engineering techniques are directly applicable to a large variety of challenging combinatorial problems in computational biology.

We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through low-level implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present some results from an ongoing study in which we are using: multiple languages, compilers, and machines; all the major variants of the comparison-based algorithms; and eight varieties of graphs with sizes of up to 130,000 vertices (in sparse graphs) or 750,000 edges (in dense graphs). 1 Introduction Finding spanning trees of minimum weight (minimum spanning trees or MSTs) is one of the best known graph problems; algorithms for this problem have a long history, for which see the article of Graham and Hell [6]. The best comparison-based algorithm to date, due to Gabow...

PATWARDHAN, JAEE. Modular Computer Aided Field Modeling of Spatial Power Combining Systems. (Under the direction of Michael B. Steer.) In this thesis a electromagnetic simulator program is further enhanced and made suitable for a user friendly environment. This electromagnetic simulator tool is capable of analyzing any user drawn structures in CIF format. It uses the Galerkin moment method technique with sub-domain sinusoidal basis functions for modeling electromagnetic structures. This tool basically consists of three main modules, the C shell which is the main controlling module and which interfaces with all the other modules of the simulator and which is the main focus of this thesis. This is the geometry interface of the simulator capable of interpreting geometric information from the CIF translator and passing it to the FORTRAN field simulator. The FORTRAN module which actually performs the moment method analysis was also developed at the Electronic Research Laboratory. The final...

The desirability of Horn clauses in logical deductive systems has long been recognized. The reasons are at least threefold. Firstly, while inference algorithms for full logics of any reasonable extent are typically intractable, for systems restricted to Horn clauses the picture is much better. (For example, in ordinary propositional logic, while the full satisfiability problem is NP-complete, a linear-time algorithm exists for Horn clauses.) Secondly, the knowledge-representation capabilities of Horn clauses, while weaker than those of the full logic, remain remarkably rich; indeed, far richer than that of simple conjunctive logic alone. Thirdly, Horn clauses define the maximal subset of a full logic which has the property of admitting generic models, which roughly means that for any set of Horn clauses, there is a least model of the clauses in that set. It is the purpose of this paper to initiate an investigation of Horn clause logic for an extended class of feature structures. After laying the groundwork for this context, we provide two key results. In the first, we show how the property of admitting

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