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39
Highly Parallel Sparse MatrixMatrix Multiplication
, 2010
"... Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on ..."
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Cited by 6 (3 self)
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Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on twodimensional block distribution of sparse matrices where serial sections use a novel hypersparse kernel for scalability. We give a stateoftheart MPI implementation of one of our algorithms. Our experiments show scaling up to thousands of processors on a variety of test scenarios.
Finger Search Trees
, 2005
"... One of the most studied problems in computer science is the problem of maintaining a sorted sequence of elements to facilitate efficient searches. The prominent solution to the problem is to organize the sorted sequence as a balanced search tree, enabling insertions, deletions and searches in logari ..."
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Cited by 5 (0 self)
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One of the most studied problems in computer science is the problem of maintaining a sorted sequence of elements to facilitate efficient searches. The prominent solution to the problem is to organize the sorted sequence as a balanced search tree, enabling insertions, deletions and searches in logarithmic time. Many different search trees have been developed and studied intensively in the literature. A discussion of balanced binary search trees can e.g. be found in [4]. This chapter is devoted to finger search trees which are search trees supporting fingers, i.e. pointers, to elements in the search trees and supporting efficient updates and searches in the vicinity of the fingers. If the sorted sequence is a static set of n elements then a simple and space efficient representation is a sorted array. Searches can be performed by binary search using 1+⌊log n⌋ comparisons (we throughout this chapter let log x denote log 2 max{2, x}). A finger search starting at a particular element of the array can be performed by an exponential search by inspecting elements at distance 2 i − 1 from the finger for increasing i followed by a binary search in a range of 2 ⌊log d ⌋ − 1 elements, where d is the rank difference in the sequence between the finger and the search element. In Figure 11.1 is shown an exponential search for the element 42 starting at 5. In the example d = 20. An exponential search requires
Identifying Occurrences of Maximal Pairs in Multiple Strings
 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching,Lecture Notes In Computer Science
, 2002
"... A molecular sequence "model" is a (structured) sequence of distinct or identical strings separated by gaps; here we design and analyze e#cient algorithms for variations of the "Model Matching" and "Model Identification" problems. ..."
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Cited by 5 (2 self)
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A molecular sequence "model" is a (structured) sequence of distinct or identical strings separated by gaps; here we design and analyze e#cient algorithms for variations of the "Model Matching" and "Model Identification" problems.
AN EFFICIENT NOMINAL UNIFICATION ALGORITHM
"... Abstract. Nominal Unification is an extension of firstorder unification where terms can contain binders and unification is performed modulo αequivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearlyreduce nominal unification problems to ..."
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Cited by 3 (1 self)
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Abstract. Nominal Unification is an extension of firstorder unification where terms can contain binders and unification is performed modulo αequivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearlyreduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for firstorder unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently. 1.
Checking Determinism of XML Schema Content Models in Optimal Time
"... We consider the determinism checking of XML Schema content models, as required by the W3C Recommendation. We argue that currently applied solutions have flaws and make processors vulnerable to exponential resource needs by pathological schemas, and we help to eliminate this potential vulnerability o ..."
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We consider the determinism checking of XML Schema content models, as required by the W3C Recommendation. We argue that currently applied solutions have flaws and make processors vulnerable to exponential resource needs by pathological schemas, and we help to eliminate this potential vulnerability of XML Schema based systems. XML Schema content models are essentially regular expressions extended with numeric occurrence indicators. A previously published polynomialtime solution to check the determinism of such expressions is improved to run in linear time, and the improved algorithm is implemented and evaluated experimentally. When compared to the corresponding method of a popular productionquality XML Schema processor, the new implementation runs orders of magnitude faster. Enhancing the solution to take further extensions of XML Schema into account without compromising its linear scalability is also discussed. Key words: Regular expression, numeric occurrence indicator, oneunambiguity, weak determinism, unique particle attribution, Java 1. Introduction and
Motif Extraction from Weighted Sequences
 Proc. 11th Symposium on String Processing and Information Retrieval (SPIRE), volume 3246 of LNCS
, 2004
"... We present in this paper three algorithms. The first extracts repeated motifs from a weighted sequence. The motifs correspond to words which occur at least q times and with hamming distance e in a weighted sequence with probability 1/k each time, where k is a small constant. The second algori ..."
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Cited by 3 (2 self)
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We present in this paper three algorithms. The first extracts repeated motifs from a weighted sequence. The motifs correspond to words which occur at least q times and with hamming distance e in a weighted sequence with probability 1/k each time, where k is a small constant. The second algorithm extracts common motifs from a set of N 2 weighted sequences with hamming distance e. In the second case, the motifs must occur twice with probability 1/k, in 1 distinct sequences of the set. The third algorithm extracts maximal pairs from a weighted sequence. A pair in a sequence is the occurrence of the same substring twice. In addition, the algorithms presented in this paper improve slightly on previous work on these problems.
Lipschitz unimodal and isotonic regression on paths and trees
, 2008
"... Let M = (V, A) be a planar graph, let γ ≥ 0 be a real parameter, and t: V → R a height function. A γLipschitz unimodal regression (γLUR) of t is a function s: V → R such that s has a unique local minimum, s(u) − s(v)  ≤ γ for each {u, v} ∈ A, and ‖s − t‖2 = ∑ v∈V (s(v) − t(v))2 is minimized. ..."
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Cited by 2 (1 self)
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Let M = (V, A) be a planar graph, let γ ≥ 0 be a real parameter, and t: V → R a height function. A γLipschitz unimodal regression (γLUR) of t is a function s: V → R such that s has a unique local minimum, s(u) − s(v)  ≤ γ for each {u, v} ∈ A, and ‖s − t‖2 = ∑ v∈V (s(v) − t(v))2 is minimized. Here, a local minimum of s is a vertex v such that s(u)> s(v) for any neighbor u of v. For a directed planar graph, s: V → R is the γLipschitz isotonic regression (γLIR) of t if s(u) ≤ s(v) ≤ s(u)+γ for each directed edge (u, v) and ‖s − t‖2 is minimized. These problems arise, for example, in topological simplification of a height function. We present nearlineartime algorithms for LUR and LIR problems for two special cases where M is a path or a tree.
Fast sortedset intersection using SIMD instructions
 In ADMS Workshop
, 2011
"... In this paper, we focus on sortedset intersection which is an important part in many algorithms, e.g., RIDlist intersection, inverted indexes, and others. In contrast to traditional scalar sortedset intersection algorithms that try to reduce the number of comparisons, we propose a parallel algori ..."
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Cited by 1 (0 self)
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In this paper, we focus on sortedset intersection which is an important part in many algorithms, e.g., RIDlist intersection, inverted indexes, and others. In contrast to traditional scalar sortedset intersection algorithms that try to reduce the number of comparisons, we propose a parallel algorithm that relies on speculative execution of comparisons. In general, our algorithm requires more comparisons but less instructions than scalar algorithms that translates into a better overall speed. We achieve this by utilizing efficient singleinstructionmultipledata (SIMD) instructions that are available in many processors. We provide different sortedset intersection algorithms for different integer data types. We propose versions that use uncompressed integer values as input and output as well as a version that uses a tailormade data layout for even faster intersections. In our experiments, we achieve speedups up to 5.3x compared to popular fast scalar algorithms. 1.
The weighted maximummean subtree and other bicriterion subtree problems
 In ACM Computing Research Repository
, 503
"... Abstract. We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the problem is trivially solved in linear time. When the ob ..."
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Abstract. We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the problem is trivially solved in linear time. When the objective is the sum of weights that are linear functions of a parameter, we show how to list all optima for all possible parameter values in O(n log n) time; this parametric optimization problem can be used to solve many bicriterion optimizations problems, in which each node has two values xi and yi associated with it, and the objective function is a bivariate function f ( ∑ xi, ∑ yi) of the sums of these two values. A special case, when f is the ratio of the two sums, is the Weighted MaximumMean Subtree Problem, or equivalently the Fractional PrizeCollecting Steiner Tree Problem on Trees; for this special case, we provide a linear time algorithm for this problem when all weights are positive, improving a previous O(n log n) solution, and prove that the problem is NPcomplete when negative weights are allowed. 1