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26
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 89 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Generic Programming — An Introduction
 3rd International Summer School on Advanced Functional Programming
, 1999
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Minimization Algorithms for Sequential Transducers
, 2000
"... We present general algorithms for minimizing sequential finitestate transducers that output strings or numbers. The algorithms are shown to be efficient since in the case of acyclic transducers and for output strings they operate in O(S+E+V+(EV+F)x(Pmax+1)) steps, where S is the sum of ..."
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Cited by 61 (11 self)
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We present general algorithms for minimizing sequential finitestate transducers that output strings or numbers. The algorithms are shown to be efficient since in the case of acyclic transducers and for output strings they operate in O(S+E+V+(EV+F)x(Pmax+1)) steps, where S is the sum of the lengths of all output labels of the resulting transducer, E the set of transitions of the given transducer, V the set of its states, F the set of final states, and Pmax one of the longest of the longest common prefixes of the output paths leaving each state of the transducer. The algorithms apply to a larger class of transducers which includes subsequential transducers.
The CacheOblivious Gaussian Elimination Paradigm: Theoretical Framework, Parallelization and Experimental Evaluation
, 2009
"... We consider triplynested loops of the type that occur in the standard Gaussian elimination algorithm, which we denote by GEP (or the Gaussian Elimination Paradigm). We present two related cacheoblivious methods IGEP and CGEP, both of which reduce the number of I/Os performed by the computation o ..."
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Cited by 26 (6 self)
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We consider triplynested loops of the type that occur in the standard Gaussian elimination algorithm, which we denote by GEP (or the Gaussian Elimination Paradigm). We present two related cacheoblivious methods IGEP and CGEP, both of which reduce the number of I/Os performed by the computation over that performed by standard GEP by a factor of √ M, where M is the size of the cache. Cacheoblivious IGEP computes inplace and solves most of the known applications of GEP including Gaussian elimination and LUdecomposition without pivoting and FloydWarshall allpairs shortest paths. Cacheoblivious CGEP uses a modest amount of additional space, but is completely general and applies to any code in GEP form. Both IGEP and CGEP produce systemindependent cacheefficient code, and are potentially applicable to being used by optimizing compilers for loop transformation. We present parallel IGEP and CGEP that achieve good speedup and match the sequential caching performance cacheobliviously for both shared and distributed caches for sufficiently large inputs. We present extensive experimental results for both incore and outofcore performance of our algorithms. We consider both sequential and parallel implementations, and compare them with finelytuned cacheaware BLAS code for matrix multiplication and Gaussian elimination without pivoting. Our results indicate that cacheoblivious GEP offers an attractive tradeoff between efficiency and portability.
Using structure indices for efficient approximation of network properties
 Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2006
"... Statistics on networks have become vital to the study of relational data drawn from areas including bibliometrics, fraud detection, bioinformatics, and the Internet. Calculating many of the most important measures—such as betweenness centrality, closeness centrality, and graph diameter—requires iden ..."
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Cited by 16 (1 self)
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Statistics on networks have become vital to the study of relational data drawn from areas including bibliometrics, fraud detection, bioinformatics, and the Internet. Calculating many of the most important measures—such as betweenness centrality, closeness centrality, and graph diameter—requires identifying short paths in these networks. However, finding these short paths can be intractable for even moderatesize networks. We introduce the concept of a network structure index (NSI), a composition of (1) a set of annotations on every node in the network and (2) a function that uses the annotations to estimate graph distance between pairs of nodes. We present several varieties of NSIs, examine their time and space complexity, and analyze their performance on synthetic and real data sets. We show that creating an NSI for a given network enables extremely efficient and accurate estimation of a wide variety of network statistics on that network.
I/Oefficient algorithms for graphs of bounded treewidth
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms (SODA’2001
, 2001
"... We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including th ..."
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Cited by 16 (5 self)
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We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including the singlesource shortest path problem and a number of problems that are NPhard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depthfirst search in G in O(N/(DB)) I/Os. As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a ktree in O(sort(N)) I/Os. The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/Oefficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/Oefficient algorithm for finding a maximal independent set of an arbitrary graph. Both algorithms take O(sort(V +E)) I/Os. The maximal matching algorithm is used in the tree decomposition algorithm.
Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics
 PLoS One
, 2010
"... Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Fin ..."
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Cited by 16 (1 self)
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Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence functionbased, centralitytype community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoomin analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications
Using ontological and document similarity to estimate museum exhibit relatedness
 ACM Journal on Computing and Cultural Heritage
, 2011
"... Exhibits within Cultural Heritage collections such as museums and art galleries are arranged by experts with intimate knowledge of the domain, but there may exist connections between individual exhibits that are not evident in this representation. For example, the visitors to such a space may have t ..."
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Cited by 11 (4 self)
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Exhibits within Cultural Heritage collections such as museums and art galleries are arranged by experts with intimate knowledge of the domain, but there may exist connections between individual exhibits that are not evident in this representation. For example, the visitors to such a space may have their own opinions on how exhibits relate to one another. In this paper, we explore the possibility of estimating the perceived relatedness of exhibits by museum visitors through a variety of ontological and document similaritybased methods. Specifically, we combine the Wikipedia category hierarchy with lexical similarity measures, and evaluate the correlation with the relatedness judgements of visitors. We compare our measure with simple document similarity calculations, based on either Wikipedia documents or web pages taken from the website for the museum of interest. We also investigate the hypothesis that physical distance in the museum space is a direct representation of the conceptual distance between exhibits. We demonstrate that ontological similarity measures are highly effective at capturing perceived relatedness and that the proposed raco (Related Article Conceptual Overlap) method is able to achieve results closest to relatedness judgements provided by human annotators compared to existing stateofthe art measures of semantic relatedness.