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Improved Dynamic Reachability Algorithms for Directed Graphs
, 2002
"... We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the ..."
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Cited by 29 (3 self)
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We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) total expected time, essentially the time needed for computing the transitive closure of the initial graph. Such a result was previously known only for acyclic graphs.
Using Multilevel Graphs for Timetable Information in Railway Systems
 IN PROCEEDINGS 4TH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX 2002), VOLUME 2409 OF SPRINGER LNCS
, 2002
"... In many fields of application shortest path finding problems in very large graphs arise. Scenarios where large numbers ofonW##O queries for shortest paths have to be processedin realtime appear for examplein tra#cinc5###HF5 systems.In such systems, the techn5Ww# con sidered to speed up the shortes ..."
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Cited by 26 (12 self)
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In many fields of application shortest path finding problems in very large graphs arise. Scenarios where large numbers ofonW##O queries for shortest paths have to be processedin realtime appear for examplein tra#cinc5###HF5 systems.In such systems, the techn5Ww# con sidered to speed up the shortest pathcomputation are usually basedon precomputed incomputed5 On approach proposedoften in thiscon text is a spacereduction where precomputed shortest paths are replaced by sin## edges with weight equal to thelenOq of the corresponres shortest path.In this paper, we give a first systematic experimen tal study of such a spacereduction approach. Wein troduce theconOkW of multilevel graph decomposition Foron specificapplication scenica from the field of timetable information in public tranc ort, we perform a detailed anai ysisan experimen tal evaluation of shortest path computation based on multilevel graph decomposition.
Betweenness Centrality: Algorithms and Lower Bounds
, 2008
"... One of the most fundamental problems in largescale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network. In this paper, we present a randomized parallel algorithm and ..."
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Cited by 2 (0 self)
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One of the most fundamental problems in largescale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network. In this paper, we present a randomized parallel algorithm and an algebraic method for computing betweenness centrality of all nodes in a network. We prove that any pathcomparison based algorithm cannot compute betweenness in less than O(nm) time.
A Randomized Parallel Algorithm for DfaMinimization
"... The problem of finding the coarsest partition of a set S with respect to another partition of S and one or more functions on S has several applications, one of which is the state minimization of finite state automata. The problem has a well known O(n log n) sequential algorithm. In this paper, we p ..."
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The problem of finding the coarsest partition of a set S with respect to another partition of S and one or more functions on S has several applications, one of which is the state minimization of finite state automata. The problem has a well known O(n log n) sequential algorithm. In this paper, we present efficient parallel randomised algorithms for the problem. Keywords: Parallelalgorithms, Partitioning, DFA minimization 1 Introduction The single function coarsest partitioning problem can be stated as follows: Problem : Given a set S of n elements, a 1 ; a 2 ; :::; a n , a partition ß = (ß 1 ; ß 2 ; :::; ß k ) of S and a function f : S ! S, we wish to find the coarsest (i.e., having the fewest blocks) partition ß 0 = (ß 0 1 ; ß 0 2 ; :::; ß 0 l ) of S, such that 1. 8a i ; a j 2 S, a i ; a j 2 ß 0 m ) 9p such that, f(a i ); f(a j ) 2 ß 0 p . 2. 8m; 1 m l; 9p; 1 p k; such that ß 0 m ` ß p . The more general version of the problem, is the multiple function coarsest ...
Parallel Algorithms for Finite Automata Problems
"... : Finite automata are among the most extensively studied and understood models of computation. They have wide ranging applications  for example, in image compression, protocol validation, game theory and computational biology  just to mention only some recent ones. Here we will survey efficien ..."
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: Finite automata are among the most extensively studied and understood models of computation. They have wide ranging applications  for example, in image compression, protocol validation, game theory and computational biology  just to mention only some recent ones. Here we will survey efficient parallel algorithms for many fundamental computational problems on finite automata. It is well known that problems involving deterministic finite automata (DFA) have polynomial time algorithms, but the problems become hard when the input automata are nondeterministic (NFA or regular expressions) . A similar difference is observed in the case of parallel algorithms: most problems involving DFA as input have NC algorithms, while NC algorithms are unlikely with NFA (or regular expression) as input. In addition to DFA and NFA, we will also consider other inputs such as unambiguous finite automata, regular expressions and prefix grammars. The problems surveyed here include the followin...
Betweenness Centrality: Algorithms and Lower Bounds Shiva Kintali ∗
, 809
"... One of the most fundamental problems in large scale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network. Currently the fastest known algorithm [5], to compute between ..."
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One of the most fundamental problems in large scale network analysis is to determine the importance of a particular node in a network. Betweenness centrality is the most widely used metric to measure the importance of a node in a network. Currently the fastest known algorithm [5], to compute betweenness of all nodes, requires O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted graphs, where n is the number of nodes and m is the number of edges in the network. In this paper, we present structural properties and lower bounds for computing betweenness. We prove that any path comparison based algorithm cannot compute betweenness of all nodes in less than O(nm) time. We resort to algebraic techniques and present an algebraic method for computing betweenness centrality of all nodes in a network. For unweighted graphs, our algorithm runs in time O(n ω Diam(G)), where ω < 2.376 is the exponent of matrix multiplication and Diam(G) is the diameter of the graph. For weighted graphs with integer weights taken from the range {1, 2,..., M}, we present an algorithm that runs in time O(Mn ω Diam(G)). Hence, our algorithms perform better for dense graphs (m ≫ n 1.376) with