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Sizeestimation framework with applications to transitive closure and reachability
 Journal of Computer and System Sciences
, 1997
"... Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min{mn, n2.38}) time ..."
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Cited by 157 (21 self)
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Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min{mn, n2
Languages That Capture Complexity Classes
 SIAM Journal of Computing
, 1987
"... this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first ..."
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Cited by 245 (21 self)
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order language of graphs (respectively groups, binary strings, etc.) together with a least fixed point operator. As another example, a property is in logspace if and only if it is expressible in first order logic together with a deterministic transitive closure operator. The roots of our approach
Practical reasoning for very expressive description logics
 Journal of the Interest Group in Pure and Applied Logics 8
, 2000
"... Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm t ..."
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Cited by 185 (22 self)
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that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is wellsuited for implementation. Additionally, we show that ALC extended
Optimising Tableaux Decision Procedures For Description Logics
, 1997
"... DLs form a family of formalisms closely related to semantic networks but with the distinguishing characteristic that the semantics of the concept description language is formally defined, so that the subsumption relationship between two concept descriptions can be computed by a suitable algorithm. D ..."
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Cited by 122 (22 self)
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reasoning for a DL with an expressive concept description language. It suggests that, while subsumption reasoning in such languages is known to be intractable in the worst case, a suitably optimised algorithm can provide acceptable performance with a realistic knowledge base. This claim is supported
Detecting Unusual Activity in Video
, 2004
"... We present an unsupervised technique for detecting unusual activity in a large video set using many simple features. No complex activity models and no supervised feature selections are used. We divide the video into equal length segments and classify the extracted features into prototypes, from whic ..."
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Cited by 182 (0 self)
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which a prototypesegment cooccurrence matrix is computed. Motivated by a similar problem in documentkeyword analysis, we seek a correspondence relationship between prototypes and video segments which satisfies the transitive closure constraint. We show that an important subfamily of correspondence
Hybrid transitive closure algorithms
, 1990
"... We present a new family of hybrid transitive closure algorithms, and present experimental results showing that these algorithms perform better than existing transitive closure algorithms, includmg matrixbased algorithms that divide a matrix into stripes or into square blocks, and graphbased algmti ..."
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Cited by 8 (0 self)
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We present a new family of hybrid transitive closure algorithms, and present experimental results showing that these algorithms perform better than existing transitive closure algorithms, includmg matrixbased algorithms that divide a matrix into stripes or into square blocks, and graph
Regular Model Checking
, 2000
"... . We present regular model checking, a framework for algorithmic verification of infinitestate systems with, e.g., queues, stacks, integers, or a parameterized linear topology. States are represented by strings over a finite alphabet and the transition relation by a regular lengthpreserving re ..."
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Cited by 164 (25 self)
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. We present regular model checking, a framework for algorithmic verification of infinitestate systems with, e.g., queues, stacks, integers, or a parameterized linear topology. States are represented by strings over a finite alphabet and the transition relation by a regular length
A Fully Dynamic Algorithm for Maintaining the Transitive Closure
 In Proc. 31st ACM Symposium on Theory of Computing (STOC'99
, 1999
"... This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form "Is there a directed path fro ..."
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Cited by 49 (1 self)
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This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form "Is there a directed path
Transitiveclosure spanners
, 2008
"... We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanner ..."
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Cited by 35 (11 self)
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We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k
Direct Algorithms for Computing the Transitive Closure of Database Relations
 Proc. 13th Int'l Conf. on Very Large Data Bases
, 1987
"... We present new algorithms for computing the transitive closure of large database relations. Unlike iterative algorithms, such as the seminaive and the logarithmic algorithms, the termination of our algorithms does not depend on the length of paths in the underlying graph (hence, the name direct alg ..."
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Cited by 39 (1 self)
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We present new algorithms for computing the transitive closure of large database relations. Unlike iterative algorithms, such as the seminaive and the logarithmic algorithms, the termination of our algorithms does not depend on the length of paths in the underlying graph (hence, the name direct
Results 1  10
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1,011