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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
Efficient Transitive Closure Computation
"... We present two new transitive closure algorithms that are based on strong component detection. The algorithms scan the input graph only once without generating partial successor sets for each node. The new algorithms eliminate the redundancy caused by strong components more efficiently than previous ..."
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Cited by 8 (3 self)
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We present two new transitive closure algorithms that are based on strong component detection. The algorithms scan the input graph only once without generating partial successor sets for each node. The new algorithms eliminate the redundancy caused by strong components more efficiently than
On the Power of Deterministic Transitive Closures
 INFORMATION AND COMPUTATION
, 1995
"... We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on finite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTCquery is bounded and the ..."
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Cited by 11 (1 self)
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We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on finite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTCquery is bounded
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
On The PVM Computations of Transitive Closure
"... We investigate experimentally, alternative approaches to the distributed parallel computation of a class of problems related to the generic transitive closure problem and the algebraic path problem. Our main result is the comparison of two parallel algorithms for transitive closure,  a straightfor ..."
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We investigate experimentally, alternative approaches to the distributed parallel computation of a class of problems related to the generic transitive closure problem and the algebraic path problem. Our main result is the comparison of two parallel algorithms for transitive closure,  a
Executable Transitive Closures
 In The Archive of Formal Proofs. http://afp.sf.net/entries/TransitiveClosureII.shtml
, 2012
"... We provide a generic worklist algorithm to compute the (reflexive)transitive closure of relations where only successors of newly detected states are generated. In contrast to our previous work [2], the relations do not have to be finite, but each element must only have finitely many (indirect) suc ..."
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Cited by 1 (1 self)
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We provide a generic worklist algorithm to compute the (reflexive)transitive closure of relations where only successors of newly detected states are generated. In contrast to our previous work [2], the relations do not have to be finite, but each element must only have finitely many (indirect
logic with transitive closure of accessibility relation
, 2009
"... A proof of the completeness theorem for the modal logic with transitive closure of accessibility relation ..."
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A proof of the completeness theorem for the modal logic with transitive closure of accessibility relation
Transitive Closure, Proximity and Intransitivities*
, 2000
"... Assignments of weak orders to complete binary relations are considered. Firstly, it is shown that assigning the transitive closure of a complete binary relation does not always assign the closest weak order according to any reasonable metric on complete binary relations. It is then shown that the as ..."
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Assignments of weak orders to complete binary relations are considered. Firstly, it is shown that assigning the transitive closure of a complete binary relation does not always assign the closest weak order according to any reasonable metric on complete binary relations. It is then shown
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
Nested pebbles and transitive closure, in
 Proceedings 23rd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2006
, 2006
"... Abstract. Firstorder logic with kary deterministic transitive closure has the same power as twoway khead deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be use ..."
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Cited by 9 (1 self)
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Abstract. Firstorder logic with kary deterministic transitive closure has the same power as twoway khead deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can
Results 1  10
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1,419