Fully Dynamic Shortest Paths and Negative Cycles Detection on Digraphs with Arbitrary Arc Weights

Frigioni, Daniele; Marchetti-Spaccamela, Alberto; Nanni, Umberto

doi:10.1007/3-540-68530-8_27

Cited by 21 publications

(23 citation statements)

References 11 publications

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“…This can be checked using the Bellman-Ford single-source shortest path algorithm. An incremental solver for these problems is also possible [13]. While satisfiability only requires a single-source shortest path algorithm, for entailment and projection we will need information on all pairs of shortest paths.…”

Section: Difference Constraintsmentioning

confidence: 99%

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A General Implementation Framework for Tabled CLP

Guzmán

Carro

Hermenegildo

et al. 2012

Functional and Logic Programming

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Abstract. This paper describes a framework to combine tabling evaluation and constraint logic programming (TCLP). While this combination has been studied previously from a theoretical point of view and some implementations exist, they either suffer from a lack of efficiency, flexibility, or generality, or have inherent limitations with respect to the programs they can execute to completion (either with success or failure). Our framework addresses these issues directly, including the ability to check for answer / call entailment, which allows it to terminate in more cases than other approaches. The proposed framework is experimentally compared with existing solutions in order to provide evidence of the mentioned advantages.

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Section: Difference Constraintsmentioning

confidence: 99%

“…We have validated the flexibility, generality, and efficiency of our framework by implementing two examples: difference constraints [13] and disequality constraints. We have also evaluated the performance of our framework w.r.t.…”

Section: Introductionmentioning

confidence: 99%

A General Implementation Framework for Tabled CLP

Guzmán

Carro

Hermenegildo

et al. 2012

Functional and Logic Programming

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“…In general, the majority of work on dynamic algorithms for directed graphs has focused on shortest/longest paths and transitive closure (e.g., [King and Sagert 1999;Demetrescu and Italiano 2000;Djidjev et al 2000;Frigioni et al 1998;Baswana et al 2002;). For undirected graphs, there has been substantially more work and a survey of this area can be found in [Italiano et al 1999].…”

Section: · 23mentioning

confidence: 99%

A dynamic topological sort algorithm for directed acyclic graphs

Pearce

2007

ACM J. Exp. Algorithmics

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We consider the problem of maintaining the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and, although this has inferior time complexity compared with the best previously known result, we find that its simplicity leads to better performance in practice. In addition, we provide an empirical comparison against the three main alternatives over a large number of random DAGs. The results show our algorithm is the best for sparse digraphs and only a constant factor slower than the best on dense digraphs.

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“…In this latter case, SetTrue must perform a consistency check on the set Π ∪Σ. To solve this problem, we make use of an incremental consistency checking algorithm based largely on an incremental shortests paths and negative cycle detection algorithm due to Frigioni 1 et al [9]. Before detailing this algorithm, we first formally state the incremental consistency checking problem in terms of constraint graphs and potential functions:…”

Section: Consistency Checksmentioning

confidence: 99%