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17
Fast and Flexible Difference Constraint Propagation for DPLL(T)
 IN PROC. SAT, VOLUME 4121 OF LNCS
, 2006
"... In the context of DPLL(T), theory propagation is the process of dynamically selecting consequences of a conjunction of constraints from a given set of candidate constraints. We present improvements to a fast theory propagation procedure for difference constraints of the form x − y ≤ c. These improve ..."
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Cited by 22 (1 self)
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In the context of DPLL(T), theory propagation is the process of dynamically selecting consequences of a conjunction of constraints from a given set of candidate constraints. We present improvements to a fast theory propagation procedure for difference constraints of the form x − y ≤ c. These improvements are demonstrated experimentally.
A Dynamic Algorithm for Topologically Sorting Directed Acyclic Graphs
, 2004
"... We consider how to maintain 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 marginally inferior time complexity compared with the best previously known result, we find that its simplicity lead ..."
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Cited by 15 (1 self)
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We consider how to maintain 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 marginally 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 three alternatives over a large number of random DAG's. The results show our algorithm is the best for sparse graphs and, surprisingly, that an alternative with poor theoretical complexity performs marginally better on dense graphs.
Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study
 In Proc. Workshop on Algorithm Engineering
, 2000
"... We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus ..."
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Cited by 11 (2 self)
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We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worstcase bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets. 1
Online Algorithms for Topological Order and Strongly Connected Components
, 2003
"... We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(#log#). In addition, we provide an empirical compari ..."
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Cited by 7 (0 self)
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We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(#log#). In addition, we provide an empirical comparison against three existing solutions using random DAG's. The results show our algorithm to out perform the others on sparse graphs. Finally, we show how the algorithm can be extended to identify strongly connected components online.
An Experimental Study of Dynamic Algorithms for Transitive Closure
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2000
"... We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algori ..."
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Cited by 7 (2 self)
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We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algorithms as well as a new variant of them, both of which were always faster than any of the other implementations of the dynamic algorithms. We also considered simpleminded algorithms that were easy to implement and likely to be fast in practice. We tested and compared the above implementations on random inputs, on nonrandom inputs that are worstcase inputs for the dynamic algorithms, and on an input motivated by a realworld graph.
Averagecase analysis of online topological ordering
 of Lecture Notes in Computer Science
, 2007
"... Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worstcase insertion sequences or only evaluated exp ..."
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Cited by 6 (2 self)
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Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worstcase insertion sequences or only evaluated experimentally on random DAGs. We present the first averagecase analysis of online topological ordering algorithms. We prove an expected runtime of O(n 2 polylog(n)) under insertion of the edges of a complete DAG in a random order for the algorithms of Alpern et
Satisfiability checking with difference constraints
 in IMPRS Computer Science, Saarbruceken
, 2005
"... This thesis studies the problem of determining the satisfiability of a Boolean combination of binary difference constraints of the form x − y ≤ c where x and y are numeric variables and c is a constant. In particular, we present an incremental and modelbased interpreter for the theory of difference ..."
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Cited by 5 (2 self)
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This thesis studies the problem of determining the satisfiability of a Boolean combination of binary difference constraints of the form x − y ≤ c where x and y are numeric variables and c is a constant. In particular, we present an incremental and modelbased interpreter for the theory of difference constraints in the context of a generic Boolean satisfiability checking procedure capable of incorporating interpreters for arbitrary theories. We show how to use the model based approach to efficiently make inferences with the option of complete inference.
Incremental Satisfiability and Implication for UTVPI Constraints
"... Unit twovariableperinequality (UTVPI) constraints form one of the largest class of integer constraints which are polynomial time solvable (unless P=NP). There is considerable interest in their use for constraint solving, abstract interpretation, spatial databases, and theorem proving. In this pap ..."
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Cited by 3 (0 self)
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Unit twovariableperinequality (UTVPI) constraints form one of the largest class of integer constraints which are polynomial time solvable (unless P=NP). There is considerable interest in their use for constraint solving, abstract interpretation, spatial databases, and theorem proving. In this paper we develop new incremental algorithms for UTVPI constraint satisfaction and implication checking that require O(m + n log n + p) time and O(n + m + p) space to incrementally check satisfiability of m UTVPI constraints on n variables and check implication of p UTVPI constraints. The algorithms can be straightforwardly extended to create nonincremental implication checking and generation of all (nonredundant) implied constraints, as well as generate minimal unsatisfiable subsets and minimal implicants. Key words: unit two variable per inequality constraints; satisfaction; implication 1.
Decremental Clique Problem
"... The clique problem consists in determining whether an undirected graph G of order n contains a clique of order ℓ. In this paper we are concerned with the decremental version of clique problem, where the property of containing an ℓclique is dynamically checked during deletions of nodes. We provide ..."
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Cited by 2 (1 self)
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The clique problem consists in determining whether an undirected graph G of order n contains a clique of order ℓ. In this paper we are concerned with the decremental version of clique problem, where the property of containing an ℓclique is dynamically checked during deletions of nodes. We provide an improved dynamic algorithm for this problem for every fixed value of ℓ ≥ 3. Our algorithm naturally applies to filtering for the constraint satisfaction problem. In particular, we show how to speed up the filtering based on an important local consistency property: the inverse consistency.