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LinearTime PointerMachine Algorithms for Least Common Ancestors, MST Verification, and Dominators
 IN PROCEEDINGS OF THE THIRTIETH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1998
"... We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, ..."
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Cited by 29 (4 self)
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We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, randomized MST construction, and computing dominators in a flowgraph.
Finding dominators in practice
 In Proceedings of the 12th Annual European Symposium on Algorithms, volume 3221 of Lecture Notes in Computer Science
, 2004
"... Abstract. The computation of dominators in a flowgraph has applications in program optimization, circuit testing, and other areas. Lengauer and Tarjan [17] proposed two versions of a fast algorithm for finding dominators and compared them experimentally with an iterative bit vector algorithm. They c ..."
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Cited by 17 (8 self)
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Abstract. The computation of dominators in a flowgraph has applications in program optimization, circuit testing, and other areas. Lengauer and Tarjan [17] proposed two versions of a fast algorithm for finding dominators and compared them experimentally with an iterative bit vector algorithm. They concluded that both versions of their algorithm were much faster than the bitvector algorithm even on graphs of moderate size. Recently Cooper et al. [9] have proposed a new, simple, treebased iterative algorithm. Their experiments suggested that it was faster than the simple version of the LengauerTarjan algorithm on graphs representing computer program control flow. Motivated by the work of Cooper et al., we present an experimental study comparing their algorithm (and some variants) with careful implementations of both versions of the LengauerTarjan algorithm and with a new hybrid algorithm. Our results suggest that, although the performance of all the algorithms is similar, the most consistently fast are the simple LengauerTarjan algorithm and the hybrid algorithm, and their advantage increases as the graph gets bigger or more complicated. 1
Combining tree partitioning, precedence, incomparability, and degree constraints, with an application to phylogenetic and orderedpath problems
, 2006
"... Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, such as precedence, incomparability, and degree constraints. The app ..."
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Cited by 16 (5 self)
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Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, such as precedence, incomparability, and degree constraints. The approach provides a sharp improvement over an existing path constraint, but can also efficiently handle tree problems, such as the phylogenetic supertree construction problem. The key point of the filtering is to take partially into account the strong interactions between the tree partitioning problem and all the side constraints. 1
Necessary condition for path partitioning constraints
 In Proceedings of CPAIOR’07, volume 4510 of LNCS
, 2007
"... Abstract. Given a directed graph G, the K nodedisjoint paths problem consists in finding a partition of G into K nodedisjoint paths, such that each path ends up in a given subset of nodes in G. This article provides a necessary condition for the K nodedisjoint paths problem which combines (1) the ..."
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Cited by 4 (1 self)
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Abstract. Given a directed graph G, the K nodedisjoint paths problem consists in finding a partition of G into K nodedisjoint paths, such that each path ends up in a given subset of nodes in G. This article provides a necessary condition for the K nodedisjoint paths problem which combines (1) the structure of the reduced graph associated with G, (2) the structure of each strongly connected component of G with respect to dominance relation between nodes, and (3) the way the nodes of two strongly connected components are interconnected. This necessary condition is next used to deal with a path partitioning constraint. 1
Improving the asymmetric TSP by considering graph structure. arXiv preprint arXiv:1206.3437
, 2012
"... Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally sho ..."
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Cited by 3 (0 self)
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Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results. 1
Revisiting the tree Constraint
 In Principles and Practice of Constraint Programming, CP
"... Abstract. This paper revisits the tree constraint introduced in [2] which partitions the nodes of a nnodes, marcs directed graph into a set of nodedisjoint antiarborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arccons ..."
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Abstract. This paper revisits the tree constraint introduced in [2] which partitions the nodes of a nnodes, marcs directed graph into a set of nodedisjoint antiarborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arcconsistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning. 1
Explaining Circuit Propagation
 CONSTRAINTS
"... The circuit constraint is used to constrain a graph represented by a successor for each node, such that the resulting edges form a circuit. Circuit and its variants are important for various kinds of tourfinding, pathfinding and graph problems. In this paper we examine how to integrate the circuit ..."
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The circuit constraint is used to constrain a graph represented by a successor for each node, such that the resulting edges form a circuit. Circuit and its variants are important for various kinds of tourfinding, pathfinding and graph problems. In this paper we examine how to integrate the circuit constraint, and its variants, into a lazy clause generation solver. To do so we must extend the constraint to explain its propagation. We consider various propagation algorithms for circuit and examine how best to explain each of them. We compare the effectiveness of each propagation algorithm once we use explanation, since adding explanation changes the tradeoff between propagation complexity and power. Simpler propagators, although less powerful, may produce more reusable explanations. Even though the most powerful propagator considered for circuit and variants creates huge explanations, we find that explanation is highly advantageous for solving problems involving this kind of constraint.
A portable and efficient implementation of global constraints: the tree constraint case
"... Abstract. Global constraints represent invaluable modeling tools for Constraint Programming (CP). Efficiently solving recurrent subproblems is a key point for CP successes. However, global constraints mainly remain strongly attached to a given constraint solver. Indeed, they heavily rely on internal ..."
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Abstract. Global constraints represent invaluable modeling tools for Constraint Programming (CP). Efficiently solving recurrent subproblems is a key point for CP successes. However, global constraints mainly remain strongly attached to a given constraint solver. Indeed, they heavily rely on internal mechanisms in order to be as efficient as possible. In this paper, we emphasize the interest of decoupling global constraint implementations from the underlying solver. We show, on a tree constraint, that even more decoupling it by providing fully dynamic algorithms enhances efficiency and, which is much more important, allow an efficient portability of the constraint. We illustrate this for the Choco and Gecode solvers. 1