Introduction to algorithms
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Incremental computation of dominator trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph
Journal of the ACM (JACM)
Solving TSP with time windows with constraints
Proceedings of the 1999 international conference on Logic programming
A fast algorithm for finding dominators in a flowgraph
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Concepts, Techniques, and Models of Computer Programming
Concepts, Techniques, and Models of Computer Programming
Principles of Compiler Design (Addison-Wesley series in computer science and information processing)
Principles of Compiler Design (Addison-Wesley series in computer science and information processing)
Necessary Condition for Path Partitioning Constraints
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Route finder: efficiently finding k shortest paths using constraint programming
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Revisiting the tree Constraint
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Dominators, directed bipolar orders, and independent spanning trees
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Resource constrained shortest paths with a super additive objective function
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Finding dominators via disjoint set union
Journal of Discrete Algorithms
Explaining circuit propagation
Constraints
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Constrained path problems have to do with finding paths in graphs subject to constraints. We present a constraint programming approach for solving the Ordered disjoint-paths problem (ODP), i.e., the Disjoint-paths problem where the pairs are associated with ordering constraints. In our approach, we reduce ODP to the Ordered simple path with mandatory nodes problem (OSPMN), i.e., the problem of finding a simple path containing a set of mandatory nodes in a given order. The reduction of the problem is motivated by the fact that we have an appropriate way of dealing with OSPMN based on DomReachability, a propagator that implements a generalized reachability constraint on a directed graph based on the concept of graph variables. The DomReachability constraint has three arguments: (1) a flow graph, i.e., a directed graph with a source node; (2) the dominance relation graph on nodes and edges of the flow graph; and (3) the transitive closure of the flow graph. Our experimental evaluation of DomReachability shows that it provides strong pruning, obtaining solutions with very little search. Furthermore, we show that DomReachability is also useful for defining a good labeling strategy. These experimental results give evidence that DomReachability is a useful primitive for solving constrained path problems over directed graphs.