Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Introduction to algorithms
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constraint Programming Based Column Generation for Crew Assignment
Journal of Heuristics
The Rough Guide to Constraint Propagation
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Arc Consistency for Global Cardinality Constraints with Costs
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
A Framework for Constraint Programming Based Column Generation
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
An Arc-Consistency Algorithm for the Minimum Weight All Different Constraint
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Undirected single source shortest paths in linear time
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Bundle type Dual-ascent Approach to Linear Multi-Commodity Min Cost Flow Problems
A Bundle type Dual-ascent Approach to Linear Multi-Commodity Min Cost Flow Problems
Shorter path constraints for the resource constrained shortest path problem
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Computers and Operations Research
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
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Many real world problems, e.g. personnel scheduling and transportation planning, can be modeled naturally as Constrained Shortest Path Problems (CSPPs), i.e., as Shortest Path Problems with additional constraints. A well studied problem in this class is the Resource Constrained Shortest Path Problem. Reduction techniques are vital ingredients of solvers for the CSPP, that is frequently NP-hard, depending on the nature of the additional constraints. Viewed as heuristics, these techniques have not been studied theoretically with respect to their efficiency, i.e., with respect to the relation of filtering power and running time. Using the concepts of Constraint Programming, we provide a theoretical study of cost-based filtering for shorter path constraints on acyclic, on undirected, and on directed graphs that do not contain negative cycles. We then show empirically how reasoning about path-substructures in combination with CP-based Lagrangian relaxation can help to improve significantly over previously developed problem-tailored filtering algorithms for the resource constrained shortest path problem and investigate the impact of required-edge detection, undirected versus directed filtering, and the choice of the algorithm optimizing the Lagrangian dual.