Data structures and network algorithms
Data structures and network algorithms
Theory of linear and integer programming
Theory of linear and integer programming
Artificial Intelligence - Special issue on knowledge representation
Scheduling real-time computations with separation constraints
Information Processing Letters
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Theoretical Computer Science
Scaling Algorithms for the Shortest Paths Problem
SIAM Journal on Computing
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
An Analysis of Zero-Clairvoyant Scheduling
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A greedy strategy for detecting negative cost cycles in networks
Future Generation Computer Systems - Special issue: High-speed networks and services for data-intensive grids: The DataTAG project
"Ratio Regions": A Technique for Image Segmentation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
Shortest Path Algorithms: Engineering Aspects
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Dynamic control of plans with temporal uncertainty
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
A Combinatorial Algorithm for Horn Programs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A mechanical verification of the stressing algorithm for negative cost cycle detection in networks
Science of Computer Programming
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This paper is concerned with the problem of checking whether a network with positive and negative costs on its arcs contains a negative cost cycle. The Negative Cost Cycle Detection (NCCD) problem is one of the more fundamental problems in network design and finds applications in a number of domains ranging from Network Optimization and Operations Research to Constraint Programming and System Verification. As per the literature, approaches to this problem have been either Relaxation-based or Contraction-based. We introduce a fundamentally new approach for negative cost cycle detection; our approach, which we term as the Stressing Algorithm, is based on exploiting the connections between the NCCD problem and the problem of checking whether a system of difference constraints is feasible. The Stressing Algorithm is an incremental, comparison-based procedure which is as efficient as the fastest known comparison-based algorithm for this problem. In particular, on a network with n vertices and m edges, the Stressing Algorithm takes O(m@?n) time to detect the presence of a negative cost cycle or to report that none exists. A very important feature of the Stressing Algorithm is that it uses zero extra space; this is in marked contrast to all known algorithms that require@W(n)extra space. It is well known that the NCCD problem is closely related to the Single Source Shortest Paths (SSSP) problem, i.e., the problem of determining the shortest path distances of all the vertices in a network, from a specified source; indeed most algorithms in the literature for the NCCD problem are modifications of approaches to the SSSP problem. At this juncture, it is not clear whether the Stressing Algorithm could be extended to solve the SSSP problem, even if O(n) extra space is available.