Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Faster scaling algorithms for network problems
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
All pairs shortest paths for graphs with small integer length edges
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Reasoning about strings in databases
Journal of Computer and System Sciences
Using acceptors as transducers
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Adding String Processing Capabilities to Data Management Systems
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
Safety, translation and evaluation of alignment calculus
ADBIS'97 Proceedings of the First East-European conference on Advances in Databases and Information systems
Cycles in Generalized Networks
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Design and implementation of a string database query language
Information Systems - Special issue: Data management in bioinformatics
Efficient timed model checking for discrete-time systems
Theoretical Computer Science
Preferential Regular Path Queries
Fundamenta Informaticae
Preferential Regular Path Queries
Fundamenta Informaticae
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We study a problem related to finding shortest paths in weighted graphs. We ask whether or not there is a path between two nodes that has a given total cost k. The edge weights of the graph can be both positive and negative integers or even integer vectors. We show that many variants of this problem are NP-complete. We develop a pseudo-polynomial algorithm for (both positive and negative) integer weights. The running time of this algorithm is O(W2n3 + |k| min(|k|, W)n2), where n is the number of nodes in the graph, W is the largest absolute value of any edge weight, and k is the target cost. The algorithm is based on preprocessing the graph with a relaxation algorithm to eliminate the effects of weight sign alternations along a path. This preprocessing stage is applicable to other problems as well. For example, we show how to find the minimum absolute cost of any path between two given nodes in a graph with integer weights in O(W2n3) time.