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
Reasoning about strings in databases
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Introduction to Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Decidability of reachability in vector addition systems (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Safety, translation and evaluation of alignment calculus
ADBIS'97 Proceedings of the First East-European conference on Advances in Databases and Information systems
Using acceptors as transducers
Theoretical Computer Science
Design and implementation of a string database query language
Information Systems - Special issue: Data management in bioinformatics
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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 is of a given cost. The edge weights of the graph can be both positive and negative integers, or even integer vectors.We show that most variants of this problem are NP-complete. We also develop a pseudopolynomial algorithm for the case where the edge weights are integers. The running time of this algorithm is O(M2N3 + |w|min(|w|, M)N2) where N is the number of nodes in the graph, M is the largest absolute value of any edge weight, and w 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.