More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Matrix-vector multiplication in sub-quadratic time: (some preprocessing required)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Stochastic Context-Free Parsing: A Stochastic Version of the Valiant Algorithm
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
General context-free recognition in less than cubic time
Journal of Computer and System Sciences
Reducing the worst case running times of a family of RNA and CFG problems, using Valiant's approach
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
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In this paper, we propose three algorithms for the problem of string edit distance with duplication and contraction operations, which improve the time complexity of previous algorithms for this problem. These include a faster algorithm for the general case of the problem, and two improvements which apply under certain assumptions on the cost function. The general algorithm is based on fast min-plus multiplication of square matrices, and obtains the running time of O(|Σ|n3 log3 log n/log2 n), where n is the length of the input strings and |Σ| is the alphabet size. This algorithm is further accelerated, under some assumption on the cost function, to O(|Σ| (n2 + nn′2 log3 log n′/log2 n′)) time, where n′ is the length of the run-length encoding of the input. Another improvement is based on a new fast matrix-vector min-plus multiplication under a certain discreteness assumption, and yields an O(|Σ| n3/log2 n) time algorithm. Furthermore, this algorithm is online, in the sense that one of the strings may be given letter by letter. As part of this algorithm we present the currently fastest online algorithm for weighted CFG parsing for discrete weighted grammars. This result is useful on its own.