We present an algorithm that solves the all-pairs shortest-paths problem on a directed graph with n vertices and m arcs in time O(nm + n(2) logn), where the arcs are assigned real, possibly negative costs. Our algorit...
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We present an algorithm that solves the all-pairs shortest-paths problem on a directed graph with n vertices and m arcs in time O(nm + n(2) logn), where the arcs are assigned real, possibly negative costs. Our algorithm is new in the following respect. It computes the distance mu(v, w) between each pair v, w of vertices even in the presence of negative cycles, where mu(v, w) is defined as the infimum of the costs of all directed paths from v to w. (C) 2002 Elsevier Science B.V. All rights reserved.
We present a new generic ∊-removal algorithm for weighted automata and transducers defined over a semiring. The algorithm can be used with any semiring covered by our framework and works with any queue discipline adop...
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We present a new generic ∊-removal algorithm for weighted automata and transducers defined over a semiring. The algorithm can be used with any semiring covered by our framework and works with any queue discipline adopted. It can be used in particular in the case of unweighted automata and transducers and weighted automata and transducers defined over the tropical semiring. It is based on a general shortest-distance algorithm that we briefly describe. We give a full description of the algorithm including its pseudocode and its running time complexity, discuss the more efficient case of acyclic automata, an on-the-fly implementation of the algorithm and an approximation algorithm in the case of the semirings not covered by our framework. We illustrate the use of the algorithm with several semirings. We also describe an input ∊-normalization algorithm for weighted transducers based on the general shortest-distance algorithm. The algorithm, which works with all semirings covered by our framework, admits an on-the-fly implementation.
We present general algorithms for minimizing sequential finite-state transducers that output strings or numbers. The algorithms are shown to be efficient since in the case of acyclic transducers and for output strings...
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We present general algorithms for minimizing sequential finite-state transducers that output strings or numbers. The algorithms are shown to be efficient since in the case of acyclic transducers and for output strings they operate in O(S + \ E \ + \ V \ + (\ E \ - \ V \ + \ F \).(\ P-max\ + 1)) steps, where S is the sum of the lengths of all output labels of the resulting transducer, E the set of transitions of the given transducer, V the set of its states, F the set of final states, and P-max one of the longest of the longest common prefixes of the output paths leaving each state of the transducer. The algorithms apply to a larger class of transducers which includes subsequential transducers. (C) 2000 Elsevier Science B.V. All rights reserved.
We carry out an experimental analysis of a number of shortest-path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper ...
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