Semirings and path spaces
TLDR
A unified algebraic theory for a class of path problems such as that of finding the shortest or, more generally, the k shortest paths in a network; the enumeration of elemementary or simple paths inA graph is developed.About:
This article is published in Discrete Mathematics.The article was published on 1979-01-01 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Shortest path problem & Longest path problem.read more
Citations
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Journal ArticleDOI
Finding the k Shortest Paths
TL;DR: K shortest paths are given for finding the k shortest paths connecting a pair of vertices in a digraph, and applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery are described.
Proceedings ArticleDOI
Finding the k shortest paths
TL;DR: K shortest paths are given for finding the k shortest paths connecting a pair of vertices in a digraph, and applications to dynamic programming problems including the knapsack problem, sequence alignment, and maximum inscribed polygons are described.
Book ChapterDOI
Bicriterion Path Problems
TL;DR: Algorithms are provided for some of the bicriterion path problems in directed graphs, including polynomial algorithms for the MAXMIN-MAXMIN problem and the MINSUM-MAX MIN problem, and a pseudo-polynomial exact algorithm as well as a fullyPolynomial approximation scheme for the MINsUM-MINSUM problem.
Book
Path Problems in Networks
TL;DR: This monograph aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work.
Proceedings ArticleDOI
Lexicographic products in metarouting
TL;DR: This work characterize exactly when lexicographic products can be used to define well-behaved routing protocols, and shows that in some cases this type of local autonomy is fully compatible with global optimality.
References
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Journal ArticleDOI
Regular Expressions and State Graphs for Automata
Robert McNaughton,Hisao Yamada +1 more
TL;DR: Algorithms are presented for converting a state graph describing thebehavior of an automaton to a regular expression describing the behavior of the same automaton, and for converting an regular expression into a stategraph.
Journal ArticleDOI
Regular Algebra Applied to Path-finding Problems
Roland Backhouse,B. A. Carre +1 more
TL;DR: In this article, the authors present an algebra for extremal path problems, which is a generalization of the algebra of regular languages, and show that it can be used for path enumeration problems.
Journal ArticleDOI
Iterative methods for determining the k shortest paths in a network
TL;DR: On the basis of both theoretical and computational evidence, one of the three methods is seen to offer an extremely effective procedure for finding the k shortest paths from a given node in a network.