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Parallel Algorithms for the All-Sources Generalized Shortest Paths Problem
Jeffrey D. Oldham,Vaughan Pratt +1 more
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This work presents parallel algorithms for the all-sources generalized shortest paths problem using Floyd-Warshall and matrix multiplication algorithms and monotonic piecewise-linear functions.Abstract:
Generalized network flo w problems generalize ordinary network flo w problems by specifying a flo w multiplier for each arc . For every unit of flo w entering the arc, units of flo w exit. We present parallel algorithms for the all-sources generalized shortest paths problem using Floyd-Warshall and matrix multiplication algorithms and monotonic piecewise-linear functions. The latter algorithm requires polylogarithmic time on a concurrent-read exclusive-write PRAM with a superpolynomial number of algorithms.read more
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Proceedings ArticleDOI
Fast algorithm to solve the most economical path problem in sparse matrices
TL;DR: In this paper a powerful algorithm is presented in large scale, sparse network, in long term road network planning problem sometimes the size of the network is very large - about hundred thousand, one point is connected with average 3 or 4 points.
References
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Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
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The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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Linear Programming and Extensions
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
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Flows in networks
D. R. Ford,D. R. Fulkerson +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI
Flows in Networks.
TL;DR: The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.