Journal ArticleDOI
On some techniques useful for solution of transportation network problems
TLDR
An efficient algorithm for solving transportation problems that requires at most n3 additions and comparisons when applied to an n-by-n assignment problem, as compared with the theoretical upper bound proportional to n4 for the number of such operations required by currently available methods.Abstract:
This paper presents an efficient algorithm for solving transportation problems. The improvement over the existing algorithms of the “primal-dual” type [3], [5] consists in modifying the “potential-raising” stages of the solution process in such a way that negative-cost arcs are removed so that the Dijkstra's algorithm may be applied. Especially, the algorithm requires at most n3 additions and comparisons when applied to an n-by-n assignment problem, as compared with the theoretical upper bound proportional to n4 for the number of such operations required by currently available methods. Furthermore, auxiliary techniques of simplifying the original network by means of “reduction” and “induction” are also introduced as useful tools to treat large-scale problems and specially-structured problems with.read more
Citations
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Journal ArticleDOI
A shortest augmenting path algorithm for dense and sparse linear assignment problems
R. Jonker,A. Volgenant +1 more
TL;DR: A shortest augmenting path algorithm for the linear assignment problem that contains new initialization routines and a special implementation of Dijkstra's shortest path method is developed.
Journal ArticleDOI
Linear-Time Approximation for Maximum Weight Matching
Ran Duan,Seth Pettie +1 more
TL;DR: This article gives an algorithm that computes a (1 − 1 − 0))-approximate maximum weight matching in O(i) time, that is, optimal linear time for any fixed ε, and should be appealing in all applications that can tolerate a negligible relative error.
ReportDOI
Network Flow Algorithms
TL;DR: This survey examines some of the recent developments in network flow research, the classical network flow problems, the maximum flow problem and the minimum-cost circulation problem, and a less standard problem, the generalized flow problem, sometimes called the problem of flows with losses and gains.
Journal ArticleDOI
Algorithms and codes for the assignment problem
TL;DR: This paper analyzes the most efficient algorithms for the Linear Min-Sum Assignment Problem and shows that they derive from a common basic procedure, and evaluates the computational complexity and the average performance on randomly-generated test problems.
Journal ArticleDOI
Reconstruction of the early Universe as a convex optimization problem
Yann Brenier,Uriel Frisch,Uriel Frisch,Michel Hénon,Grégoire Loeper,Sabino Matarrese,Roya Mohayaee,A. Sobolevskiĭ +7 more
TL;DR: In this article, it was shown that the deterministic past history of the universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Book
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.
Journal ArticleDOI
An Appraisal of Some Shortest-Path Algorithms
TL;DR: In this article, five discrete shortest-path problems are treated: finding the shortest path between two specified nodes of a network, determining the shortest paths between all pairs of nodes in a network; determining the second, third, etc., shortest path; 4 determining the fastest path through a network with travel times depending on the departure time; and 5 finding the short path between specified endpoints that passes through specified intermediate nodes.