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A Short Path to the Shortest Path
The American Mathematical Monthly, 1995(1995). A Short Path to the Shortest Path. The American Mathematical Monthly: Vol. 102, No. 2, pp. 158-159.
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The fuzzy shortest path length and the corresponding shortest path in a network
Computers & Operations Research, 2005The fuzzy shortest path (SP) problem aims at providing decision makers with the fuzzy shortest path length (FSPL) and the SP in a network with fuzzy arc lengths. In this paper, each arc length is represented as a triangular fuzzy set and a new algorithm is proposed to deal with the fuzzy SP problem.
Tzung-Nan Chuang, Jung-Yuan Kung
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Shortest Path to Mechanism Design
2015Mechanism design is concerned with the problem to compute desired outcomes in situations where data is distributed among selfish agents. We discuss some of the most fundamental questions in the design of mechanisms, and derive simple answers by interpreting the problem in graph theoretic terms.
Rudolf Müller, Marc Uetz
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Journal of Physics A: Mathematical and General, 1985
The separation of two points on a percolation network is characterised not only by the distance between them, but also by the length of a path on the network which connects them. The wetting velocity nu provides a measure of the lengths of the shortest connecting paths on the network above the percolation concentration pc.
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The separation of two points on a percolation network is characterised not only by the distance between them, but also by the length of a path on the network which connects them. The wetting velocity nu provides a measure of the lengths of the shortest connecting paths on the network above the percolation concentration pc.
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1986
Recently there has been considerable research activity on algorithms for finding shortest paths in geometries induced by obstacles. A typical problem is finding the shortest path between two points on the Euclidean plane avoiding a given set of polygonal obstacles (see Figure 1). We review this area and isolate several interesting open problems.
Christos H. Papadimitriou+1 more
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Recently there has been considerable research activity on algorithms for finding shortest paths in geometries induced by obstacles. A typical problem is finding the shortest path between two points on the Euclidean plane avoiding a given set of polygonal obstacles (see Figure 1). We review this area and isolate several interesting open problems.
Christos H. Papadimitriou+1 more
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Annals of Operations Research, 1989
This paper develops a polynomial-time algorithm that reconstructs a shortest path between two vertices using only the all pairs shortest path distance matrix. For graphs with positive edge weights, the algorithm requiresO(⦹V|log|V|) time. When the graph contains both positive and negative, but not zero, edge weights, and all cycles have positive length,
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This paper develops a polynomial-time algorithm that reconstructs a shortest path between two vertices using only the all pairs shortest path distance matrix. For graphs with positive edge weights, the algorithm requiresO(⦹V|log|V|) time. When the graph contains both positive and negative, but not zero, edge weights, and all cycles have positive length,
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2000
Consider a digraph G = (V, E) with non- negative costs c(e) = c ij (∀ e = (i, j) ∈ E) associated with the edges in G. To simplify further notation we define c ij := ∞ for all (i, j) ∉ E.
Kathrin Klamroth, Horst W. Hamacher
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Consider a digraph G = (V, E) with non- negative costs c(e) = c ij (∀ e = (i, j) ∈ E) associated with the edges in G. To simplify further notation we define c ij := ∞ for all (i, j) ∉ E.
Kathrin Klamroth, Horst W. Hamacher
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1970
The first image that comes to mind when the word ‘network’ is mentioned is a traffic network, whether it be road or air traffic. Most of us are familiar with such networks since one rarely travels from one location to another without consulting a ‘map’, which is, in our terminology, a ‘network’.
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The first image that comes to mind when the word ‘network’ is mentioned is a traffic network, whether it be road or air traffic. Most of us are familiar with such networks since one rarely travels from one location to another without consulting a ‘map’, which is, in our terminology, a ‘network’.
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The shortest path tree problem is a classical and widely studied combinatorial problem. The scope of this article is to provide an extensive treatment of the major classical approaches. It then proceeds focusing on the auction algorithm and some of its recently developed variants.
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