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28,558
On dynamic shortest paths problems
, 2004
"... We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs ..."
Abstract
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Cited by 41 (2 self)
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We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all
On the Bottleneck Shortest Path Problem
, 2006
"... The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze ..."
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Cited by 4 (0 self)
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The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we
The Generalized Shortest Path Problem
"... this paper we show that the generalized shortest path problem can be solved efficiently for multiplicative weights. The solution is running Dijkstra's algorithm in reverse. In the case of additive weights there is a dynamic programming approach and a pseudo-polynomial algorithm. Finally, if the ..."
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Cited by 1 (0 self)
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this paper we show that the generalized shortest path problem can be solved efficiently for multiplicative weights. The solution is running Dijkstra's algorithm in reverse. In the case of additive weights there is a dynamic programming approach and a pseudo-polynomial algorithm. Finally
Robust shortest path problems
"... This paper is a state of the art on the shortest path problems for which it ex-ists uncertainty and inaccuracy factors on arc values. Two uncertainty models are distinguished: the so-called interval model and the discrete set of scenarios model. Different measures and approaches of robustness are ..."
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This paper is a state of the art on the shortest path problems for which it ex-ists uncertainty and inaccuracy factors on arc values. Two uncertainty models are distinguished: the so-called interval model and the discrete set of scenarios model. Different measures and approaches of robustness
Incremental Shortest-Path Problem
"... The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also
ON ASSOCIATIVE SHORTEST PATH PROBLEMS By
"... We consider a wide classof shortest path problems in acyclic di graphs. In the problems, the length of a path is defined by using an associative binary operation. We derive recursive equations in dynamic programming for the problems, which involve additive, multiplicative, multiplicative-additive, m ..."
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We consider a wide classof shortest path problems in acyclic di graphs. In the problems, the length of a path is defined by using an associative binary operation. We derive recursive equations in dynamic programming for the problems, which involve additive, multiplicative, multiplicative
On the History of the Shortest Path Problem
- DOCUMENTA MATH.
, 2012
"... It is difficult to trace back the history of the shortest path problem. One can imagine that even in very primitive (even animal) societies, finding short paths (for instance, to food) is essential. Compared with other combinatorial optimization problems, like shortest spanning tree, assignment and ..."
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It is difficult to trace back the history of the shortest path problem. One can imagine that even in very primitive (even animal) societies, finding short paths (for instance, to food) is essential. Compared with other combinatorial optimization problems, like shortest spanning tree, assignment
On the robust shortest path problem
- Computers and Operations Research
, 1998
"... The shortest path (SP) problem in a network with nonnegative arc lengths can be solved easily by Dijkstra’s labeling algorithm in polynomial time. In the case of significant uncertainty of the arc lengths, a robustness approach is more appropriate. In this paper, we study the SP problem under arc le ..."
Abstract
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Cited by 27 (0 self)
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The shortest path (SP) problem in a network with nonnegative arc lengths can be solved easily by Dijkstra’s labeling algorithm in polynomial time. In the case of significant uncertainty of the arc lengths, a robustness approach is more appropriate. In this paper, we study the SP problem under arc
On the Inverse Shortest Paths Problem
"... In this paper we survey a variant of the inverse shortest paths problem. Given is a network in which certain node-pairs require connections over specific predefined single paths. The aim is to find link weights such that the desired paths are uniquely induced by a shortest-path algorithm. Further we ..."
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In this paper we survey a variant of the inverse shortest paths problem. Given is a network in which certain node-pairs require connections over specific predefined single paths. The aim is to find link weights such that the desired paths are uniquely induced by a shortest-path algorithm. Further
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