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An Incremental Algorithm for a Generalization of the ShortestPath Problem
, 1992
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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Cited by 116 (1 self)
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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the singlesource shortestpath problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortestpath problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edgelength changes.
On the Computational Complexity of Dynamic Graph Problems
 THEORETICAL COMPUTER SCIENCE
, 1996
"... ..."
Shortest Path Algorithms in Transportation Models: Classical and Innovative Aspects
, 1998
"... Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists ..."
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Cited by 51 (3 self)
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Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of view, and also for the memory requirements. Since no "best" algorithm currently exists for every kind of transportation problem, research in this field has recently moved to the design and implementation of "ad hoc" shortest path procedures, which are able to capture the peculiarities of the problems under consideration. The aim of this work is to present in a unifying framework both the main algorithmic approaches that have been proposed in the past years for solving the shortest path problems arising most frequently in the transportation field, and also some important implementation techniques ...
Speeding up dynamic shortest path algorithms
 AT&T labs Research Technical Report, TD5RJ8B, Florham Park, NJ
, 2003
"... doi 10.1287/ijoc.1070.0231 ..."
A New Algorithm for Reoptimizing Shortest Paths When the Arc Costs Change
, 2001
"... We propose an algorithm which reoptimizes shortest paths in a very general situation, that is when any subset of arcs of the input graph is aected by a change of the arc costs, which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the lit ..."
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Cited by 11 (0 self)
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We propose an algorithm which reoptimizes shortest paths in a very general situation, that is when any subset of arcs of the input graph is aected by a change of the arc costs, which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far.
A New Dual Algorithm for Shortest Path Reoptimization
 TRANSPORTATION AND NETWORK ANALYSIS  CURRENT TRENDS
, 2001
"... Shortest path problems are among the most studied network flow problems, with interesting applications in various fields. In large scale transportation systems, a sequence of shortest path problems must often be solved, where the (k+1) th problem differs only slightly from the k th one. Signi ..."
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Cited by 3 (1 self)
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Shortest path problems are among the most studied network flow problems, with interesting applications in various fields. In large scale transportation systems, a sequence of shortest path problems must often be solved, where the (k+1) th problem differs only slightly from the k th one. Significant reduction in computational time may be obtained with an efficient reoptimization procedure that exploits the useful information available after each shortest path computation in the sequence. Such reduction in computational time is essential in many online applications. This work is devoted to the development of such reoptimization algorithm. We shall focus on the sequence of shortest path problems to be solved for which problems differ by the origin node of the path set. After reviewing the classical algorithms described in the literature so far, which essentially show a Dijkstra's like behavior, a new dual approach will be proposed, which could be particularly promising in p...
Shortest paths on dynamic graphs
, 2008
"... Among the variants of the well known shortest path problem, those that refer to a dynamically changing graphs are theoretically interesting, as well as computationally challenging. Applicationwise, there is an industrial need for computing pointtopoint shortest paths on largescale road networks w ..."
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Cited by 2 (2 self)
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Among the variants of the well known shortest path problem, those that refer to a dynamically changing graphs are theoretically interesting, as well as computationally challenging. Applicationwise, there is an industrial need for computing pointtopoint shortest paths on largescale road networks whose arcs are weighted with a travelling time which depends on traffic conditions. We survey recent techniques for dynamic graph weights as well as dynamic graph topology. 1