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ABSTRACT: Given an alphabet σ, a (directed) graph G whose edges are weighted and σ-labeled, and a formal language L
Í\subseteq
σ*, we consider the problem of finding a shortest (simple) path p in G complying with the additional constraint that l(p) ∃ L. Here l(p) denotes the unique word given by concatenating the σ-labels in G along the path p.
We consider the computational complexity of the problem for different classes of formal languages (finite, regular, context
free and context sensitive), different classes of graphs (unrestricted, grids, treewidth bounded) and different type of path
(shortest and shortest simple).
A number of variants of the problem are considered and both polynomial time algorithms as well as hardness results (NP-, PSPACE-hardness) are obtained. The hardness and the polynomial time algorithms presented here are a step towards finding such classes
of graphs for which polynomial time query evaluation is possible.
06/2006: pages 234-245;
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[show abstract]
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ABSTRACT: For transportation planning applications, it is useful to not only model each individual traveler, but also the decisionmaking process leading to her travel demand.
12/2002;
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Algorithms - ESA 2002, 10th Annual European Symposium, Rome, Italy, September 17-21, 2002, Proceedings; 01/2002
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ABSTRACT: We describe and analyze empirically an implementation of some generalizations of Dijkstra’s algorithm for shortest paths in
graphs. The implementation formed a part of the TRANSIMS project at the Los Alamos National Laboratory. Besides offering the
first implementation of the shortest path algorithm with regular language constraints, our code also solves problems with
time-dependent edge delays in a quite general first-in-first-out model.
We describe some details of our implementation and then analyze the behavior of the algorithm on real but extremely large
transportation networks. Even though the questions we consider in our experiments are fundamental and natural, it appears
that they have not been carefully examined before. A methodological contribution of the present work is theus e of formal
statistical methods to analyzetheb ehaviour of our algorithms. Although the statistical methods employed are simple, they
provide a possibly novel approach to the experimental analysis of algorithms.
Our results provide evidence for our claims of effciency of the algorithms described in a very practical setting.
12/2001: pages 313-319;
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SIAM J. Comput. 01/2000; 30:809-837.
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[show abstract]
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ABSTRACT: Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigma-labeled, and a formal language L ` Sigma , we consider the problem of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denotes the unique word given by concatenating the Sigma-labels of the edges along the path p. The main contributions of this paper include the following: 1. We show that the problem of finding a shortest path between source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time. When the mode choice is specified as a regular language we provide algorithms with improved space and time bounds. 2. In contrast, we show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to fixed simple regular languages and very simple graphs (complete grids) 3. For the class of treewidth bounded gr...
08/1999;
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[show abstract]
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ABSTRACT: We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic as well as exact solutions and associated data structures affect the computational performance of the software developed for realistic transportation networks. For this purpose we have used a road network representing with high degree of resolution the Dallas Ft-Worth urban area. We discuss and experimentally analyze various one-to-one shortest path algorithms. These include classical exact algorithms studied in the literature as well as heuristic solutions that are designed to take into account the geometric structure of the input instances. Computational results are provided to empirically compare the efficiency of various algorithms. Our studies indicate that a modified Dijkstra's algorithm is computationally fast and an ex...
08/1999;
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[show abstract]
[hide abstract]
ABSTRACT: We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic and exact solutions, associated data structures affected the computational performance of the software developed especially for realistic transportation networks. For this purpose we have used Dallas Ft-Worth road network with very high degree of resolution. The following general results are obtained. 1. We discuss and experimentally analyze various one-one shortest path algorithms. These include classical exact algorithms studied in the literature as well as heuristic solutions that are designed to take into account the geometric structure of the input instances. 2. We describe a number of extensions to the basic shortest path algorithm. These extensions were primarily motivated by practical problems arising in TRANSIMS and ...
02/1999;
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ACM Journal of Experimental Algorithmics. 01/1999; 4:6.
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[show abstract]
[hide abstract]
ABSTRACT: We carry out an experimental analysis of a number of shortest path (routing) algorithms investigated in the context of the TRANSIMS (TRansportation ANalysis and SIMulation System) project. The main focus of the paper is to study how various heuristic and exact solutions, associated data structures affected the computational performance of the software developed especially for realistic transportation networks. For this purpose we have used Dallas Ft-Worth road network with very high degree of resolution. The following general results are obtained. 1. We discuss and experimentally analyze various one-one shortest path algorithms. These include classical exact algorithms studied in the literature as well as heuristic solutions that are designed to take into account the geometric structure of the input instances. 2. We describe a number of extensions to the basic shortest path algorithm. These extensions were primarily motivated by practical problems arising in TRANSIMS and ...
09/1998;
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[show abstract]
[hide abstract]
ABSTRACT: For transportation planning applications, it is useful to not only model each individual traveler, but also the decisionmaking process leading to her travel demand.
09/1998;
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Algorithm Theory - SWAT '98, 6th Scandinavian Workshop on Algorithm Theory, Stockholm, Sweden, July, 8-10, 1998, Proceedings; 01/1998
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Algorithm Engineering, 2nd International Workshop, WAE '92, Saarbrücken, Germany, August 20-22, 1998, Proceedings; 01/1998
