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Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We as ..."
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Cited by 53 (14 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
A New Approach to AllPairs Shortest Paths on RealWeighted Graphs
 Theoretical Computer Science
, 2003
"... We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Her ..."
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Cited by 26 (2 self)
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We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Here m and n are the number of edges and vertices, respectively.
Combining SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In m ..."
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Cited by 20 (6 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
A shortest path algorithm for realweighted undirected graphs
 in 13th ACMSIAM Symp. on Discrete Algs
, 1985
"... Abstract. We present a new scheme for computing shortest paths on realweighted undirected graphs in the fundamental comparisonaddition model. In an efficient preprocessing phase our algorithm creates a linearsize structure that facilitates singlesource shortest path computations in O(m log α) ti ..."
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Cited by 12 (3 self)
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Abstract. We present a new scheme for computing shortest paths on realweighted undirected graphs in the fundamental comparisonaddition model. In an efficient preprocessing phase our algorithm creates a linearsize structure that facilitates singlesource shortest path computations in O(m log α) time, where α = α(m, n) is the very slowly growing inverseAckermann function, m the number of edges, and n the number of vertices. As special cases our algorithm implies new bounds on both the allpairs and singlesource shortest paths problems. We solve the allpairs problem in O(mnlog α(m, n)) time and, if the ratio between the maximum and minimum edge lengths is bounded by n (log n)O(1) , we can solve the singlesource problem in O(m + nlog log n) time. Both these results are theoretical improvements over Dijkstra’s algorithm, which was the previous best for real weighted undirected graphs. Our algorithm takes the hierarchybased approach invented by Thorup. Key words. singlesource shortest paths, allpairs shortest paths, undirected graphs, Dijkstra’s
A Faster Allpairs Shortest Path Algorithm for Realweighted Sparse Graphs
 In Proc. 29th Int'l Colloq. on Automata, Languages, and Programming (ICALP'02), LNCS
, 2002
"... We present a faster allpairs shortest paths algorithm for arbitrary realweighted directed graphs. ..."
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Cited by 10 (3 self)
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We present a faster allpairs shortest paths algorithm for arbitrary realweighted directed graphs.
On the ComparisonAddition Complexity of AllPairs Shortest Paths
 In Proc. 13th Int'l Symp. on Algorithms and Computation (ISAAC'02
, 2002
"... We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in a ..."
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Cited by 6 (5 self)
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We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in approaches based on Dijkstra's algorithm, and for graphs with O(n) edges our algorithm is within a tiny O(log (n; n)) factor of optimal. Our algorithm can be implemented to run in polynomial time (granted, a large polynomial). We leave open the problem of providing an efficient implementation.
Geometric Travel Planning
, 2003
"... This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computational geometry. Given a set ..."
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Cited by 3 (2 self)
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This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computational geometry. Given a set
Geometric Shortest Path Containers
, 2004
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be onl ..."
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Cited by 2 (1 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge.
Engineering Shortest Path Algorithms
"... In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths. In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra's shortest path algorithm. In this context, we show that studying ..."
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Cited by 1 (0 self)
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In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths. In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra's shortest path algorithm. In this context, we show that studying heuristics that are e#cient in practice can yield interesting clues to the combinatorial properties of the problem, and eventually lead to new theoretically e#cient algorithms.
www.elsevier.com/locate/comcom
"... 9 Application Level Multicast is a promising approach to overcome the deployment problems of IP level multicast by establishing deliv10 ery trees using overlay links among end systems. This paper presents algorithms to support traffic engineering, to improve the reliability 11 of multicast delivery ..."
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9 Application Level Multicast is a promising approach to overcome the deployment problems of IP level multicast by establishing deliv10 ery trees using overlay links among end systems. This paper presents algorithms to support traffic engineering, to improve the reliability 11 of multicast delivery, and to facilitate secure group communications. First, we introduce the socalled backup multicast tree algorithm to 12 compute a set of n 1 backup multicast delivery trees from the default multicast tree. Each backup multicast tree has exactly one link of 13 the default multicast tree that is replaced by a backup link from the set of available links. The algorithm can calculate this set of trees with 14 a complexity of O(m log n), which is identical with the complexity of well known minimum spanning tree algorithms. The socalled 15 reduced multicast tree algorithm is based on the backup multicast tree algorithm and can calculate a tree from the default multicast tree 16 by removing a particular node and by replacing the links of the removed node. Using the algorithms trees can be calculated individually 17 by each of the nodes but it requires global topology knowledge. We therefore discuss distributed versions of the algorithms. 18 Ó 2006 Published by Elsevier B.V.