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Undirected Single Source Shortest Paths in Linear Time
 J. Assoc. Comput. Mach
, 1997
"... The single source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a weighted graph G with a source vertex s, find the shortest path from s to all other vertices in the graph. Since 1959 all theoretical developments in SSSP have been based on Dijkstra& ..."
Abstract

Cited by 50 (3 self)
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The single source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a weighted graph G with a source vertex s, find the shortest path from s to all other vertices in the graph. Since 1959 all theoretical developments in SSSP have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s. Thus, any implementation of Dijkstra 's algorithm sorts the vertices according to their distances from s. However, we do not know how to sort in linear time. Here, a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with integer weights. The algorithm avoids the sorting bottleneck by building a hierechical bucketing structure, identifying vertex pairs that may be visited in any order. 1 Introduction Let G = (V; E), jV j = n, jEj = m, be an undirected connected graph with an integer edge weight function ` : E ! N and a distinguished source vertex...
Computing the n x m Shortest Paths Efficiently
"... . Computation of all the shortest paths between multiple sources and multiple destinations on various networks is required in many problems, such as the traveling salesperson problem (TSP) and the vehicle routing problem (VRP). This paper proposes new algorithms that compute the set of shortest path ..."
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Cited by 2 (0 self)
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. Computation of all the shortest paths between multiple sources and multiple destinations on various networks is required in many problems, such as the traveling salesperson problem (TSP) and the vehicle routing problem (VRP). This paper proposes new algorithms that compute the set of shortest paths efficiently by using the A 3 algorithm. The efficiency and properties of these algorithms are examined by using the results of experiments on an actual road network. 1 Introduction Computation of all the shortest paths between multiple sources and multiple destinations on various networks is required in many problems, such as the traveling salesperson problem (TSP), the vehicle routing problem (VRP), the warehouse location problem (WLP), and the quadratic assignment problem (QAP). Accordingly, a function for performing such computation is required in geographical information systems (GISs), logistics tools, and so on. There are many fast heuristic algorithms for solving such problems as...
An Extended Shortest Path Problem with Switch Cost Between Arcs
"... Abstract—Computing the shortest path in a graph is an important problem and it is very useful in various applications. The standard shortest path problem has been studied extensively and intensively, but it can’t handle the situation when there is a switch cost between arcs. For example, in a train ..."
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Abstract—Computing the shortest path in a graph is an important problem and it is very useful in various applications. The standard shortest path problem has been studied extensively and intensively, but it can’t handle the situation when there is a switch cost between arcs. For example, in a train transportation network, the switch cost between arcs contains waiting time in stations, times of transfer and so on. Obviously, the switch cost is an important factor for users to make decisions. Taking into consideration of the switch cost between arcs, we extend the standard shortest path problem and propose an algorithm and its optimized version to solve the extended single source shortest path problem. Test results show that the proposed algorithms can give reasonable and acceptable results for users.