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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 49 (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...
An Efficient DelayConstrained Minimum Spanning Tree Heuristic
 the Fifth International Conference on Computer Communications and Networks
, 1996
"... Many distributed realtime applications require broadcasting information to all participants. This information must be received within some delay bound, and at the lowest possible cost. We formulate the problem of constructing broadcast trees for realtime traffic with delay constraints in networks ..."
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Cited by 3 (0 self)
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Many distributed realtime applications require broadcasting information to all participants. This information must be received within some delay bound, and at the lowest possible cost. We formulate the problem of constructing broadcast trees for realtime traffic with delay constraints in networks with asymmetric link loads as a delayconstrained minimum spanning tree (DCMST) problem in directed networks. Then we prove that this problem is NPcomplete, and we propose an efficient heuristic to solve the problem based on Prim's algorithm for the unconstrained minimum spanning tree problem. This is the first heuristic designed specifically for solving the DCMST problem. Simulation results under realistic networking conditions show that our heuristic's performance is close to optimal when the link loads are symmetric as well as when asymmetric link loads are used. Delayconstrained minimum Steiner tree heuristics can also be used to solve the DCMST problem. Simulation results indicate th...
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"... Grouping connected components using minimal path techniques. Application to reconstruction of vessels in 2D and 3D images. ..."
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Grouping connected components using minimal path techniques. Application to reconstruction of vessels in 2D and 3D images.