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Online exact shortest distance query processing
 Proceedings of the International Conference on Extending Database Technology (EDBT), 2009
"... Shortestpath query processing not only serves as a long established routine for numerous applications in the past but also is of increasing popularity to support novel graph applications in very large databases nowadays. For a large graph, there is the new scenario to query intensively against ar ..."
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Shortestpath query processing not only serves as a long established routine for numerous applications in the past but also is of increasing popularity to support novel graph applications in very large databases nowadays. For a large graph, there is the new scenario to query intensively against arbitrary nodes, asking to quickly return node distance or even shortest paths. And traditional main memory algorithms and shortest paths materialization become inadequate. We are interested in graph labelings to encode the underlying graphs and assign labels to nodes to support efficient query processing. Surprisingly, the existing work of this category mainly emphasizes on reachability query processing, while no sufficient effort has been given to distance labelings to support querying exact shortest distances between nodes. Distance labelings must be developed on the graph in whole to correctly retain node distance information. It makes many existing methods to be inapplicable. We focus on fast computing distanceaware 2hop covers, which can encode the allpairs shortest paths of a graph in O(V  · E1/2) space. Our approach exploits strongly connected components collapsing and graph partitioning to gain speed, while it can overcome the challenges in correctly retaining node distance information and appropriately encoding allpairs shortest paths with small overhead. Furthermore, our approach avoids precomputing allpairs shortest paths, which can be prohibitive over large graphs. We conducted extensive performance studies, and confirm the efficiency of our proposed new approaches. 1.
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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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
An InverseAckermann Type Lower Bound for Online Minimum Spanning Tree Verification
 Combinatorica
"... Given a spanning tree T of some graph G, the problem of minimum spanning tree verication is to decide whether T = MST(G). A celebrated result of Komlos shows that this problem can be solved in linear time. Somewhat unexpectedly, MST verication turns out to be useful in actually computing minimum spa ..."
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Given a spanning tree T of some graph G, the problem of minimum spanning tree verication is to decide whether T = MST(G). A celebrated result of Komlos shows that this problem can be solved in linear time. Somewhat unexpectedly, MST verication turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to wonder whether a more flexible version of MST Verification could be used to derive a faster deterministic minimum spanning tree algorithm.
A Review and Evaluations of Real Time Shortest Path according to current traffic on road
"... Abstract The Shortest Path Problem (SPP) is one of the most fundamental and important in combinatorial Problem. SPP is an important problem in graph theory and has applications in communications, transportation, and electronics problems. In this paper different algorithm for solving SPP with their ..."
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Abstract The Shortest Path Problem (SPP) is one of the most fundamental and important in combinatorial Problem. SPP is an important problem in graph theory and has applications in communications, transportation, and electronics problems. In this paper different algorithm for solving SPP with their advantage, disadvantage and application has been discussed. But all these algorithms are work on original shortest path but many times original shortest path don’t work properly due to many reasons like traffic problem and road blocking problem and many more called real time problems. To remove these real time problems be proposed a technique "A Review and Evaluations of Real Time Shortest Path according to current traffic on road". According to this technique we can find the shortest path according to traffic on road at current time. So we can save the time of all types of driver.