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Fast fully dynamic landmarkbased estimation of shortest path distances in very large graphs
 In ACM Conference on Information and Knowledge Management (CIKM
, 2011
"... Computing the shortest path between a pair of vertices in a graph is a fundamental primitive in graph algorithmics. Classical exact methods for this problem do not scale up to contemporary, rapidly evolving social networks with hundreds of millions of users and billions of connections. A number of a ..."
Abstract

Cited by 13 (1 self)
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Computing the shortest path between a pair of vertices in a graph is a fundamental primitive in graph algorithmics. Classical exact methods for this problem do not scale up to contemporary, rapidly evolving social networks with hundreds of millions of users and billions of connections. A number of approximate methods have been proposed, including several landmarkbased methods that have been shown to scale up to very large graphs with acceptable accuracy. This paper presents two improvements to existing landmarkbased shortest path estimation methods. The first improvement relates to the use of shortestpath trees (SPTs). Together with appropriate shortcutting heuristics, the use of SPTs allows to achieve higher accuracy with acceptable time and memory overhead. Furthermore, SPTs can be maintained incrementally under edge insertions and deletions, which allows for a fullydynamic algorithm. The second improvement is a new landmark selection strategy that seeks to maximize the coverage of all shortest paths by the selected landmarks. The improved method is evaluated on the DBLP, Orkut, Twitter and Skype social networks.
MemoryEfficient Fast Shortest Path Estimation in Large Social Networks
"... As the sizes of contemporary social networks surpass billions of users, so grows the need for fast graph algorithms to analyze them. A particularly important basic operation is the computation of shortest paths between nodes. Classical exact algorithms for this problem are prohibitively slow on ..."
Abstract
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As the sizes of contemporary social networks surpass billions of users, so grows the need for fast graph algorithms to analyze them. A particularly important basic operation is the computation of shortest paths between nodes. Classical exact algorithms for this problem are prohibitively slow on large graphs, which motivates the development of approximate methods. Of those, landmarkbased methods have been actively studied in recent years. Landmarkbased estimation methods start by picking a fixed set of landmark nodes, precomputing the distance from each node in the graph to each landmark, and storing the precomputed distances in a data structure. Prior work has shown that the number of landmarks required to achieve a given level of precision grows with the size of the graph. Simultaneously, the size of the data structure is proportional to the product of the size of the graph and the number of landmarks. In this work we propose an alternative landmarkbased distance estimation approach that substantially reduces space requirements by means of pruning: computing distances from each node to only a small subset of the closest landmarks. We evaluate our method on the DBLP, Orkut, Twitter and Skype social networks and demonstrate that the resulting estimation algorithms are comparable in query time and potentially superior in approximation quality to equivalent nonpruned landmarkbased methods, while requiring less memory or disk space. 1