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26
Y.: Fast exact shortestpath distance queries on large networks by pruned landmark labeling
 In: SIGMOD 2013
, 2013
"... We propose a new exact method for shortestpath distance queries on largescale networks. Our method precomputes distance labels for vertices by performing a breadthfirst search from every vertex. Seemingly too obvious and too inefficient at first glance, the key ingredient introduced here is pruni ..."
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Cited by 21 (1 self)
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We propose a new exact method for shortestpath distance queries on largescale networks. Our method precomputes distance labels for vertices by performing a breadthfirst search from every vertex. Seemingly too obvious and too inefficient at first glance, the key ingredient introduced here is pruning during breadthfirst searches. While we can still answer the correct distance for any pair of vertices from the labels, it surprisingly reduces the search space and sizes of labels. Moreover, we show that we can perform 32 or 64 breadthfirst searches simultaneously exploiting bitwise operations. We experimentally demonstrate that the combination of these two techniques is efficient and robust on various kinds of largescale realworld networks. In particular, our method can handle social networks and web graphs with hundreds of millions of edges, which are two orders of magnitude larger than the limits of previous exact methods, with comparable query time to those of previous methods.
Exploring the design space of social networkbased Sybil defense
 In Proceedings of the 4th International Conference on Communication Systems and Network (COMSNETS’12
, 2012
"... Abstract—Recently, there has been significant research interest in leveraging social networks to defend against Sybil attacks. While much of this work may appear similar at first glance, existing social networkbased Sybil defense schemes can be divided into two categories: Sybil detection and Sybil ..."
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Cited by 14 (7 self)
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Abstract—Recently, there has been significant research interest in leveraging social networks to defend against Sybil attacks. While much of this work may appear similar at first glance, existing social networkbased Sybil defense schemes can be divided into two categories: Sybil detection and Sybil tolerance. These two categories of systems both leverage global properties of the underlying social graph, but they rely on different assumptions and provide different guarantees: Sybil detection schemes are applicationindependent and rely only on the graph structure to identify Sybil identities, while Sybil tolerance schemes rely on applicationspecific information and leverage the graph structure and transaction history to bound the leverage an attacker can gain from using multiple identities. In this paper, we take a closer look at the design goals, models, assumptions, guarantees, and limitations of both categories of social networkbased Sybil defense systems. I.
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 ..."
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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.
Canal: Scaling Social NetworkBased Sybil Tolerance Schemes
"... There has been a flurry of research on leveraging social networks to defend against multiple identity, or Sybil, attacks. A series of recent works does not try to explicitly identify Sybil identities and, instead, bounds the impact that Sybil identities can have. We call these approaches Sybil toler ..."
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Cited by 10 (3 self)
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There has been a flurry of research on leveraging social networks to defend against multiple identity, or Sybil, attacks. A series of recent works does not try to explicitly identify Sybil identities and, instead, bounds the impact that Sybil identities can have. We call these approaches Sybil tolerance; they have shown to be effective in applications including reputation systems, spam protection, online auctions, and content rating systems. All of these approaches use a social network as a credit network, rendering multiple identities ineffective to an attacker without a commensurate increase in social links to honest users (which are assumed to be hard to obtain). Unfortunately, a hurdle to practical adoption is that Sybil tolerance relies on computationally expensive network analysis, thereby limiting widespread deployment.
On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Cited by 9 (0 self)
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Efficient Shortest Paths on Massive Social Graphs
"... Abstract—Analysis of large networks is a critical component of many of today’s application environments, including online social networks, protein interactions in biological networks, and Internet traffic analysis. The arrival of massive network graphs with hundreds of millions of nodes, e.g. social ..."
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Cited by 7 (3 self)
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Abstract—Analysis of large networks is a critical component of many of today’s application environments, including online social networks, protein interactions in biological networks, and Internet traffic analysis. The arrival of massive network graphs with hundreds of millions of nodes, e.g. social graphs, presents a unique challenge to graph analysis applications. Most of these applications rely on computing distances between node pairs, which for large graphs can take minutes to compute using traditional algorithms such as breadthfirstsearch (BFS). In this paper, we study ways to enable scalable graph processing for today’s massive networks. We explore the design space of graph coordinate systems, a new approach that accurately approximates node distances in constant time by embedding graphs into coordinate spaces. We show that a hyperbolic embedding produces relatively low distortion error, and propose Rigel, a hyperbolic graph coordinate system that lends itself to efficient parallelization across a compute cluster. Rigel produces significantly more accurate results than prior systems, and is naturally parallelizable across compute clusters, allowing it to provide accurate results for graphs up to 43 million nodes. Finally, we show that Rigel’s functionality can be easily extended to locate (near) shortest paths between node pairs. After a onetime preprocessing cost, Rigel answers nodedistance queries in 10’s of microseconds, and also produces shortest path results up to 18 times faster than prior shortestpath systems with similar levels of accuracy. I.
ISLABEL: an IndependentSet based Labeling Scheme for PointtoPoint Distance Querying
"... We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 mil ..."
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Cited by 7 (2 self)
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We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of these indexes can only process graphs of size barely up to 1 million vertices, which is rather small in view of many of the fastgrowing realworld graphs today such as social networks and Web graphs. We propose an efficient index, which is a novel labeling scheme based on the independent set of a graph. We show that our method can handle graphs of size orders of magnitude larger than existing indexes. 1.
Approximate shortest distance computing: A querydependent local landmark scheme
 In ICDE
, 2012
"... Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an ..."
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Cited by 7 (1 self)
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Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an embedding. To handle a shortest distance query between two nodes, the precomputed distances from the landmarks to the query nodes are used to compute an approximate shortest distance based on the triangle inequality. In this paper, we analyze the factors that affect the accuracy of the distance estimation in the landmark embedding approach. In particular we find that a globally selected, queryindependent landmark set plus the triangulation based distance estimation introduces a large relative error, especially for nearby query nodes. To address this issue, we propose a querydependent local landmark scheme, which identifies a local landmark close to the specific query nodes and provides a more accurate distance estimation than the traditional global landmark approach. Specifically, a local landmark is defined as the least common ancestor of the two query nodes in the shortest path tree rooted at a global landmark. We propose efficient local landmark indexing and retrieval techniques, which are crucial to achieve low offline indexing complexity and online query complexity. Two optimization techniques on graph compression and graph online search are also proposed, with the goal to further reduce index size and improve query accuracy. Our experimental results on largescale social networks and road networks demonstrate that the local landmark scheme reduces the shortest distance estimation error significantly when compared with global landmark embedding. I.
ShortestPath Queries for Complex Networks: Exploiting Low Treewidth Outside the Core
"... We present new and improved methods for efficient shortestpath query processing. Our methods are tailored to work for two specific classes of graphs: graphs with small treewidth and complex networks. Seemingly unrelated at first glance, these two classes of graphs have some commonalities: complex ne ..."
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Cited by 5 (3 self)
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We present new and improved methods for efficient shortestpath query processing. Our methods are tailored to work for two specific classes of graphs: graphs with small treewidth and complex networks. Seemingly unrelated at first glance, these two classes of graphs have some commonalities: complex networks are known to have a core–fringe structure with a dense core and a treelike fringe. Our main contributions are efficient algorithms and data structures on three different levels. First, we provide two new methods for graphs with small but not necessarily constant treewidth. Our methods achieve new tradeoffs between space and query time. Second, we present an improved treedecompositionbased method for complex networks, utilizing the methods for graphs with small treewidth. Third, we extend our method to handle the highly interconnected core with existing exact and approximate methods. We evaluate our algorithms both analytically and experimentally. We prove that our algorithms for lowtreewidth graphs achieve improved tradeoffs between space and query time. Our experiments on several realworld complex networks further confirm the efficiency of our methods: Both the exact and the hybrid method have faster preprocessing and query times than existing methods. The hybrid method in particular provides an improved tradeoff between space and accuracy.
Querying Shortest Path Distance with Bounded Errors in Large Graphs
"... Abstract. Shortest paths and shortest path distances are important primary queries for users to query in a large graph. In this paper, we propose a new approach to answer shortest path and shortest path distance queries efficiently with an error bound. The error bound is controlled by a userspecif ..."
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Cited by 4 (2 self)
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Abstract. Shortest paths and shortest path distances are important primary queries for users to query in a large graph. In this paper, we propose a new approach to answer shortest path and shortest path distance queries efficiently with an error bound. The error bound is controlled by a userspecified parameter, and the online query efficiency is achieved with prepossessing offline. In the offline preprocessing, we take a reference node embedding approach which computes the singlesource shortest paths from each reference node to all the other nodes. To guarantee the userspecified error bound, we design a novel coveragebased reference node selection strategy, and show that selecting the optimal set of reference nodes is NPhard. We propose a greedy selection algorithm which exploits the submodular property of the formulated objective function, and use a graph partitioningbased heuristic to further reduce the offline computational complexity of reference node embedding. In the online query answering, we use the precomputed distances to provide a lower bound and an upper bound of the true shortest path distance based on the triangle inequality. In addition, we propose a linear algorithm which computes the approximate shortest path between two nodes within the error bound. We perform extensive experimental evaluation on a largescale road network and a social network and demonstrate the effectiveness and efficiency of our proposed methods. 1