On the bordification of outer space

We give a simple construction of an equivariant deformation retract of Outer space which is homeomorphic to the Bestvina-Feighn bordification. This results in a much easier proof that the bordification is (2n-5)-connected at infinity, and hence that $Out(F_n)$ is a virtual duality group.Comment: Accepted version, to appear in the Journal of the London MS. Section 7, giving the homeomorphism to the Bestvina-Feighn bordification, has been substantially revise

Truss Decomposition in Massive Networks

The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core which is also efficient to compute, k-truss represents the "core" of a k-core that keeps the key information of, while filtering out less important information from, the k-core. However, existing algorithms for computing k-truss are inefficient for handling today's massive networks. We first improve the existing in-memory algorithm for computing k-truss in networks of moderate size. Then, we propose two I/O-efficient algorithms to handle massive networks that cannot fit in main memory. Our experiments on real datasets verify the efficiency of our algorithms and the value of k-truss.Comment: VLDB201

Geo-Social Group Queries with Minimum Acquaintance Constraint

The prosperity of location-based social networking services enables geo-social group queries for group-based activity planning and marketing. This paper proposes a new family of geo-social group queries with minimum acquaintance constraint (GSGQs), which are more appealing than existing geo-social group queries in terms of producing a cohesive group that guarantees the worst-case acquaintance level. GSGQs, also specified with various spatial constraints, are more complex than conventional spatial queries; particularly, those with a strict $k$NN spatial constraint are proved to be NP-hard. For efficient processing of general GSGQ queries on large location-based social networks, we devise two social-aware index structures, namely SaR-tree and SaR*-tree. The latter features a novel clustering technique that considers both spatial and social factors. Based on SaR-tree and SaR*-tree, efficient algorithms are developed to process various GSGQs. Extensive experiments on real-world Gowalla and Dianping datasets show that our proposed methods substantially outperform the baseline algorithms based on R-tree.Comment: This is the preprint version that is accepted by the Very Large Data Bases Journa

A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs

Cyber security is one of the most significant technical challenges in current times. Detecting adversarial activities, prevention of theft of intellectual properties and customer data is a high priority for corporations and government agencies around the world. Cyber defenders need to analyze massive-scale, high-resolution network flows to identify, categorize, and mitigate attacks involving networks spanning institutional and national boundaries. Many of the cyber attacks can be described as subgraph patterns, with prominent examples being insider infiltrations (path queries), denial of service (parallel paths) and malicious spreads (tree queries). This motivates us to explore subgraph matching on streaming graphs in a continuous setting. The novelty of our work lies in using the subgraph distributional statistics collected from the streaming graph to determine the query processing strategy. We introduce a "Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named "Relative Selectivity" that is used to select between different query processing strategies. Our experiments performed on real online news, network traffic stream and a synthetic social network benchmark demonstrate 10-100x speedups over selectivity agnostic approaches.Comment: in 18th International Conference on Extending Database Technology (EDBT) (2015

On star-forest ascending subgraph decomposition

Preprin

Rank gradient, cost of groups and the rank versus Heegaard genus problem

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in topological dynamics