TopCom: Index for Shortest Distance Query in Directed Graph

Finding shortest distance between two vertices in a graph is an important problem due to its numerous applications in diverse domains, including geo-spatial databases, social network analysis, and information retrieval. Classical algorithms (such as, Dijkstra) solve this problem in polynomial time, but these algorithms cannot provide real-time response for a large number of bursty queries on a large graph. So, indexing based solutions that pre-process the graph for efficiently answering (exactly or approximately) a large number of distance queries in real-time is becoming increasingly popular. Existing solutions have varying performance in terms of index size, index building time, query time, and accuracy. In this work, we propose T OP C OM , a novel indexing-based solution for exactly answering distance queries. Our experiments with two of the existing state-of-the-art methods (IS-Label and TreeMap) show the superiority of T OP C OM over these two methods considering scalability and query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic graph) structure in the graph, which makes it significantly faster than the existing methods if the SCCs (strongly connected component) of the input graph are relatively small

Efficient Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs

Graphs are an important tool to model data in different domains, including social networks, bioinformatics and the world wide web. Most of the networks formed in these domains are directed graphs, where all the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network $G$ and a vertex $r \in V(G)$, we propose a new exact algorithm to compute betweenness score of $r$. Our algorithm pre-computes a set $\mathcal{RV}(r)$, which is used to prune a huge amount of computations that do not contribute in the betweenness score of $r$. Time complexity of our exact algorithm depends on $|\mathcal{RV}(r)|$ and it is respectively $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|)$ and $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|+|\mathcal{RV}(r)|\cdot|V(G)|\log |V(G)|)$ for unweighted graphs and weighted graphs with positive weights. $|\mathcal{RV}(r)|$ is bounded from above by $|V(G)|-1$ and in most cases, it is a small constant. Then, for the cases where $\mathcal{RV}(r)$ is large, we present a simple randomized algorithm that samples from $\mathcal{RV}(r)$ and performs computations for only the sampled elements. We show that this algorithm provides an $(\epsilon,\delta)$-approximation of the betweenness score of $r$. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that in most cases, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also show that our proposed algorithm computes betweenness scores of all vertices in the sets of sizes 5, 10 and 15, much faster and more accurate than the most efficient existing algorithms.Comment: arXiv admin note: text overlap with arXiv:1704.0735

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

High-Performance Reachability Query Processing under Index Size Restrictions

In this paper, we propose a scalable and highly efficient index structure for the reachability problem over graphs. We build on the well-known node interval labeling scheme where the set of vertices reachable from a particular node is compactly encoded as a collection of node identifier ranges. We impose an explicit bound on the size of the index and flexibly assign approximate reachability ranges to nodes of the graph such that the number of index probes to answer a query is minimized. The resulting tunable index structure generates a better range labeling if the space budget is increased, thus providing a direct control over the trade off between index size and the query processing performance. By using a fast recursive querying method in conjunction with our index structure, we show that in practice, reachability queries can be answered in the order of microseconds on an off-the-shelf computer - even for the case of massive-scale real world graphs. Our claims are supported by an extensive set of experimental results using a multitude of benchmark and real-world web-scale graph datasets.Comment: 30 page

Privacy-Preserving Shortest Path Computation

Navigation is one of the most popular cloud computing services. But in virtually all cloud-based navigation systems, the client must reveal her location and destination to the cloud service provider in order to learn the fastest route. In this work, we present a cryptographic protocol for navigation on city streets that provides privacy for both the client's location and the service provider's routing data. Our key ingredient is a novel method for compressing the next-hop routing matrices in networks such as city street maps. Applying our compression method to the map of Los Angeles, for example, we achieve over tenfold reduction in the representation size. In conjunction with other cryptographic techniques, this compressed representation results in an efficient protocol suitable for fully-private real-time navigation on city streets. We demonstrate the practicality of our protocol by benchmarking it on real street map data for major cities such as San Francisco and Washington, D.C.Comment: Extended version of NDSS 2016 pape

RDF-TR: Exploiting structural redundancies to boost RDF compression

The number and volume of semantic data have grown impressively over the last decade, promoting compression as an essential tool for RDF preservation, sharing and management. In contrast to universal compressors, RDF compression techniques are able to detect and exploit specific forms of redundancy in RDF data. Thus, state-of-the-art RDF compressors excel at exploiting syntactic and semantic redundancies, i.e., repetitions in the serialization format and information that can be inferred implicitly. However, little attention has been paid to the existence of structural patterns within the RDF dataset; i.e. structural redundancy. In this paper, we analyze structural regularities in real-world datasets, and show three schema-based sources of redundancies that underpin the schema-relaxed nature of RDF. Then, we propose RDF-Tr (RDF Triples Reorganizer), a preprocessing technique that discovers and removes this kind of redundancy before the RDF dataset is effectively compressed. In particular, RDF-Tr groups subjects that are described by the same predicates, and locally re-codes the objects related to these predicates. Finally, we integrate RDF-Tr with two RDF compressors, HDT and k2-triples. Our experiments show that using RDF-Tr with these compressors improves by up to 2.3 times their original effectiveness, outperforming the most prominent state-of-the-art techniques

Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical Mechanics and its Application