PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. PReaCH-indices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances

K-Reach: Who is in Your Small World

We study the problem of answering k-hop reachability queries in a directed graph, i.e., whether there exists a directed path of length k, from a source query vertex to a target query vertex in the input graph. The problem of k-hop reachability is a general problem of the classic reachability (where k=infinity). Existing indexes for processing classic reachability queries, as well as for processing shortest path queries, are not applicable or not efficient for processing k-hop reachability queries. We propose an index for processing k-hop reachability queries, which is simple in design and efficient to construct. Our experimental results on a wide range of real datasets show that our index is more efficient than the state-of-the-art indexes even for processing classic reachability queries, for which these indexes are primarily designed. We also show that our index is efficient in answering k-hop reachability queries.Comment: VLDB201

Access Control in Social Networks: A reachability-Based Approach

Nowadays, social networks are attracting more and more users. These social network subscribers may share personal and sensitive information with a large number of possibly unknown other users, which is in constant evolution. This raises the need of giving users more control on the distribution of their shared content which can be accessed by a community far wider than they may expect. Our concern is to devise and enforce an appropriate access control model for online social networks that enables users to specify their privacy preferences in an expressive way, and, scales well over small, as well as, large social graphs (i.e., regardless to the size of the social graph). In this paper, we propose an access control model for online social networks based on connection characteristics between users, in an extended sense that includes indirect connections. This model provides a conditional access to shared resources based on reachability constraints, between the owner and the requester of a piece of information. Then, we describe the work that we have done to scale the access control enforcement performances over large social graphs. This paper describes PhD work carried out at Télécom ParisTech under the guidance of Talel Abdessalem

Graph Reachability on Parallel Many-Core Architectures

Many modern applications are modeled using graphs of some kind. Given a graph, reachability, that is, discovering whether there is a path between two given nodes, is a fundamental problem as well as one of the most important steps of many other algorithms. The rapid accumulation of very large graphs (up to tens of millions of vertices and edges) from a diversity of disciplines demand efficient and scalable solutions to the reachability problem. General-purpose computing has been successfully used on Graphics Processing Units (GPUs) to parallelize algorithms that present a high degree of regularity. In this paper, we extend the applicability of GPU processing to graph-based manipulation, by re-designing a simple but efficient state-of-the-art graph-labeling method, namely the GRAIL (Graph Reachability Indexing via RAndomized Interval) algorithm, to many-core CUDA-based GPUs. This algorithm firstly generates a label for each vertex of the graph, then it exploits these labels to answer reachability queries. Unfortunately, the original algorithm executes a sequence of depth-first visits which are intrinsically recursive and cannot be efficiently implemented on parallel systems. For that reason, we design an alternative approach in which a sequence of breadth-first visits substitute the original depth-first traversal to generate the labeling, and in which a high number of concurrent visits is exploited during query evaluation. The paper describes our strategy to re-design these steps, the difficulties we encountered to implement them, and the solutions adopted to overcome the main inefficiencies. To prove the validity of our approach, we compare (in terms of time and memory requirements) our GPU-based approach with the original sequential CPU-based tool. Finally, we report some hints on how to conduct further research in the area

Transit Node Routing Reconsidered

Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing by an order of magnitude approaching the time for just finding a CH (which alone has two orders of magnitude larger query time). We also develop a very effective purely graph theoretical locality filter without any compromise in query times. Finally, we show that a specialization to the online many-to-one (or one-to-many) shortest path further speeds up query time by an order of magnitude. This variant even has better query time than the fastest known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201

Efficiently answering reachability and path queries on temporal bipartite graphs

Bipartite graphs are naturally used to model relationships between two different types of entities, such as people-location, authorpaper, and customer-product. When modeling real-world applications like disease outbreaks, edges are often enriched with temporal information, leading to temporal bipartite graphs. While reachability has been extensively studied on (temporal) unipartite graphs, it remains largely unexplored on temporal bipartite graphs. To fill this research gap, in this paper, we study the reachability problem on temporal bipartite graphs. Specifically, a vertex u reaches a vertex w in a temporal bipartite graph G if u and w are connected through a series of consecutive wedges with time constraints. Towards efficiently answering if a vertex can reach the other vertex, we propose an index-based method by adapting the idea of 2-hop labeling. Effective optimization strategies and parallelization techniques are devised to accelerate the index construction process. To better support real-life scenarios, we further show how the index is leveraged to efficiently answer other types of queries, e.g., singlesource reachability query and earliest-arrival path query. Extensive experiments on 16 real-world graphs demonstrate the effectiveness and efficiency of our proposed techniques