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

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

FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search

We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees. We evaluate FLASH on several real, high-dimensional datasets from different domains, including text, malicious URL, click-through prediction, social networks, etc. Our experiments shed new light on the difficulties associated with datasets having several million dimensions. Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH. FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force ($n^2D$), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results

Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs

Many problems in areas as diverse as recommendation systems, social network analysis, semantic search, and distributed root cause analysis can be modeled as pattern search on labeled graphs (also called "heterogeneous information networks" or HINs). Given a large graph and a query pattern with node and edge label constraints, a fundamental challenge is to nd the top-k matches ac- cording to a ranking function over edge and node weights. For users, it is di cult to select value k . We therefore propose the novel notion of an any-k ranking algorithm: for a given time budget, re- turn as many of the top-ranked results as possible. Then, given additional time, produce the next lower-ranked results quickly as well. It can be stopped anytime, but may have to continues until all results are returned. This paper focuses on acyclic patterns over arbitrary labeled graphs. We are interested in practical algorithms that effectively exploit (1) properties of heterogeneous networks, in particular selective constraints on labels, and (2) that the users often explore only a fraction of the top-ranked results. Our solution, KARPET, carefully integrates aggressive pruning that leverages the acyclic nature of the query, and incremental guided search. It enables us to prove strong non-trivial time and space guarantees, which is generally considered very hard for this type of graph search problem. Through experimental studies we show that KARPET achieves running times in the order of milliseconds for tree patterns on large networks with millions of nodes and edges.Comment: To appear in WWW 201

Keyword Search on RDF Graphs - A Query Graph Assembly Approach

Keyword search provides ordinary users an easy-to-use interface for querying RDF data. Given the input keywords, in this paper, we study how to assemble a query graph that is to represent user's query intention accurately and efficiently. Based on the input keywords, we first obtain the elementary query graph building blocks, such as entity/class vertices and predicate edges. Then, we formally define the query graph assembly (QGA) problem. Unfortunately, we prove theoretically that QGA is a NP-complete problem. In order to solve that, we design some heuristic lower bounds and propose a bipartite graph matching-based best-first search algorithm. The algorithm's time complexity is $O(k^{2l} \cdot l^{3l})$, where $l$ is the number of the keywords and $k$ is a tunable parameter, i.e., the maximum number of candidate entity/class vertices and predicate edges allowed to match each keyword. Although QGA is intractable, both $l$ and $k$ are small in practice. Furthermore, the algorithm's time complexity does not depend on the RDF graph size, which guarantees the good scalability of our system in large RDF graphs. Experiments on DBpedia and Freebase confirm the superiority of our system on both effectiveness and efficiency