1,149 research outputs found
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
Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data
As data are increasingly modeled as graphs for expressing complex
relationships, the tree pattern query on graph-structured data becomes an
important type of queries in real-world applications. Most practical query
languages, such as XQuery and SPARQL, support logical expressions using
logical-AND/OR/NOT operators to define structural constraints of tree patterns.
In this paper, (1) we propose generalized tree pattern queries (GTPQs) over
graph-structured data, which fully support propositional logic of structural
constraints. (2) We make a thorough study of fundamental problems including
satisfiability, containment and minimization, and analyze the computational
complexity and the decision procedures of these problems. (3) We propose a
compact graph representation of intermediate results and a pruning approach to
reduce the size of intermediate results and the number of join operations --
two factors that often impair the efficiency of traditional algorithms for
evaluating tree pattern queries. (4) We present an efficient algorithm for
evaluating GTPQs using 3-hop as the underlying reachability index. (5)
Experiments on both real-life and synthetic data sets demonstrate the
effectiveness and efficiency of our algorithm, from several times to orders of
magnitude faster than state-of-the-art algorithms in terms of evaluation time,
even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page
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
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
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
- …