1,043 research outputs found
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
Conditional Lower Bounds for Space/Time Tradeoffs
In recent years much effort has been concentrated towards achieving
polynomial time lower bounds on algorithms for solving various well-known
problems. A useful technique for showing such lower bounds is to prove them
conditionally based on well-studied hardness assumptions such as 3SUM, APSP,
SETH, etc. This line of research helps to obtain a better understanding of the
complexity inside P.
A related question asks to prove conditional space lower bounds on data
structures that are constructed to solve certain algorithmic tasks after an
initial preprocessing stage. This question received little attention in
previous research even though it has potential strong impact.
In this paper we address this question and show that surprisingly many of the
well-studied hard problems that are known to have conditional polynomial time
lower bounds are also hard when concerning space. This hardness is shown as a
tradeoff between the space consumed by the data structure and the time needed
to answer queries. The tradeoff may be either smooth or admit one or more
singularity points.
We reveal interesting connections between different space hardness
conjectures and present matching upper bounds. We also apply these hardness
conjectures to both static and dynamic problems and prove their conditional
space hardness.
We believe that this novel framework of polynomial space conjectures can play
an important role in expressing polynomial space lower bounds of many important
algorithmic problems. Moreover, it seems that it can also help in achieving a
better understanding of the hardness of their corresponding problems in terms
of time
Answering Regular Path Queries on Workflow Provenance
This paper proposes a novel approach for efficiently evaluating regular path
queries over provenance graphs of workflows that may include recursion. The
approach assumes that an execution g of a workflow G is labeled with
query-agnostic reachability labels using an existing technique. At query time,
given g, G and a regular path query R, the approach decomposes R into a set of
subqueries R1, ..., Rk that are safe for G. For each safe subquery Ri, G is
rewritten so that, using the reachability labels of nodes in g, whether or not
there is a path which matches Ri between two nodes can be decided in constant
time. The results of each safe subquery are then composed, possibly with some
small unsafe remainder, to produce an answer to R. The approach results in an
algorithm that significantly reduces the number of subqueries k over existing
techniques by increasing their size and complexity, and that evaluates each
subquery in time bounded by its input and output size. Experimental results
demonstrate the benefit of this approach
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