86,852 research outputs found
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 and a vertex , we propose a new exact algorithm to
compute betweenness score of . Our algorithm pre-computes a set
, which is used to prune a huge amount of computations that do
not contribute in the betweenness score of . Time complexity of our exact
algorithm depends on and it is respectively
and
for unweighted graphs and weighted graphs with positive weights.
is bounded from above by and in most cases, it
is a small constant. Then, for the cases where is large, we
present a simple randomized algorithm that samples from and
performs computations for only the sampled elements. We show that this
algorithm provides an -approximation of the betweenness
score of . 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
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Exploring Communities in Large Profiled Graphs
Given a graph and a vertex , the community search (CS) problem
aims to efficiently find a subgraph of whose vertices are closely related
to . Communities are prevalent in social and biological networks, and can be
used in product advertisement and social event recommendation. In this paper,
we study profiled community search (PCS), where CS is performed on a profiled
graph. This is a graph in which each vertex has labels arranged in a
hierarchical manner. Extensive experiments show that PCS can identify
communities with themes that are common to their vertices, and is more
effective than existing CS approaches. As a naive solution for PCS is highly
expensive, we have also developed a tree index, which facilitate efficient and
online solutions for PCS
Detecting Blackholes and Volcanoes in Directed Networks
In this paper, we formulate a novel problem for finding blackhole and volcano
patterns in a large directed graph. Specifically, a blackhole pattern is a
group which is made of a set of nodes in a way such that there are only inlinks
to this group from the rest nodes in the graph. In contrast, a volcano pattern
is a group which only has outlinks to the rest nodes in the graph. Both
patterns can be observed in real world. For instance, in a trading network, a
blackhole pattern may represent a group of traders who are manipulating the
market. In the paper, we first prove that the blackhole mining problem is a
dual problem of finding volcanoes. Therefore, we focus on finding the blackhole
patterns. Along this line, we design two pruning schemes to guide the blackhole
finding process. In the first pruning scheme, we strategically prune the search
space based on a set of pattern-size-independent pruning rules and develop an
iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer
strategy to further exploit the pruning results from the first pruning scheme.
Indeed, a target directed graphs can be divided into several disconnected
subgraphs by the first pruning scheme, and thus the blackhole finding can be
conducted in each disconnected subgraph rather than in a large graph. Based on
these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally,
experimental results on real-world data show that the iBlackhole-DC algorithm
can be several orders of magnitude faster than the iBlackhole algorithm, which
has a huge computational advantage over a brute-force method.Comment: 18 page
- β¦