60,438 research outputs found
Algorithms on Evolving Graphs
Today's applications process large scale graphs which are evolving in nature. We study new com-
putational and data model to study such graphs. In this framework, the algorithms are unaware
of the changes happening in the evolving graphs. The algorithms are restricted to probe only lim-
ited portion of graph data and are expected to produce a solution close to the optimal one and
that too at each time step. This frameworks assumes no constraints on resources like memory and
computation time. The limited resource for such algorithms is the limited portion of graph that is
allowed to probe (e.g. the number of queries an algorithm can make in order to learn about the
graph). We apply this framework to two classical graph theory problems: Shortest Path problem
and Maximum Flow problem. We study the way algorithm behaves under evolving model and how
does the evolving nature of the graph aects the solution given by the algorithm
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
A generative model for sparse, evolving digraphs
Generating graphs that are similar to real ones is an open problem, while the
similarity notion is quite elusive and hard to formalize. In this paper, we
focus on sparse digraphs and propose SDG, an algorithm that aims at generating
graphs similar to real ones. Since real graphs are evolving and this evolution
is important to study in order to understand the underlying dynamical system,
we tackle the problem of generating series of graphs. We propose SEDGE, an
algorithm meant to generate series of graphs similar to a real series. SEDGE is
an extension of SDG. We consider graphs that are representations of software
programs and show experimentally that our approach outperforms other existing
approaches. Experiments show the performance of both algorithms
Efficient Truss Maintenance in Evolving Networks
Truss was proposed to study social network data represented by graphs. A
k-truss of a graph is a cohesive subgraph, in which each edge is contained in
at least k-2 triangles within the subgraph. While truss has been demonstrated
as superior to model the close relationship in social networks and efficient
algorithms for finding trusses have been extensively studied, very little
attention has been paid to truss maintenance. However, most social networks are
evolving networks. It may be infeasible to recompute trusses from scratch from
time to time in order to find the up-to-date -trusses in the evolving
networks. In this paper, we discuss how to maintain trusses in a graph with
dynamic updates. We first discuss a set of properties on maintaining trusses,
then propose algorithms on maintaining trusses on edge deletions and
insertions, finally, we discuss truss index maintenance. We test the proposed
techniques on real datasets. The experiment results show the promise of our
work
Evolving graphs: dynamical models, inverse problems and propagation
Applications such as neuroscience, telecommunication, online social networking,
transport and retail trading give rise to connectivity patterns that change over time.
In this work, we address the resulting need for network models and computational
algorithms that deal with dynamic links. We introduce a new class of evolving
range-dependent random graphs that gives a tractable framework for modelling and
simulation. We develop a spectral algorithm for calibrating a set of edge ranges from
a sequence of network snapshots and give a proof of principle illustration on some
neuroscience data. We also show how the model can be used computationally and
analytically to investigate the scenario where an evolutionary process, such as an
epidemic, takes place on an evolving network. This allows us to study the cumulative
effect of two distinct types of dynamics
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