20,403 research outputs found
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
Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality
We consider the all pairs all shortest paths (APASP) problem, which maintains
the shortest path dag rooted at every vertex in a directed graph G=(V,E) with
positive edge weights. For this problem we present a decremental algorithm
(that supports the deletion of a vertex, or weight increases on edges incident
to a vertex). Our algorithm runs in amortized O(\vstar^2 \cdot \log n) time per
update, where n=|V|, and \vstar bounds the number of edges that lie on shortest
paths through any given vertex. Our APASP algorithm can be used for the
decremental computation of betweenness centrality (BC), a graph parameter that
is widely used in the analysis of large complex networks. No nontrivial
decremental algorithm for either problem was known prior to our work. Our
method is a generalization of the decremental algorithm of Demetrescu and
Italiano [DI04] for unique shortest paths, and for graphs with \vstar =O(n), we
match the bound in [DI04]. Thus for graphs with a constant number of shortest
paths between any pair of vertices, our algorithm maintains APASP and BC scores
in amortized time O(n^2 \log n) under decremental updates, regardless of the
number of edges in the graph.Comment: An extended abstract of this paper will appear in Proc. ISAAC 201
Fully Dynamic Single-Source Reachability in Practice: An Experimental Study
Given a directed graph and a source vertex, the fully dynamic single-source
reachability problem is to maintain the set of vertices that are reachable from
the given vertex, subject to edge deletions and insertions. It is one of the
most fundamental problems on graphs and appears directly or indirectly in many
and varied applications. While there has been theoretical work on this problem,
showing both linear conditional lower bounds for the fully dynamic problem and
insertions-only and deletions-only upper bounds beating these conditional lower
bounds, there has been no experimental study that compares the performance of
fully dynamic reachability algorithms in practice. Previous experimental
studies in this area concentrated only on the more general all-pairs
reachability or transitive closure problem and did not use real-world dynamic
graphs.
In this paper, we bridge this gap by empirically studying an extensive set of
algorithms for the single-source reachability problem in the fully dynamic
setting. In particular, we design several fully dynamic variants of well-known
approaches to obtain and maintain reachability information with respect to a
distinguished source. Moreover, we extend the existing insertions-only or
deletions-only upper bounds into fully dynamic algorithms. Even though the
worst-case time per operation of all the fully dynamic algorithms we evaluate
is at least linear in the number of edges in the graph (as is to be expected
given the conditional lower bounds) we show in our extensive experimental
evaluation that their performance differs greatly, both on generated as well as
on real-world instances
Analysis and operational challenges of dynamic ride sharing demand responsive transportation models
There is a wide body of evidence that suggests sustainable mobility is not only a technological question, but that automotive technology will be a part of the solution in becoming a necessary albeit insufficient condition. Sufficiency is emerging as a paradigm shift from car ownership to vehicle usage, which is a consequence of socio-economic changes. Information and Communication Technologies (ICT) now make it possible for a user to access a mobility service to go anywhere at any time. Among the many emerging mobility services, Multiple Passenger Ridesharing and its variants look the most promising. However, challenges arise in implementing these systems while accounting specifically for time dependencies and time windows that reflect users’ needs, specifically in terms of real-time fleet dispatching and dynamic route calculation. On the other hand, we must consider the feasibility and impact analysis of the many factors influencing the behavior of the system – as, for example, service demand, the size of the service fleet, the capacity of the shared vehicles and whether the time window requirements are soft or tight. This paper analyzes - a Decision Support System that computes solutions with ad hoc heuristics applied to variants of Pick Up and Delivery Problems with Time Windows, as well as to Feasibility and Profitability criteria rooted in Dynamic Insertion Heuristics. To evaluate the applications, a Simulation Framework is proposed. It is based on a microscopic simulation model that emulates real-time traffic conditions and a real traffic information system. It also interacts with the Decision Support System by feeding it with the required data for making decisions in the simulation that emulate the behavior of the shared fleet. The proposed simulation framework has been implemented in a model of Barcelona’s Central Business District. The obtained results prove the potential feasibility of the mobility concept.Postprint (published version
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