1,200,143 research outputs found
Distance Oracles for Time-Dependent Networks
We present the first approximate distance oracle for sparse directed networks
with time-dependent arc-travel-times determined by continuous, piecewise
linear, positive functions possessing the FIFO property.
Our approach precomputes approximate distance summaries from
selected landmark vertices to all other vertices in the network. Our oracle
uses subquadratic space and time preprocessing, and provides two sublinear-time
query algorithms that deliver constant and approximate
shortest-travel-times, respectively, for arbitrary origin-destination pairs in
the network, for any constant . Our oracle is based only on
the sparsity of the network, along with two quite natural assumptions about
travel-time functions which allow the smooth transition towards asymmetric and
time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of
EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An
extended abstract also appeared in the 41st International Colloquium on
Automata, Languages, and Programming (ICALP 2014, track-A
Diffusion in networks with time-dependent transmission conditions
We study diffusion in a network which is governed by non-autonomous Kirchhoff
conditions at the vertices of the graph. Also the diffusion coefficients may
depend on time. We prove at first a result on existence and uniqueness using
form methods. Our main results concern the long-term behavior of the solution.
In the case when the conductivity and the diffusion coefficients match (so that
mass is conserved) we show that the solution converges exponentially fast to an
equilibrium. We also show convergence to a special solution in some other
cases.Comment: corrected typos, references removed, revised Lemma A.3. Appl. Math.
Optim. (2013
Optimal Time-dependent Sequenced Route Queries in Road Networks
In this paper we present an algorithm for optimal processing of
time-dependent sequenced route queries in road networks, i.e., given a road
network where the travel time over an edge is time-dependent and a given
ordered list of categories of interest, we find the fastest route between an
origin and destination that passes through a sequence of points of interest
belonging to each of the specified categories of interest. For instance,
considering a city road network at a given departure time, one can find the
fastest route between one's work and his/her home, passing through a bank, a
supermarket and a restaurant, in this order. The main contribution of our work
is the consideration of the time dependency of the network, a realistic
characteristic of urban road networks, which has not been considered previously
when addressing the optimal sequenced route query. Our approach uses the A*
search paradigm that is equipped with an admissible heuristic function, thus
guaranteed to yield the optimal solution, along with a pruning scheme for
further reducing the search space. In order to compare our proposal we extended
a previously proposed solution aimed at non-time dependent sequenced route
queries, enabling it to deal with the time-dependency. Our experiments using
real and synthetic data sets have shown our proposed solution to be up to two
orders of magnitude faster than the temporally extended previous solution.Comment: 10 pages, 12 figures To be published as a short paper in the 23rd ACM
SIGSPATIA
Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
Network science is an interdisciplinary endeavor, with methods and
applications drawn from across the natural, social, and information sciences. A
prominent problem in network science is the algorithmic detection of
tightly-connected groups of nodes known as communities. We developed a
generalized framework of network quality functions that allowed us to study the
community structure of arbitrary multislice networks, which are combinations of
individual networks coupled through links that connect each node in one network
slice to itself in other slices. This framework allows one to study community
structure in a very general setting encompassing networks that evolve over
time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting
material. This is the accepted version of the manuscript (the definitive
version appeared in Science), with typographical corrections included her
K shortest paths in stochastic time-dependent networks
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs
Social networks: evolving graphs with memory dependent edges
The plethora, and mass take up, of digital communication tech-
nologies has resulted in a wealth of interest in social network data
collection and analysis in recent years. Within many such networks
the interactions are transient: thus those networks evolve over time.
In this paper we introduce a class of models for such networks using
evolving graphs with memory dependent edges, which may appear and
disappear according to their recent history. We consider time discrete
and time continuous variants of the model. We consider the long
term asymptotic behaviour as a function of parameters controlling
the memory dependence. In particular we show that such networks
may continue evolving forever, or else may quench and become static
(containing immortal and/or extinct edges). This depends on the ex-
istence or otherwise of certain inïŹnite products and series involving
age dependent model parameters. To test these ideas we show how
model parameters may be calibrated based on limited samples of time
dependent data, and we apply these concepts to three real networks:
summary data on mobile phone use from a developing region; online
social-business network data from China; and disaggregated mobile
phone communications data from a reality mining experiment in the
US. In each case we show that there is evidence for memory dependent
dynamics, such as that embodied within the class of models proposed
here
System optimizing flow and externalities in time-dependent road networks
This paper develops a framework for analysing and calculating system optimizing flow and
externalities in time-dependent road networks. The externalities are derived by using a novel
sensitivity analysis of traffic models. The optimal network flow is determined by solving a
state-dependent optimal control problem, which assigns traffic such that the total system cost
of the network system is minimized. This control theoretic formulation can work with general
travel time models and cost functions. Deterministic queue is predominantly used in dynamic
network models. The analysis in this paper is more general and is applied to calculate the
system optimizing flow for Frieszâs whole link traffic model. Numerical examples are
provided for illustration and discussion. Finally, some concluding remarks are given
- âŠ