762 research outputs found
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
Finding the K shortest hyperpaths using reoptimization
The shortest hyperpath problem is an extension of the classical shortest path problem and has applications in many different areas. Recently, algorithms for finding the K shortest hyperpaths in a directed hypergraph have been developed by Andersen, Nielsen and Pretolani. In this paper we improve the worst-case computational complexity of an algorithm for finding the K shortest hyperpaths in an acyclic hypergraph. This result is obtained by applying new reoptimization techniques for shortest hyperpaths. The algorithm turns out to be quite effective in practice and has already been successfully applied in the context of stochastic time-dependent networks, for finding the K best strategies and for solving bicriterion problems.Network programming; Directed hypergraphs; K shortest hyperpaths; K shortest paths
Bicriterion a priori route choice in stochastic time-dependent networks.
In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy corresponds to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and min-max criteria are considered and a solution method based on the two-phase approach is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to previously reported results for the time-adaptive caseStochastic time-dependent networks; Bicriterion shortest path; A priori route choice; Two-phase method
A note on “Multicriteria adaptive paths in stochastic, time-varying networks”
In a recent paper, Opasanon and Miller-Hooks study multicriteria adaptive paths in stochastic time-varying networks. They propose a label correcting algorithm for finding the full set of efficient strategies. In this note we show that their algorithm is not correct, since it is based on a property that does not hold in general. Opasanon and Miller-Hooks also propose an algorithm for solving a parametric problem. We give a simplified algorithm which is linear in the input size.Multiple objective programming; shortest paths; stochastic time-dependent networks; time-adaptive strategies
Utility-service provision as an example of a complex system
Utility–service provision is a process in which products are transformed by appropriate devices into services satisfying human needs and wants. Utility products required for these transformations are usually delivered to households via separate infrastructures, i.e., real-world networks such as, e.g., electricity grids and water distribution systems. owever, provision of utility products in appropriate quantities does not itself guarantee hat the required services will be delivered because the needs satisfaction task requires not only utility products but also fully functional devices. Utility infrastructures form complex networks and have been analyzed as such using complex network theory. However, little research has been conducted to date on integration of utilities and associated services
within one complex network. This paper attempts to fill this gap in knowledge by modelling utility–service provision within a household with a hypergraph in which products and services are represented with nodes whilst devices are hyperedges
spanning between them. Since devices usually connect more than two nodes, a
standard graph would not suffice to describe utility–service provision problem
and therefore a hypergraph was chosen as a more appropriate representation
of the system. This paper first aims to investigate the properties of hypergraphs,
such as cardinality of nodes, betweenness, degree distribution, etc. Additionally,
it shows how these properties can be used while solving and optimizing utility–
service provision problem, i.e., constructing a so-called transformation graph. The
transformation graph is a standard graph in which nodes represent the devices,
storages for products, and services, while edges represent the product or service
carriers. Construction of different transformation graphs to a defined utility–
service provision problem is presented in the paper to show how the methodology
is applied to generate possible solutions to provision of services to households
under given local conditions, requirements and constraints
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Alignment and integration of complex networks by hypergraph-based spectral clustering
Complex networks possess a rich, multi-scale structure reflecting the
dynamical and functional organization of the systems they model. Often there is
a need to analyze multiple networks simultaneously, to model a system by more
than one type of interaction or to go beyond simple pairwise interactions, but
currently there is a lack of theoretical and computational methods to address
these problems. Here we introduce a framework for clustering and community
detection in such systems using hypergraph representations. Our main result is
a generalization of the Perron-Frobenius theorem from which we derive spectral
clustering algorithms for directed and undirected hypergraphs. We illustrate
our approach with applications for local and global alignment of
protein-protein interaction networks between multiple species, for tripartite
community detection in folksonomies, and for detecting clusters of overlapping
regulatory pathways in directed networks.Comment: 16 pages, 5 figures; revised version with minor corrections and
figures printed in two-column format for better readability; algorithm
implementation and supplementary information available at Google code at
http://schype.googlecode.co
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