3,447 research outputs found
A note on âMulticriteria adaptive paths in stochastic, time-varying networksâ
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
Modeling the Internet
We model the Internet as a network of interconnected Autonomous Systems which
self-organize under an absolute lack of centralized control. Our aim is to
capture how the Internet evolves by reproducing the assembly that has led to
its actual structure and, to this end, we propose a growing weighted network
model driven by competition for resources and adaptation to maintain
functionality in a demand and supply ``equilibrium''. On the demand side, we
consider the environment, a pool of users which need to transfer information
and ask for service. On the supply side, ASs compete to gain users, but to be
able to provide service efficiently, they must adapt their bandwidth as a
function of their size. Hence, the Internet is not modeled as an isolated
system but the environment, in the form of a pool of users, is also a
fundamental part which must be taken into account. ASs compete for users and
big and small come up, so that not all ASs are identical. New connections
between ASs are made or old ones are reinforced according to the adaptation
needs. Thus, the evolution of the Internet can not be fully understood if just
described as a technological isolated system. A socio-economic perspective must
also be considered.Comment: Submitted to the Proceedings of the 3rd International Conference
NEXT-SigmaPh
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
OPTIMIZATION OF STATION LOCATIONS AND TRACK ALIGNMENTS FOR RAIL TRANSIT LINES
Designing urban rail transit systems is a complex problem, which involves the determination of station locations, track geometry, right-of-way type, and various other system characteristics. The existing studies overlook the complex interactions between railway alignments and station locations in a practical design process. This study proposes a comprehensive methodology that helps transit planners to concurrently optimize station locations and track alignments for an urban rail transit line. The modeling framework resolves the essential trade-off between an economically efficient system with low initial and operation cost and an effective system that provides convenient service for the public. The proposed method accounts for various geometric requirements and real-world design constraints for track alignment and stations plans. This method integrates a genetic algorithm (GA) for optimization with comprehensive evaluation of various important measures of effectiveness based on processing Geographical Information System (GIS) data.
The base model designs the track alignment through a sequence of preset stations. Detailed assumptions and formulations are presented for geometric requirements, design constraints, and evaluation criteria. Three extensions of the base model are proposed. The first extension explicitly incorporates vehicle dynamics in the design of track alignments, with the objective of better balancing the initial construction cost with the operation and user costs recurring throughout the system's life cycle. In the second extension, an integrated optimization model of rail transit station locations and track alignment is formulated for situations in which the locations of major stations are not preset. The concurrent optimization model searches through additional decision variables for station locations and station types, estimate rail transit demand, and incorporates demand and station cost in the evaluation framework. The third extension considers the existing road network when selecting sections of the alignment. Special algorithms are developed to allow the optimized alignment to take advantage of links in an existing network for construction cost reduction, and to account for disturbances of roadway traffic at highway/rail crossings. Numerical results show that these extensions have significantly enhanced the applicability of the proposed optimization methodology in concurrently selecting rail transit station locations and generating track alignment
Geometry of the Complex of Curves I: Hyperbolicity
The Complex of Curves on a Surface is a simplicial complex whose vertices are
homotopy classes of simple closed curves, and whose simplices are sets of
homotopy classes which can be realized disjointly. It is not hard to see that
the complex is finite-dimensional, but locally infinite. It was introduced by
Harvey as an analogy, in the context of Teichmuller space, for Tits buildings
for symmetric spaces, and has been studied by Harer and Ivanov as a tool for
understanding mapping class groups of surfaces.
In this paper we prove that, endowed with a natural metric, the complex is
hyperbolic in the sense of Gromov. In a certain sense this hyperbolicity is an
explanation of why the Teichmuller space has some negative-curvature properties
in spite of not being itself hyperbolic: Hyperbolicity in the Teichmuller space
fails most obviously in the regions corresponding to surfaces where some curve
is extremely short. The complex of curves exactly encodes the intersection
patterns of this family of regions (it is the "nerve" of the family), and we
show that its hyperbolicity means that the Teichmuller space is "relatively
hyperbolic" with respect to this family. A similar relative hyperbolicity
result is proved for the mapping class group of a surface.
We also show that the action of pseudo-Anosov mapping classes on the complex
is hyperbolic, with a uniform bound on translation distance.Comment: Revised version of IMS preprint. 36 pages, 6 Figure
Advanced Multilevel Node Separator Algorithms
A node separator of a graph is a subset S of the nodes such that removing S
and its incident edges divides the graph into two disconnected components of
about equal size. In this work, we introduce novel algorithms to find small
node separators in large graphs. With focus on solution quality, we introduce
novel flow-based local search algorithms which are integrated in a multilevel
framework. In addition, we transfer techniques successfully used in the graph
partitioning field. This includes the usage of edge ratings tailored to our
problem to guide the graph coarsening algorithm as well as highly localized
local search and iterated multilevel cycles to improve solution quality even
further. Experiments indicate that flow-based local search algorithms on its
own in a multilevel framework are already highly competitive in terms of
separator quality. Adding additional local search algorithms further improves
solution quality. Our strongest configuration almost always outperforms
competing systems while on average computing 10% and 62% smaller separators
than Metis and Scotch, respectively
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
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