1,596 research outputs found
Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models
Consider networks on vertices at average density 1 per unit area. We seek
a network that minimizes total length subject to some constraint on journey
times, averaged over source-destination pairs. Suppose journey times depend on
both route-length and number of hops. Then for the constraint corresponding to
an average of 3 hops, the length of the optimal network scales as .
Alternatively, constraining the average number of hops to be 2 forces the
network length to grow slightly faster than order . Finally, if we
require the network length to be O(n) then the mean number of hops grows as
order . Each result is an upper bound in the worst case (of vertex
positions), and a lower bound under randomness or equidistribution assumptions.
The upper bounds arise in simple hub and spoke models, which are therefore
optimal in an order of magnitude sense
Transitions in spatial networks
Networks embedded in space can display all sorts of transitions when their
structure is modified. The nature of these transitions (and in some cases
crossovers) can differ from the usual appearance of a giant component as
observed for the Erdos-Renyi graph, and spatial networks display a large
variety of behaviors. We will discuss here some (mostly recent) results about
topological transitions, `localization' transitions seen in the shortest paths
pattern, and also about the effect of congestion and fluctuations on the
structure of optimal networks. The importance of spatial networks in real-world
applications makes these transitions very relevant and this review is meant as
a step towards a deeper understanding of the effect of space on network
structures.Comment: Corrected version and updated list of reference
Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU
A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to
solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses
binary and integer encoding and genetic operators adapted to this problem. Our
GA is improved by generated initial solution with hubs located at middle nodes.
The obtained experimental results are compared with the best known solutions on
all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own
randomly generated instances up to 6000 nodes. Our approach outperforms most
well-known heuristics in terms of solution quality and time execution and it
allows hitherto unsolved problems to be solved
Travelling on Graphs with Small Highway Dimension
We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP)
in graphs of low highway dimension. This graph parameter was introduced by
Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP
and STP naturally occur for various applications in logistics. It was
previously shown [Feldmann et al. ICALP 2015] that these problems admit a
quasi-polynomial time approximation scheme (QPTAS) on graphs of constant
highway dimension. We demonstrate that a significant improvement is possible in
the special case when the highway dimension is 1, for which we present a
fully-polynomial time approximation scheme (FPTAS). We also prove that STP is
weakly NP-hard for these restricted graphs. For TSP we show NP-hardness for
graphs of highway dimension 6, which answers an open problem posed in [Feldmann
et al. ICALP 2015]
Community structure detection in the evolution of the United States airport network
This is the post-print version of the Article. Copyright © 2013 World Scientific PublishingThis paper investigates community structure in the US Airport Network as it evolved from 1990 to 2010 by looking at six bi-monthly intervals in 1990, 2000 and 2010, using data obtained from the Bureau of Transportation Statistics of the US Department of Transport. The data contained monthly records of origin-destination pairs of domestic airports and the number of passengers carried. The topological properties and the volume of people traveling are both studied in detail, revealing high heterogeneity in space and time. A recently developed community structure detection method, accounting for the spatial nature of these networks, is applied and reveals a picture of the communities within. The patterns of communities plotted for each bi-monthly interval reveal some interesting seasonal variations of passenger flows and airport clusters that do not occupy a single US region. The long-term evolution of the network between those years is explored and found to have consistently improved its stability. The more recent structure of the network (2010) is compared with migration patterns among the four US macro-regions (West, Midwest, Northeast and South) in order to identify possible relationships and the results highlight a clear overlap between US domestic air travel and migration
Cargo Consolidation and Distribution Through a Terminals-Network: A Branch-And-Price Approach
Less-than-truckload is a transport modality that includes many practical variations to convey a number of transportation-requests from the origin locations to their destinations by using the possibility of goods-transshipments on the carrier?s terminals-network. In this way logistics companies are required to consolidate shipments from different suppliers in the outbound vehicles at a terminal of the network. We present a methodology for finding near-optimal solutions to a less-than-truckload shipping modality used for cargo consolidation and distribution through a terminals-network. The methodology uses column generation combined with an incomplete branch-and-price procedure.Fil: Dondo, Rodolfo Gabriel. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica. Universidad Nacional del Litoral. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica; Argentin
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