The cable trench problem: combining the shortest path and minimum spanning tree problems

Vasko, Francis J.; Barbieri, Robert S.; Rieksts, Brian Q.; Reitmeyer, Kenneth L.; Stott, Kenneth L.

doi:10.1016/s0305-0548(00)00083-6

Cited by 29 publications

(64 citation statements)

References 7 publications

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“…It provides a smooth, Gaussian distribution of visibilities in the (u,v) plane, and thus a near-Gaussian NenuFAR beam pattern. The layout of trenches and cables connecting the LF tiles to the FR606 backend was optimized using a reasonable cost ratio per unit length of trench/cable in input to a specific optimization algorithm [5]. The obtained LF tiles distribution and layout is displayed in Fig.3.…”

Section: The Mini-arraymentioning

confidence: 99%

NenUFAR: Instrument description and science case

Zarka

Tagger

Denis³

et al. 2015

2015 International Conference on Antenna Theory and Techniques (ICATT)

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International audienceNenuFAR is both a giant extension of the LOFAR and a large standalone instrument in the low-frequency range (10-85 MHz). It was designed in Nançay with national and international collaboration. Antenna radiators were modeled on the LWA antenna design whereas preamplifiers were designed in France. Antennas will be distributed in 96 mini-arrays of 19 dual-polarized elements, densely covering a disk of 400 m in diameter. A few mini-arrays are expected to lie at distances of 2-3 km. A silent control-command system was designed, and the computer dialog with LOFAR defined. Receivers will include the LOFAR backend, a local beamformer and a local correlator. NenuFAR is in construction in Nançay and it was recently granted by the SKA office the official label of SKA pathfinder. Its exploitation will expand the scope of LOFAR scientific studies as well as permit new studies, preparing for SKA science. The NenuFAR concept has many points in common with GURT (the Giant Ukrainian Radio Telescope), with which it shares some technical studies, an its exploitation will benefit from a coordination with UTR-2. We describe the instrument, technical developments and science case

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Section: The Mini-arraymentioning

confidence: 99%

NenUFAR: Instrument description and science case

Zarka

Tagger

Denis³

et al. 2015

2015 International Conference on Antenna Theory and Techniques (ICATT)

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“…In addition, we solved instances of a specific class of CNRP models known as the cable trench problem (CTP) (Vasko et al, 2002) constructed from data available in the library of vehicle routing problem instances maintained by author Ralphs (www.BranchAndCut.org/VRP/data). Because the CTP is a difficult model, we created the instances by randomly sampling sets of 15 customers to create networks that were generally easy enough to solve repeatedly in the several tests that we ran, but varied enough to draw reasonably broad conclusions about the methods.…”

Section: Setupmentioning

confidence: 99%

An improved algorithm for solving biobjective integer programs

2006

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A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that provides access to all Pareto outcomes. Extensive computational tests on instances of the biobjective knapsack problem and a capacitated network routing problem are presented.

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“…The system is to be designed so as to minimize the cost of digging the trenches, proportional to their length, plus the cost of the cables, also proportional to the total length of cable. We call this problem the p-cable-trench problem (p-CTP), since it is an extension of the cable trench problem by Vasko et al [1], in which there is only one facility whose location is known.…”

Section: Introductionmentioning

confidence: 99%

“…The problem we solve, besides being a generalization of the cable trench problem of Vasko et al [1], can also be considered as a generalization of other well known problems in the location and network design fields: the p-median problem (p-MP, [3]), consisting of locating p facilities and allocating customers to their closest facilities, in such a way as to minimize the total cable length (or distance) between facilities and demand; and the network design problem (NDP, [4]), that finds a network that connects a set of known points, at the least construction cost and travel or delay cost.…”

Section: Introductionmentioning

confidence: 99%

“…Vasko et al [1] show that the cable trench problem is NPcomplete, even though it is a combination of the shortest path problem and the minimum spanning tree problem, both polynomially solvable. They analyze the properties of the solutions, formulate an integer programming model of the problem and propose a heuristic procedure that finds good solutions to this problem.…”

Section: Introductionmentioning

confidence: 99%

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