A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application

This paper provides an initial introduction to, and definition of, the ‘Dynamically Powered Relays for a Flexible Optical Network’ (DPR-FON) problem for opto-electro-optical (OEO) regenerators used in optical networks. In such networks, optical transmission parameters can be varied dynamically as traffic patterns change. This will provide different bandwidths, but also change the regeneration limits as a result. To support this flexibility, OEOs (‘relays’) may be switched on and off as required, thus saving power. DPR-FON is shown to be NP-complete; consequently, solving such a dynamic problem in real-time requires a fast heuristic capable of delivering an acceptable approximation to the optimal configuration with low complexity. In this paper, just such an algorithm is developed, implemented, and evaluated against more computationally-demanding alternatives for two known cases. A number of real-world extensions are considered as the paper develops, combining to produce the ‘Generalised Dynamically Powered Relays for a Flexible Optical Network’ (GDPR-FON) problem. This, too, is analysed and an associated fast heuristic proposed, along with an exploration of the further research that is required

Regenerator Location Problem and survivable extensions: A hub covering location perspective

Cataloged from PDF version of article.In a telecommunications network the reach of an optical signal is the maximum distance it can traverse before its quality degrades. Regenerators are devices to extend the optical reach. The regenerator placement problem seeks to place the minimum number of regenerators in an optical network so as to facilitate the communication of a signal between any node pair. In this study, the Regenerator Location Problem is revisited from the hub location perspective directing our focus to applications arising in transportation settings. Two new dimensions involving the challenges of survivability are introduced to the problem. Under partial survivability, our designs hedge against failures in the regeneration equipment only, whereas under full survivability failures on any of the network nodes are accounted for by the utilization of extra regeneration equipment. All three variations of the problem are studied in a unifying framework involving the introduction of individual flow-based compact formulations as well as cut formulations and the implementation of branch and cut algorithms based on the cut formulations. Extensive computational experiments are conducted in order to evaluate the performance of the proposed solution methodologies and to gain insights from realistic instances. (C) 2014 Elsevier Ltd. All rights reserved

Integer programming formulation for contention aware connected dominating set in wireless multi-hop network

Efficient data propagation across the mobile nodes is an essential concern in wireless networks. Broadcasting with Minimum Connected Dominating Set (MCDS) is used to reduce redundant transmission. Contention occurs when a group of nodes want to transmit over a shared channel at the same time. During contention, nodes defer transmissions for a random time. Using Contention-aware Connected Dominating Set (CACDS) to minimize contention is a new concept. We study computationally (using CPLEX) Integer Programming for MCDS and CACDS and use Benders Decomposition to solve the problem. To find a connected dominating set, we use one state-of-art approach based on the shortest path algorithm, and ours one is based on the number of connected components.We propose IP formulation of selection forwarding-nodes based on Dominant Pruning and Contention-aware Dominant Pruning. The result shows that our approach performs better than the state-of-art approach in large networks. CACDS results better in minimizing contention

Reformulations and solution algorithms for the maximum leaf spanning tree problem

Given a graph G = (V, E), the maximum leaf spanning tree problem (MLSTP) is to find a spanning tree of G with as many leaves as possible. The problem is easy to solve when G is complete. However, for the general case, when the graph is sparse, it is proven to be NP-hard. In this paper, two reformulations are proposed for the problem. The first one is a reinforced directed graph version of a formulation found in the literature. The second recasts the problem as a Steiner arborescence problem over an associated directed graph. Branch-and-Cut algorithms are implemented for these two reformulations. Additionally, we also implemented an improved version of a MLSTP Branch-and-Bound algorithm, suggested in the literature. All of these algorithms benefit from pre-processing tests and a heuristic suggested in this paper. Computational comparisons between the three algorithms indicate that the one associated with the first reformulation is the overall best. It was shown to be faster than the other two algorithms and is capable of solving much larger MLSTP instances than previously attempted in the literature. © 2010 Springer-Verlag.73289311Aneja, Y.P., An integer linear programming approach to the Steiner problem in graphs (1980) Networks, 10, pp. 167-178Chopra, S., Gorres, E., Rao, M.R., Solving Steiner tree problem on a graph using branch and cut (1992) ORSA J Comput, 4 (3), pp. 320-335Edmonds, J., Matroids and the greedy algorithm (1971) Math Prog, 1, pp. 127-136Fernandes, M.L., Gouveia, L., Minimal spanning trees with a constraint on the number of leaves (1998) Eur J Oper Res, 104, pp. 250-261Fujie, T., An exact algorithm for the maximum-leaf spanning tree problem (2003) Comput Oper Res, 30, pp. 1931-1944Fujie, T., The maximum-leaf spanning tree problem: Formulations and facets (2004) Networks, 43 (4), pp. 212-223Galbiati, G., Maffioli, F., Morzenti, A., A short note on the approximability of the maximum leaves spanning tree problem (1994) Info Proc Lett, 52, pp. 45-49Garey, M.R., Johnson, D.S., (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness, , New York: W. H. FreemanGuha, S., Khuller, S., Approximation algorithms for connected dominating sets (1998) Algorithmica, 20 (4), pp. 374-387Koch, T., Martin, A., Solving Steiner tree problems in graphs to optimality (1998) Networks, 33, pp. 207-232Lu, H., Ravi, R., Approximating maximum leaf spanning trees in almost linear time (1998) J Algo, 29, pp. 132-141Poggi de Aragão, M., Uchoa, E., Werneck, R., Dual heuristics on the exact solution of large Steiner problems (2001) Electron Notes Discret Math, 7, pp. 150-153Polzin, T., Daneshmand, S.V., Improved algorithms for the Steiner problem in networks (2001) Discret Appl Math, 112 (1-3), pp. 263-300Resende, M.G.C., Pardalos, P.M., (2006) Handbook of Optimization in Telecommunications, , New York: SpringerSolis-Oba, S., 2-approximation algorithm for finding a spanning tree with maximum number of leaves (1998) Lect Notes Comput Sci, 1461, pp. 441-452Wong, R., A dual ascent approach for Steiner tree problems on a directed graph (1984) Math Prog, 28, pp. 271-28

Maximum Leaf Spanning Tree Problem Benchmarks

This database contains experimental problems designed to study the Maximum Leaf Spanning Tree Problem (MLSTP). More specifically, the dataset can be used to evaluate the performance of algorithms developed to solve MLSTP. We generated a set of large-scale instances. We also collected existing benchmarks {Lucena, A., Maculan, N. & Simonetti, L. Reformulations and solution algorithms for the maximum leaf spanning tree problem. Comput Manag Sci 7, 289–311 (2010). https://doi.org/10.1007/s10287-009-0116-5, GENDRON, B., LUCENA, A., DA CUNHA, A. S. & SIMONETTI, L. (2014), "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem", INFORMS Journal on Computing, 26, 645-657, doi: https://doi.org/10.1287/ijoc.2013.0589.} which were included in the dataset. These instances are used in a study entitled “A New Formulation and Algorithm for Maximum Leaf Spanning Tree Problem with an Application in the Forest Fire Detection” which will be appeared in ----. DOI reference: http://dx.doi.org/10.17632/w98s4tvfn8.

Maximum Leaf Spanning Tree Problem Benchmarks

This database contains experimental problems designed to study the Maximum Leaf Spanning Tree Problem (MLSTP). More specifically, the dataset can be used to evaluate the performance of algorithms developed to solve MLSTP. We generated a set of large-scale instances. We also collected existing benchmarks {Lucena, A., Maculan, N. & Simonetti, L. Reformulations and solution algorithms for the maximum leaf spanning tree problem. Comput Manag Sci 7, 289–311 (2010). https://doi.org/10.1007/s10287-009-0116-5, GENDRON, B., LUCENA, A., DA CUNHA, A. S. & SIMONETTI, L. (2014), "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem", INFORMS Journal on Computing, 26, 645-657, doi: https://doi.org/10.1287/ijoc.2013.0589.} which were included in the dataset. These instances are used in a study entitled “A New Formulation and Algorithm for Maximum Leaf Spanning Tree Problem with an Application in the Forest Fire Detection” which will be appeared in ----. DOI reference: http://dx.doi.org/10.17632/w98s4tvfn8.