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18
BranchandCutandPrice for Capacitated Connected Facility Location
, 2010
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Modelling the hop constrained connected facility location problem on layered graphs
 IN: INTERNATIONAL SYMPOSIUM ON COMBINATORIAL OPTIMIZATION (ISCO 2010), HAMMAMET, TUNISIA. ELECTRONIC NOTES IN DISCRETE MATHEMATICS
, 2010
"... Gouveia et al. [3] show how to model the Hop Constrained Minimum Spanning tree problem as Steiner tree problem on a layered graph. Following their ideas, we provide three possibilities to model the Hop Constrained (HC) Connected Facility Location problem (ConFL) as ConFL on layered graphs. We show t ..."
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Gouveia et al. [3] show how to model the Hop Constrained Minimum Spanning tree problem as Steiner tree problem on a layered graph. Following their ideas, we provide three possibilities to model the Hop Constrained (HC) Connected Facility Location problem (ConFL) as ConFL on layered graphs. We show that on all three layered graphs the respective LP relaxations of two cut based models are of the same quality. In our computational study we compare a compact hopindexed tree model against the two cut based models on the simplest layered graph. We provide results for instances with up to 1300 nodes and 115000 arcs.
Layered graph approaches to the hop constrained connected facility location problem
 INFORMS Journal on Computing
, 2013
"... Given a set of customers, a set of potential facility locations and some interconnection nodes, the goal of the Connected Facility Location problem (ConFL) is to find the minimumcost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. ..."
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Given a set of customers, a set of potential facility locations and some interconnection nodes, the goal of the Connected Facility Location problem (ConFL) is to find the minimumcost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. The sum of costs needed for building the Steiner tree, facility opening costs and the assignment costs needs to be minimized. If the number of edges between a prespecified node (the socalled root) and each open facility is limited, we speak of the Hop Constrained Facility Location problem (HC ConFL). This problem is of importance in the design of datamanagement and telecommunication networks. In this article we provide the first theoretical and computational study for this new problem that has not been studied in the literature so far. We propose two disaggregation techniques that enable to model HC ConFL: i) as directed (asymmetric) ConFL on layered graphs, or ii) as the Steiner arborescence problem (SA) on layered graphs. This allows for usage of bestknown MIP models for ConFL or SA to solve the corresponding hop constrained problem to optimality. In our polyhedral study, we compare the obtained models with respect to the quality of their LP lower bounds. These models are finally computationally compared in an extensive computational study on a set of publicly available benchmark instances. Optimal values are reported for instances with up to 1300 nodes and 115 000 edges.
MIP modeling of incremental connected facility location
 In Proceedings of the 5th International Network Optimization Conference (INOC), volume 6701 of Lecture Notes in Computer Science
, 2011
"... Abstract. We consider the incremental connected facility location problem, in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of cus ..."
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Abstract. We consider the incremental connected facility location problem, in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of customers to be served, the assignment of these customers to the open facilities, and a network that connects the open facilities. Once a customer is served, it must also be served in subsequent periods. Furthermore, in each time period the total demand of all customers served must be at least equal to a given minimum coverage requirement for that period. The objective is to maximize the net present value of the network, which is given by the discounted revenues of serving the customers and by the discounted investments and maintenance costs for the facilities and the network. We study different MIP models for this problem, discuss some valid inequalities to strengthen these formulations, and present a branch and cut algorithm for finding its solution. Finally, we report (preliminary) computational results of our implementation of this algorithm. 1
A Node Splitting Technique for Two Level Network Design Problems with Transition Nodes
, 2011
"... The Two Level Network Design (TLND) problem arises when local broadband access networks are planned in areas, where no existing infrastructure can be used, i.e., in the socalled greenfield deployments. Mixed strategies of FiberToTheHome and FiberToTheCurb, i.e., some customers are served by c ..."
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The Two Level Network Design (TLND) problem arises when local broadband access networks are planned in areas, where no existing infrastructure can be used, i.e., in the socalled greenfield deployments. Mixed strategies of FiberToTheHome and FiberToTheCurb, i.e., some customers are served by copper cables, some by fiber optic lines, can be modeled by an extension of the TLND. We are given two types of customers (primary and secondary), an additional set of Steiner nodes and fixed costs for installing either a primary or a secondary technology on each edge. The TLND problem seeks a minimum cost connected subgraph obeying a treetree topology, i.e., the primary nodes are connected by a rooted primary tree; the secondary nodes can be connected using both primary and secondary technology. In this paper we study an important extension of TLND in which additional transition costs need to be paid for intermediate facilities placed at the transition nodes, i.e., nodes where the change of technology takes place. We call this problem TLNDF. The introduction of transition node costs leads to a problem with a rich structure per
The Constrained Virtual Steiner Arborescence Problem: Formal Definition, SingleCommodity Integer Programming Formulation and Computational Evaluation
, 2013
"... Abstract. As the Internet becomes more virtualized and softwaredefined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Bas ..."
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Abstract. As the Internet becomes more virtualized and softwaredefined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Based on this new networking paradigm, we formulate the Constrained Virtual Steiner Arborescence Problem (CVSAP) which asks for optimal locations to perform innetwork processing, in order to jointly minimize processing costs and network traffic while respecting link and node capacities. We prove that CVSAP cannot be approximated (unless NP = P), and accordingly, develop the exact algorithm VirtuCast to compute optimal solutions to CVSAP. VirtuCast consists of: (1) a compact singlecommodity flow Integer Programming (IP) formulation; (2) a flow decomposition algorithm to reconstruct individual routes from the IP solution. The compactness of the IP formulation allows for computing lower bounds even on large instances quickly, speeding up the algorithm. We rigorously prove VirtuCast’s correctness. To complement our theoretical findings, we have implemented VirtuCast and present an extensive computational evaluation, showing that VirtuCast can solve realistically sized instances (close to) optimality. We show that VirtuCast significantly improves upon naive multicommodity formulations and also initiate the study of primal heuristics to generate feasible solutions during the branchandbound process. 1
VirtuCast: Multicast and Aggregation with InNetwork Processing An Exact SingleCommodity Algorithm
"... Abstract. As the Internet becomes more virtualized and softwaredefined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Bas ..."
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Abstract. As the Internet becomes more virtualized and softwaredefined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Based on this new networking paradigm, we formulate the Constrained Virtual Steiner Arborescence Problem (CVSAP) which asks for optimal locations to perform innetwork processing, in order to jointly minimize processing costs and network traffic while respecting link and node capacities. We prove that CVSAP cannot be approximated (unless NP ⊆ P), and accordingly, develop the exact algorithm VirtuCast to compute optimal solutions to CVSAP. VirtuCast consists of: (1) a compact singlecommodity flow Integer Programming (IP) formulation; (2) a flow decomposition algorithm to reconstruct individual routes from the IP solution. The compactness of the IP formulation allows for computing lower bounds even on large instances quickly, speeding up the algorithm significantly. We rigorously prove VirtuCast’s correctness and show its applicability to solve realistically sized instances close to optimality.