A Constant Factor Approximation for the Single Sink Edge Installation Problem

We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(log |R|), where R is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant load balanced facility location and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor

Approximation Algorithms for Union and Intersection Covering Problems

In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least k nodes of an edge-weighted graph. Here nodes and edges represent requests and items, respectively. In this paper, we initiate the study of a new family of multi-layer covering problems. Each such problem consists of a collection of h distinct instances of a standard covering problem (layers), with the constraint that all layers share the same set of requests. We identify two main subfamilies of these problems: - in a union multi-layer problem, a request is satisfied if it is satisfied in at least one layer; - in an intersection multi-layer problem, a request is satisfied if it is satisfied in all layers. To see some natural applications, consider both generalizations of k-MST. Union k-MST can model a problem where we are asked to connect a set of users to at least one of two communication networks, e.g., a wireless and a wired network. On the other hand, intersection k-MST can formalize the problem of connecting a subset of users to both electricity and water. We present a number of hardness and approximation results for union and intersection versions of several standard optimization problems: MST, Steiner tree, set cover, facility location, TSP, and their partial covering variants

On Exploiting Flow Allocation with Rate Adaptation for Green Networking

Network power consumption can be reduced considerably by adapting link data rates to their offered traffic loads. In this paper, we exploit how to leverage rate adaptation for green networking by studying the following flow allocation problem in wired networks: Given a set of candidate paths for each end-to-end communication session, determine how to allocate flow (data traffic) along these paths such that power consumption is minimized, subject to the constraint that the traffic demand of each session is satisfied. According to recent measurement studies, we consider a discrete step increasing function for link power consumption. We address both the single and multiple communication session cases and formulate them as two optimization problems, namely, the Single-session Flow allocation with Rate Adaptation Problem (SF-RAP), and the Multisession Flow Allocation with Rate Adaptation Problem (MFRAP). We first show that both problems are NP-hard and present a Mixed Integer Linear Programming (MILP) formulation for the MF-RAP to provide optimal solutions. Then we present a 2-approximation algorithm for the SF-RAP, and a general flow allocation framework as well as an LP-based heuristic algorithm for the MF-RAP. Simulation results show that the algorithm proposed for the SF-RAP consistently outperforms a shortest path based baseline solution and the algorithms proposed for the MF-RAP provide close-to-optimal solutions

LP-Based Approximation Algorithms for Facility Location in Buy-at-Bulk Network Design

Abstract We study problems that integrate buy-at-bulk network design into the classical (connected) facility location problem. In such problems, we need to open facilities, build a routing network, and route every client demand to an open facility. Furthermore, capacities of the edges can be purchased in discrete units from K different cable types with costs that satisfy economies of scale. We extend the linear programming frame-work of Talwar [IPCO 2002] for the single-source buy-at-bulk problem to these variants and prove integrality gap upper bounds for both facility location and connected facility location buy-at-bulk problems. For the unconnected variant we prove an integrality gap bound of O(K), and for the connected version, we get an improved bound of O(1).

Network Design via Core Detouring for Problems Without a Core

Some of the currently best-known approximation algorithms for network design are based on random sampling. One of the key steps of such algorithms is connecting a set of source nodes to a random subset of them. In a recent work [Eisenbrand,Grandoni,Rothvo\ss,Schäfer-SODA'08], a new technique, \emph{core-detouring}, is described to bound the mentioned connection cost. This is achieved by defining a sub-optimal connection scheme, where paths are detoured through a proper connected subgraph (core). The cost of the detoured paths is bounded against the cost of the core and of the distances from the sources to the core. The analysis then boils down to proving the \emph{existence} of a convenient core. For some problems, such as connected facility location and single-sink rent-or-buy, the choice of the core is obvious (i.e., the Steiner tree in the optimum solution). Other, more complex network design problems do not exhibit any such core. In this paper we show that core-detouring can be nonetheless successfully applied. The basic idea is constructing a convenient core by manipulating the optimal solution in a proper (not necessarily trivial) way. We illustrate that by presenting improved approximation algorithms for two well-studied problems: virtual private network design and single-sink buy-at-bulk

Fiber to the home

In den letzten Jahren gab es zunehmenden Bedarf für breitbandige Telekommunikations Netzwerke. Eine von Telekommunikationsunternehmen angewandte Strategie um die Bandbreite entlang der last-mile des Netzwerks zu erhöhen ist, Glasfaserkabel direkt bis zum Endkunden zu verlegen. Diese Strategie wird fiber to the home (FTTH) genannt. In der vorliegenden Arbeit wird das local access network design problem (LAN) und die Variante mit prize-collecting (PC-LAN) verwendet, um das Problem der FTTH Planung zu modellieren. Das LAN Problem zielt darauf ab eine kostenminimale Lösung zu finden und gestattet es sowohl verschiedene Kabeltechnologien und existierende Infrastruktur, als auch die Zusatzkosten zu modellieren, die anfallen wenn neue Verbindungen hergestellt werden. Darüber hinaus, erlaubt das PC-LAN Problem den Aspekt zu modellieren, dass nicht unbedingt alle Kunden mit FTTH versorgt werden müssen. Stattdessen wird eine Teilmenge der Kunden versorgt mit dem Ziel den Profit zu maximieren. Um LAN und PC-LAN Problem Instanzen zu lösen, werden folgende Methoden des Operations Research angewandt: Preprocessing, ganzzahlige Programmierung, Stärkung der mathematischen Modelle durch Disaggregation der Variablen, Benders' Dekomposition und adaptive Multi-Start-Heuristiken. In einem Projekt von Universität Wien und Telekom Austria wurden große FTTH Datensätze untersucht und die hier vorgestellten Methoden entworfen. Diese Lösungsansätze wurden als Computerprogramme implementiert und ihre Tauglichkeit zur Behandlung von FTTH Planungsfragen konnte gezeigt werden.Within recent years the request for broadband telecommunication networks has been constantly increasing. A strategy employed by telecommunication companies to increase the bandwidth on the last mile of the network is to lay optical fiber directly to the end customer. This strategy is denoted as fiber to the home (FTTH). In this thesis the local access network design problem (LAN) and its prize-collecting variant (PC-LAN) are used to formalize the planning of FTTH networks. The LAN problem asks for a cost minimal solution and allows to model different cable technologies, existing infrastructure and the overhead cost incurred by building new connections. In addition, the PC-LAN problem covers the aspect, that not all customers must necessarily be connected with FTTH, but instead we search for a subset of customers in order to maximize profits. To solve LAN and PC-LAN instances, the following operations research methods are employed: Preprocessing, mixed integer programming, model strengthening by variable disaggregation, Benders' decomposition and adaptive multi-start heuristics. In a project between University of Vienna and Telekom Austria, large real world data sets for FTTH planning were investigated and the methods presented in this thesis have been designed. These solution methods have been implemented as computer programs and empirically verified to be reasonable approaches to FTTH network design problems