Robust Fault Tolerant uncapacitated facility location

In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns the robust fault-tolerant version of the uncapacitated facility location problem (RFTFL). In this problem, one or more facilities might fail, and each demand should be supplied by the closest open facility that did not fail. It is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities that did not fail, after the failure of up to \alpha facilities. We present a polynomial time algorithm that yields a 6.5-approximation for this problem with at most one failure and a 1.5 + 7.5\alpha-approximation for the problem with at most \alpha > 1 failures. We also show that the RFTFL problem is NP-hard even on trees, and even in the case of a single failure

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Robust Assignments via Ear Decompositions and Randomized Rounding

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling problems, where a set of tasks needs to be assigned to the available set of machines or personnel (resources), in a way that all tasks have assigned resources, and no two tasks share the same resource. In its nominal form, the resulting computational problem becomes the \emph{assignment problem} on general bipartite graphs. This paper deals with a robust variant of the assignment problem modeling situations where certain edges in the corresponding graph are \emph{vulnerable} and may become unavailable after a solution has been chosen. The goal is to choose a minimum-cost collection of edges such that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all tasks. We present approximation results and hardness proofs for this type of problems, and establish several connections to well-known concepts from matching theory, robust optimization and LP-based techniques.Comment: Full version of ICALP 2016 pape

Algorithms for Constructing Overlay Networks For Live Streaming

We present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. We construct networks consisting of three stages of nodes. The nodes in the first stage are the entry points that act as sources for the live streams. Each source forwards each of its streams to one or more nodes in the second stage that are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage that act as sinks and are located in edge networks near end-users. As the packets in a stream travel from one stage to the next, some of them may be lost. A sink combines the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. Our primary contribution is an algorithm that constructs an overlay network that provably satisfies capacity and reliability constraints to within a constant factor of optimal, and minimizes cost to within a logarithmic factor of optimal. Further in the common case where only the transmission costs are minimized, we show that our algorithm produces a solution that has cost within a factor of 2 of optimal. We also implement our algorithm and evaluate it on realistic traces derived from Akamai's live streaming network. Our empirical results show that our algorithm can be used to efficiently construct large-scale overlay networks in practice with near-optimal cost

Alocação de recursos com máxima conectividade em redes com topologia arbitrária

Orientador: Prof. Dr. Elias P. Duarte Jr.Coorientador: Prof. Dr. Jaime CohenDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 27/08/2018Inclui referências: p.33-35Área de concentração: Ciência da ComputaçãoResumo: O posicionamento de recursos em redes é um problema que encontra diversas variantes, desde o posicionamento de servidores na arquitetura tradicional cliente-servidor, passando pelo posicionamento de controladores em redes SDN, ou caches em redes CDN, entre vários outros. Este trabalho apresenta o problema de posicionar o número mínimo de recursos de modo a maximizar o número de caminhos vértice-disjuntos entre um recurso e seus clientes. Uma das contribuições do trabalho é a prova de que o problema de encontrar o número mínimo de recursos sob essas condições é NP-completo. Uma solução exata para o problema foi implementada e sua execução se mostrou viável em diversas redes de topologia arbitrária. Apresentamos os resultados comparando-os com o problema clássico da p-mediana em que é minimizada a soma das distâncias entre os clientes e seus recursos. Resultados experimentais usando redes de The Internet Topology Zoo avaliam o ganho de conectividade e o aumento da soma das distâncias quando a solução proposta é aplicada. Palavras-chave: Alocamento de Recursos, vértice-conectividade, localização de origens, pmediana.Abstract: Resource placement is a problem that has several variants in computer networks, from server placement in the traditional client-server architecture to the allocation of controllers in SDN networks, or caches in CDN networks, among many others. This work presents the problem of placing the minimum number of resources in order to maximize the number of vertex-disjoint paths between a resource and its clients. One of the contributions of this work is the proof that the problem of finding the minimum number of resources under these conditions is NP-complete. An exact solution to this problem was implemented and experiments showed its feasibility for several arbitrary topology networks. This work presents a comparison between the connectivity based resource location problem with the classical p-median problem in which the sum of the distances between clients and their resources is minimized. Experimental results using networks from The Internet Topology Zoo show both the connectivity gains and the impact on the sum of the distances when the proposed solution is applied to real Internet-based networks. Keywords: Resource Allocation, vertex-connectivity, source location, p-median

Χωροθέτηση και ενοικίαση κοινόχρηστων πόρων. Πειραματική αξιολόγηση αλγορίθμων

Στην εργασία αυτή μελετάται το πρόβλημα της χωροθέτησης (facility location) και ενοικίασης (facility leasing) κοινόχρηστων πόρων και συγκεκριμένα η εκδοχή του προβλήματος που απαιτεί ανοχή σε σφάλματα των κοινόχρηστων πόρων μέσω πλεονασμού (fault tolerant facility location). Εξετάζεται πειραματικά η δυσκολία του προβλήματος της χωροθέτησης καθώς και της ενοικίασης. Επίσης υλοποιούνται και αξιολογούνται δύο ευρέως αποδεκτοί αλγόριθμοι και εξετάζεται αναλυτικά η προσέγγιση τους στις βέλτιστες τιμές και η διακύμανση της με διάφορους παράγοντες. Με βάση τα αποτελέσματα προτείνονται δύο νέοι αλγόριθμοι με καλύτερη συμπεριφορά.In this work, we deal with facility location problems and especially with fault tolerant facility location and offline facility leasing. We perform an experimental study of the difficulty of these two problems. Also two well known algorithms are implemented and evaluated and their approximation to the optimal solution is being studied as it fluctuates when changing various factors. Based on the results we propose two new algorithms which perform even better