Dynamic Facility Location via Exponential Clocks

The \emph{dynamic facility location problem} is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: there is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities, and connect every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use \emph{no clustering} and we allow clients to connect through paths of \emph{arbitrary lengths}. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem

Fully Dynamic Consistent Facility Location

We consider classic clustering problems in fully dynamic data streams, where data elements can be both inserted and deleted. In this context, several parameters are of importance: (1) the quality of the solution after each insertion or deletion, (2) the time it takes to update the solution, and (3) how different consecutive solutions are. The question of obtaining efficient algorithms in this context for facility location, k-median and k-means has been raised in a recent paper by Hubert-Chan et al. [WWW'18] and also appears as a natural follow-up on the online model with recourse studied by Lattanzi and Vassilvitskii [ICML'17] (i.e.: in insertion-only streams). In this paper, we focus on general metric spaces and mainly on the facility location problem. We give an arguably simple algorithm that maintains a constant factor approximation, with O(n log n) update time, and total recourse O(n). This improves over the naive algorithm which consists in recomputing a solution at each time step and that can take up to O(n^2) update time, and O(n^2) total recourse. These bounds are nearly optimal: in general metric space, inserting a point take O(n) times to describe the distances to other points, and we give a simple lower bound of O(n) for the recourse. Moreover, we generalize this result for the k-medians and k-means problems: our algorithm maintains a constant factor approximation in time O˜(n+k^2). We complement our analysis with experiments showing that the cost of the solution maintained by our algorithm at any time t is very close to the cost of a solution obtained by quickly recomputing a solution from scratch at time t while having a much better running time

Habanero-Scala: A Hybrid Programming model integrating Fork/Join and Actor models

This study presents a hybrid concurrent programming model combining the previously developed Fork-Join model (FJM) and Actor model (AM). With the advent of multi-core computers, there is a renewed interest in programming models that reduce the burden of reasoning about and writing efficient concurrent programs. The proposed hybrid model shows how the divide-and-conquer approach of the FJM and the no-shared mutable state and event-driven philosophy of the AM can be combined to solve certain classes of problems more efficiently and productively than either of the aforementioned models individually. The hybrid model adds actor creation and coordination to into the FJM, while also enabling parallelization within actors. This study uses the Habanero-Java and Scala programming languages as the base for the FJM and AM respectively, and provides an implementation of the hybrid model as an extension of the Scala language called Habanero-Scala. The hybrid model adds to the foundations of parallel programs, and to the tools available for the programmer to aid in productivity and performance while developing parallel software

A Simple and Deterministic Competitive Algorithm for Online Facility Location

This paper presents a deterministic and efficient algorithm for online facility location. The algorithm is based on a simple hierarchical partitioning and is extremely simple to implement. It also applies to a variety of models, i.e., models where the facilities can be placed anywhere in the region, or only at customer sites, or only at fixed locations. The paper shows that the algorithm is O(log n)-competitive under these various models, where n is the total number of customers. It also shows that the algorithm is O(1)-competitive with high probability and for any arrival order when customers are uniformly distributed or when they follow a distribution satisfying a smoothness property. Experimental results for a variety of scenarios indicate that the algorithm behaves extremely well in practice.

Security Configuration Management in Intrusion Detection and Prevention Systems

Intrusion Detection and/or Prevention Systems (IDPS) represent an important line of defense against a variety of attacks that can compromise the security and proper functioning of an enterprise information system. IDPSs can be network or host-based and can collaborate in order to provide better detection of malicious traffic. Although several IDPS systems have been proposed, their appropriate con figuration and control for e effective detection/ prevention of attacks and efficient resource consumption is still far from trivial. Another concern is related to the slowing down of system performance when maximum security is applied, hence the need to trade o between security enforcement levels and the performance and usability of an enterprise information system. In this dissertation, we present a security management framework for the configuration and control of the security enforcement mechanisms of an enterprise information system. The approach leverages the dynamic adaptation of security measures based on the assessment of system vulnerability and threat prediction, and provides several levels of attack containment. Furthermore, we study the impact of security enforcement levels on the performance and usability of an enterprise information system. In particular, we analyze the impact of an IDPS con figuration on the resulting security of the network, and on the network performance. We also analyze the performance of the IDPS for different con figurations and under different traffic characteristics. The analysis can then be used to predict the impact of a given security con figuration on the prediction of the impact on network performance

Local and online algorithms for facility location

Diese Arbeit beschäftigt sich mit dem Facility Location Problem. Dies ist ein Optimierungsproblem, bei dem festgelegt werden muss an welchen Positionen Ressourcen zur Verfügung gestellt werden, so dass diese von Nutzern gut erreicht werden können. Es sollen dabei Kosten minimiert werden, die zum einen durch Bereitstellung von Ressourcen und zum anderen durch Verbindungskosten zwischen Nutzern und Ressourcen entstehen. In dieser Arbeit werden drei Varianten des Problems modelliert und neue Algorithmen für sie entwickelt und bezüglich ihres Approximationsfaktors und ihrer Laufzeit analysiert. Jede dieser drei untersuchten Varianten hat einen besonderen Schwerpunkt. Bei der ersten Varianten handelt es sich um ein Online Problem, da hier die Eingabe nicht von Anfang an bekannt ist, sondern Schritt für Schritt enthüllt wird. Die Schwierigkeit hierbei besteht darin unwiderrufliche Entscheidungen treffen zu müssen ohne dabei die Zukunft zu kennen und trotzdem eine zu jeder Zeit gute Lösung angeben zu können. Der Schwerpunkt der zweiten Variante liegt auf Lokalität. Hier soll eine Lösung verteilt und nur mit Hilfe von lokalen Information berechnet werden. Schließlich beschäftigt sich die dritte Variante mit einer verteilten Berechnung, bei welcher nur eine stark beschränkte Datenmenge verschickt werden darf und dabei trotzdem ein sehr guter Approximationsfaktor erreicht werden muss. Die bei der Analyse der Approximationsfaktoren bzw. der Kompetitivität verwendeten TecTechniken basieren zum großen Teil auf Abschätzung der primalen Lösung mit Hilfe einer Lösung des zugehörigen dualen Problems. Für die Modellierung von Lokalität wird das weitverbreitete LOCAL Modell verwendet. In diesem Modell werden für die Algorithmen subpolynomielle obere Laufzeitschranken gezeigt.The topic of this thesis is approximation and online algorithms for an optimization problem known as Facility Location. This problem, or one of its many variants, arises as a sub problem in many practical applications, and is thus of significant importance in the field of Operations Research. Furthermore, it is also one of the most studied optimization problems in theoretical computer science with hundreds of research papers published during the last decades. In this thesis, we focus on the theoretical aspects of Facility Location by designing and analyzing approximation and online algorithms. Our algorithms deal with three distinct scenarios in which Facility Location occurs: (i) networks that are exposed to perpetual changes, (ii) wireless sensor networks with strong locality constraints, and (iii) distributed settings where the focus lies, first and foremost, on the quality of the computed approximation. Chapter 2 covers Scenario (i). It presents an online algorithm designed for a highly dynamic network where additional nodes are perpetually added. The difficulty here is that these new nodes' requests have to be handled efficiently without any knowledge of the network's future development. Scenario (ii) is considered in Chapter 3. Two distributed algorithms for wireless sensor networks are presented here. Due to the nodes' limited communication range, locality is of high importance in this scenario. Additional aspects like inaccurate measurement data, power consumption, and dynamics are also taken into account. Finally, Scenario (iii) is considered in Chapter 4. Our objective here is to distributedly compute a solution with an approximation ratio that is as close as possible to the best achievable ratio. In order to accomplish this, we allow, compared to Scenario (ii), a higher running time, but still require that the algorithm terminates in sub-linear time.Tag der Verteidigung: 28.10.2013Paderborn, Univ., Diss., 201

Algorithms For Clustering Problems:Theoretical Guarantees and Empirical Evaluations

Clustering is a classic topic in combinatorial optimization and plays a central role in many areas, including data science and machine learning. In this thesis, we first focus on the dynamic facility location problem (i.e., the facility location problem in evolving metrics). We present a new LP-rounding algorithm for facility location problems, which yields the first constant factor approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on clients and facilities, and connects every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use \emph{no clustering} and we enable clients to connect through paths of \emph{arbitrary lengths}. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem. Furthermore, we present both empirical and theoretical aspects of the $k$-means problem. The best known algorithm for $k$-means with a provable guarantee is a simple local-search heuristic that yields an approximation guarantee of $9+\epsilon$, a ratio that is known to be tight with respect to such methods. We overcome this barrier by presenting a new primal-dual approach that enables us (1) to exploit the geometric structure of $k$-means and (2) to satisfy the hard constraint that at most $k$ clusters are selected without deteriorating the approximation guarantee. Our main result is a $6.357$-approximation algorithm with respect to the standard LP relaxation. Our techniques are quite general and we also show improved guarantees for the general version of $k$-means where the underlying metric is not required to be Euclidean and for $k$-median in Euclidean metrics. We also improve the running time of our algorithm to almost linear running time and still maintain a provable guarantee. We compare our algorithm with {\sc K-Means++} (a widely studied algorithm) and show that we obtain better accuracy with comparable and even better running time