Facility Location in Evolving Metrics

Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, or urban planning. During the past decade, data has been collected on such networks but has yet to be fully analyzed. We propose to use information on the dynamics of the data to find stable partitions of the network into groups. For that purpose, we introduce a time-dependent, dynamic version of the facility location problem, that includes a switching cost when a client's assignment changes from one facility to another. This might provide a better representation of an evolving network, emphasizing the abrupt change of relationships between subjects rather than the continuous evolution of the underlying network. We show that in realistic examples this model yields indeed better fitting solutions than optimizing every snapshot independently. We present an $O(\log nT)$-approximation algorithm and a matching hardness result, where $n$ is the number of clients and $T$ the number of time steps. We also give an other algorithms with approximation ratio $O(\log nT)$ for the variant where one pays at each time step (leasing) for each open facility

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

Reallocating Multiple Facilities on the Line

We study the multistage $K$-facility reallocation problem on the real line, where we maintain $K$ facility locations over $T$ stages, based on the stage-dependent locations of $n$ agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. $K$-facility reallocation was introduced by de Keijzer and Wojtczak, where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online $K$-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical $K$-server problem, we present a constant-competitive algorithm for $K = 2$ facilities

Online Facility Location with Deletions

In this paper we study three previously unstudied variants of the online Facility Location problem, considering an intrinsic scenario when the clients and facilities are not only allowed to arrive to the system, but they can also depart at any moment. We begin with the study of a natural fully-dynamic online uncapacitated model where clients can be both added and removed. When a client arrives, then it has to be assigned either to an existing facility or to a new facility opened at the client\u27s location. However, when a client who has been also one of the open facilities is to be removed, then our model has to allow to reconnect all clients that have been connected to that removed facility. In this model, we present an optimal O(log(n_{act}) / log log(n_{act}))-competitive algorithm, where n_{act} is the number of active clients at the end of the input sequence. Next, we turn our attention to the capacitated Facility Location problem. We first note that if no deletions are allowed, then one can achieve an optimal competitive ratio of O(log(n) / log(log n)), where n is the length of the sequence. However, when deletions are allowed, the capacitated version of the problem is significantly more challenging than the uncapacitated one. We show that still, using a more sophisticated algorithmic approach, one can obtain an online O(log N + log c log n)-competitive algorithm for the capacitated Facility Location problem in the fully dynamic model, where N is number of points in the input metric and c is the capacity of any open facility

Data clustering

U ovom radu razmatramo problem grupiranja elemenata skupa $mathcal{A}$ u disjunktne neprazne podskupove - klastere, pri čemu pretpostavljamo da su elementi skupa $mathcal{A}$ određeni s jednim ili dva obilježja. Za rješavanje problema koristi se kriterij najmanjih kvadrata te kriterij najmanjih apsolutnih udaljenosti. Naveden je niz primjera koji ilustriraju razlike među tim kriterijima. Izrađena je odgovarajuća programska podrška s ciljem da zainteresirani stručnjaci u svom znanstvenom ili stručnom radu mogu olakšano koristiti ovu metodologiju i pristup.In this paper we consider a clustering problem for a data-points set $mathcal{A}$ into disjoint nonempty subsets - clusters, whereby it is assumed that elements of the set $mathcal{A}$ are determined by one or two characteristics. Least square criteria and least absolute deviation criteria are used for solving the problem. A number of examples illustrating differences between these criteria are given. Corresponding software support is developed for the purpose of facilitating scientific or professional work by using this methodology and approach

Data clustering

U ovom radu razmatramo problem grupiranja elemenata skupa $mathcal{A}$ u disjunktne neprazne podskupove - klastere, pri čemu pretpostavljamo da su elementi skupa $mathcal{A}$ određeni s jednim ili dva obilježja. Za rješavanje problema koristi se kriterij najmanjih kvadrata te kriterij najmanjih apsolutnih udaljenosti. Naveden je niz primjera koji ilustriraju razlike među tim kriterijima. Izrađena je odgovarajuća programska podrška s ciljem da zainteresirani stručnjaci u svom znanstvenom ili stručnom radu mogu olakšano koristiti ovu metodologiju i pristup.In this paper we consider a clustering problem for a data-points set $mathcal{A}$ into disjoint nonempty subsets - clusters, whereby it is assumed that elements of the set $mathcal{A}$ are determined by one or two characteristics. Least square criteria and least absolute deviation criteria are used for solving the problem. A number of examples illustrating differences between these criteria are given. Corresponding software support is developed for the purpose of facilitating scientific or professional work by using this methodology and approach

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

Multi-robot Coverage and Redeployment Algorithms

In this thesis, we focus on two classes of multi-robot task allocation and deployment problems motivated by applications in ride-sourcing transportation networks and service robots: 1) coverage control with multiple robots, and 2) robots servicing tasks arriving sequentially over time. The first problem considers the deployment of multiple robots to cover a domain. The multi-robot problem consists of multiple robots with sensors on-board observing the spatially distributed events in an environment. The objective is to maximize the sensing quality of the events via optimally distributing the robots in the environment. This problem has been studied extensively in the literature and several algorithms have been proposed for different variants of this problem. However, there has been a lack of theoretical results on the quality of the solutions provided by these algorithms. In this thesis, we provide a new distributed multi-robot coverage algorithm with theoretical guarantees on the solution quality, run-time complexity, and communication complexity. The theoretical bound on the solution quality holds for on-board sensors where the sensing quality of the sensors is a sub-additive function of the distance to the event location in convex and non-convex environments. A natural extension of the multi-robot coverage control problem is considered in this thesis where each robot is equipped with a set of different sensors and observes different event types in the environment. Servicing a task in this problem corresponds to sensing an event occurring at a particular location and does not involve visiting the task location. Each event type has a different distribution over the domain. The robots are heterogeneous in that each robot is capable of sensing a subset of the event types. The objective is to deploy the robots into the domain to maximize the total coverage of the multiple event types. We propose a new formulation for the heterogeneous coverage problem. We provide a simple distributed algorithm to maximize the coverage. Then, we extend the result to the case where the event distribution is unknown before the deployment and provide a distributed algorithm and prove the convergence of the approach to a locally optimal solution. The third problem considers the deployment of a set of autonomous robots to efficiently service tasks that arrive sequentially in an environment over time. Each task is serviced when a robot visits the corresponding task location. Robots can then redeploy while waiting for the next task to arrive. The objective is to redeploy the robots taking into account the next N task arrivals. We seek to minimize a linear combination of the expected cost to service tasks and the redeployment cost between task arrivals. In the single robot case, we propose a one-stage greedy algorithm and prove its optimality. For multiple robots, the problem is NP-hard, and we propose two constant-factor approximation algorithms, one for the problem with a horizon of two task arrivals and the other for the infinite horizon when the redeployment cost is weighted more heavily than the service cost. Finally, we extend the second problem to scenarios where the robots are self-interested service units maximizing their payoff. The payoff of a robot is a linear combination of its relocation cost and its expected revenue from servicing the tasks in its vicinity. In this extension, the global objective is either to minimize the expected time or minimize the maximum time to respond to the tasks. We introduce two indirect control methods to relocate the self-interested service units: 1) an information sharing method, and 2) a method that incentivizes relocation with payments. We prove NP-hardness of finding the optimal controls and provide algorithms to find the near-optimal control. We quantify the performance of the proposed algorithms with analytical upper-bounds and real-world data from ride-sourcing applications