Super-Fast Distributed Algorithms for Metric Facility Location

This paper presents a distributed O(1)-approximation algorithm, with expected-$O(\log \log n)$ running time, in the $\mathcal{CONGEST}$ model for the metric facility location problem on a size-$n$ clique network. Though metric facility location has been considered by a number of researchers in low-diameter settings, this is the first sub-logarithmic-round algorithm for the problem that yields an O(1)-approximation in the setting of non-uniform facility opening costs. In order to obtain this result, our paper makes three main technical contributions. First, we show a new lower bound for metric facility location, extending the lower bound of B\u{a}doiu et al. (ICALP 2005) that applies only to the special case of uniform facility opening costs. Next, we demonstrate a reduction of the distributed metric facility location problem to the problem of computing an O(1)-ruling set of an appropriate spanning subgraph. Finally, we present a sub-logarithmic-round (in expectation) algorithm for computing a 2-ruling set in a spanning subgraph of a clique. Our algorithm accomplishes this by using a combination of randomized and deterministic sparsification.Comment: 15 pages, 2 figures. This is the full version of a paper that appeared in ICALP 201

A Super-Fast Distributed Algorithm for Bipartite Metric Facility Location

The \textit{facility location} problem consists of a set of \textit{facilities} $\mathcal{F}$, a set of \textit{clients} $\mathcal{C}$, an \textit{opening cost} $f_i$ associated with each facility $x_i$, and a \textit{connection cost} $D(x_i,y_j)$ between each facility $x_i$ and client $y_j$. The goal is to find a subset of facilities to \textit{open}, and to connect each client to an open facility, so as to minimize the total facility opening costs plus connection costs. This paper presents the first expected-sub-logarithmic-round distributed O(1)-approximation algorithm in the $\mathcal{CONGEST}$ model for the \textit{metric} facility location problem on the complete bipartite network with parts $\mathcal{F}$ and $\mathcal{C}$. Our algorithm has an expected running time of $O((\log \log n)^3)$ rounds, where $n = |\mathcal{F}| + |\mathcal{C}|$. This result can be viewed as a continuation of our recent work (ICALP 2012) in which we presented the first sub-logarithmic-round distributed O(1)-approximation algorithm for metric facility location on a \textit{clique} network. The bipartite setting presents several new challenges not present in the problem on a clique network. We present two new techniques to overcome these challenges. (i) In order to deal with the problem of not being able to choose appropriate probabilities (due to lack of adequate knowledge), we design an algorithm that performs a random walk over a probability space and analyze the progress our algorithm makes as the random walk proceeds. (ii) In order to deal with a problem of quickly disseminating a collection of messages, possibly containing many duplicates, over the bipartite network, we design a probabilistic hashing scheme that delivers all of the messages in expected-$O(\log \log n)$ rounds.Comment: 22 pages. This is the full version of a paper that appeared in DISC 201

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

Large-Scale Distributed Algorithms for Facility Location with Outliers

This paper presents fast, distributed, O(1)-approximation algorithms for metric facility location problems with outliers in the Congested Clique model, Massively Parallel Computation (MPC) model, and in the k-machine model. The paper considers Robust Facility Location and Facility Location with Penalties, two versions of the facility location problem with outliers proposed by Charikar et al. (SODA 2001). The paper also considers two alternatives for specifying the input: the input metric can be provided explicitly (as an n x n matrix distributed among the machines) or implicitly as the shortest path metric of a given edge-weighted graph. The results in the paper are: - Implicit metric: For both problems, O(1)-approximation algorithms running in O(poly(log n)) rounds in the Congested Clique and the MPC model and O(1)-approximation algorithms running in O~(n/k) rounds in the k-machine model. - Explicit metric: For both problems, O(1)-approximation algorithms running in O(log log log n) rounds in the Congested Clique and the MPC model and O(1)-approximation algorithms running in O~(n/k) rounds in the k-machine model. Our main contribution is to show the existence of Mettu-Plaxton-style O(1)-approximation algorithms for both Facility Location with outlier problems. As shown in our previous work (Berns et al., ICALP 2012, Bandyapadhyay et al., ICDCN 2018) Mettu-Plaxton style algorithms are more easily amenable to being implemented efficiently in distributed and large-scale models of computation

Design Issues of Reserved Delivery Subnetworks, Doctoral Dissertation, May 2006

The lack of per-flow bandwidth reservation in today\u27s Internet limits the quality of service that an information service provider can provide. This dissertation introduces the reserved delivery subnetwork (RDS), a mechanism that provides consistent quality of service by implementing aggregate bandwidth reservation. A number of design and deployment issues of RDSs are studied. First, the configuration problem of a single-server RDS is formulated as a minimum concave cost network flow problem, which properly reflects the economy of bandwidth aggregation, but is also an NP-hard problem. To make the RDS configuration problem tractable, an efficient approximation heuristic, largest demands first (LDF), is presented and studied. In addition, performance improvements with local search heuristic is investigated. A traditional negative cycle reduction and a new negative bicycle reduction algorithms are applied and evaluated. The study of RDS configuration problems is then extended to multi-server RDSs. The configuration problem can be similarly formulated as the single-server RDS configuration problem; however, the major challenge of multi-server RDS configuration is the optimal server locations. A number of server placement algorithms are evaluated using simulations. The simulation results show that a class of greedy algorithms provide the best solutions. In addition to configuration problem, the dynamic load redistribution mechanism is studied to improve the tolerance to server failures. A configuration algorithm to build redistribution subnetworks is proposed and evaluated to deal with single server failures in a group of servers. Besides the exclusive bandwidth access, there are potentials to further improve end-to-end performance in an RDS because end hosts can utilize the knowledge about the underlying networks to achieve better performance than in the ordinary Internet. These improvements are illustrated with a source traffic regulation technique to resolve the unbalanced bandwidth utilization problem in an RDS. A per-connection and an aggregated regulation algorithm for single-server and multi-server RDSs are presented and studied

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Resource and Supply Allocation and Relief Center Location for Humanitarian Logistics

This dissertation examines two salient issues that arise in the strategic planning of disaster management operations for providing relief to populations that are impacted by a disaster, such as an earthquake. The first issue is the alleviation of destitution faced by affected populations in the immediate aftermath of a disaster. The second is the establishment of an infrastructure for provision of relief, for a much longer period of time, until normalcy is restored. Central to the alleviation of destitution is the avoidance of critical shortages in meeting the demand for relief supplies. The literature on pro-active and strategic planning of relief operations primarily focuses on the minimization of unmet demand to address shortfalls in meeting required levels of relief. However, compromised handling capacity, which can be attributed to insufficient manpower, can deteriorate provision of supplies. The same is true for transport capacity of which there can be limited capability in the immediate aftermath of a disaster. Better planning and management of resource and supply allocations is made possible by quantifying the destitution faced by affected populations and revealing its relationship to delays in provision of relief. The second issue is that of on-going provision of relief, whether supplies, resources, or information. Key to such relief provision is the establishment of relief centers that are easily accessible by affected populations using the available transport network. Both issues are addressed using mathematical programming in the context of strategic planning of humanitarian logistics for a catastrophic earthquake in Istanbul, of which there is a high probability of occurrence over the first thirty years of the 21st Century. Bringing visibility to the impact of critical shortages on affected and vulnerable population segments caused by the lack of any commodity has not been addressed in the literature on relief operations. Extant research is on post-disaster reactive operations. While disasters cannot be forecasted with pinpoint accuracy, it is possible to devise pro-active contingency plans for regions of the world that are prone to natural disasters. Proactive contingency plans, proposed in this dissertation, focus on the strategic planning of the geographical and temporal staging of relief supplies with a view to minimize the impact of critical shortages. The manner in which destitution can be alleviated by revealing the impact of delays in the provision of supplies, the availability of transport units, and the deployment of manpower has not been explicitly addressed in the literature. Delays can lead to a critical shortage of one or more of the supplied commodities causing destitution which is quantified by the number of periods a population segment is without provision of supplies. The destitution levels of population segments as they are replenished with supplies that become available over time are tracked using a complex mixed-integer goal programming model which is developed. The model is used to study the impacts of delays in providing relief on destitution and criticality among affected populations for a highly probable (62±15%), catastrophic earthquake in the greater Istanbul area. Making use of the estimates for seismic hazard and damage for the districts of Istanbul that are provided in the report published by Japan International Cooperation Agency (JICA) in collaboration with the Istanbul Metropolitan Municipality, an empirical study reveals the impacts of the three sources of delay and their significance for different types of supplies and need in different segments of impacted populations. Centers for relief operations meet the continued need for resources, supplies, and information among affected populations until the restoration of normalcy. The literature on location-allocation of centers for humanitarian logistics have employed location methodology which comprises a suite of models such as the p-median or maximal cover models. These models have not accounted for traffic networks, the travel times on links of the network, and the potential delays that can occur due to congestion on the links. The centrality of the existing traffic network and travel times on links of the network as the flow of traffic increases in locating relief centers is not accounted for in such models. In this dissertation two significant aspects of locating centers are addressed in a new mathematical programming model: First, the number of, and locations for, the centers to be established to provide a given level of access to populations in various neighborhoods of the affected region. Second, the implementation plan for the centers, detailing the identification of the specific centers that are made available over time. Further, the model also addresses the two key issues of the implied capacity of each center and of the assumed patterns of access to, and demand at, each center. These two issues are intertwined in that varying frequencies of access among different population segments dictate that populations be provided with equally, with respect to travel time, accessible alternative relief centers. The inherent stochasticity of frequency of access needs necessarily to be accounted for when determining the locations of centers. The optimization model that is developed to determine locations of supply sites and locations of centers is a two-stage stochastic mixed integer non-linear programming model over a network in which supplies move from selected supply sites to selected relief centers and subsequently acquired by affected populations accessing the relief centers over the traffic network. The travel time on each link grows exponentially with the traffic, or flow, on the link. The nonlinearity reflects the behavior of populations headed from any neighborhood, i.e. population center, to any one of centers that can be made available to them. The model identifies relief centers to locate from among a set of potential sites for centers such that the total travel time over the network is optimized. The model assumes different levels of access for populations in different neighborhoods that are defined by pre-specified distance thresholds for access to a center. The solution of the model is addressed via a piece-wise linear approximation of the objective function which is separable, convex, and monotone increasing. The model is employed in a computational study for the identification of supply sites and relief centers for stochastically varying frequencies of access by populations in the one hundred twenty-three neighborhood of Greater Istanbul. The stochastic variations examined range from fixed daily, bi-weekly, and weekly access frequencies to totally randomized access frequencies during an hour. Further, a computational study reveals an implementation plan for establishing relief centers to ensure that easy access with minimal degradation of travel times is enabled for all populations in the neighborhoods of Greater Istanbul

On the design of efficient caching systems

Content distribution is currently the prevalent Internet use case, accounting for the majority of global Internet traffic and growing exponentially. There is general consensus that the most effective method to deal with the large amount of content demand is through the deployment of massively distributed caching infrastructures as the means to localise content delivery traffic. Solutions based on caching have been already widely deployed through Content Delivery Networks. Ubiquitous caching is also a fundamental aspect of the emerging Information-Centric Networking paradigm which aims to rethink the current Internet architecture for long term evolution. Distributed content caching systems are expected to grow substantially in the future, in terms of both footprint and traffic carried and, as such, will become substantially more complex and costly. This thesis addresses the problem of designing scalable and cost-effective distributed caching systems that will be able to efficiently support the expected massive growth of content traffic and makes three distinct contributions. First, it produces an extensive theoretical characterisation of sharding, which is a widely used technique to allocate data items to resources of a distributed system according to a hash function. Based on the findings unveiled by this analysis, two systems are designed contributing to the abovementioned objective. The first is a framework and related algorithms for enabling efficient load-balanced content caching. This solution provides qualitative advantages over previously proposed solutions, such as ease of modelling and availability of knobs to fine-tune performance, as well as quantitative advantages, such as 2x increase in cache hit ratio and 19-33% reduction in load imbalance while maintaining comparable latency to other approaches. The second is the design and implementation of a caching node enabling 20 Gbps speeds based on inexpensive commodity hardware. We believe these contributions advance significantly the state of the art in distributed caching systems