An O(1)-Approximation for Minimum Spanning Tree Interdiction

Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is minimum spanning tree (MST) interdiction. Here, an undirected multigraph with nonnegative edge weights and positive interdiction costs on its edges is given, together with a positive budget B. The goal is to find a subset of edges R, whose total interdiction cost does not exceed B, such that removing R leads to a graph where the weight of an MST is as large as possible. Frederickson and Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction, where m is the number of edges. Since then, no further progress has been made regarding approximations, and the question whether MST interdiction admits an O(1)-approximation remained open. We answer this question in the affirmative, by presenting a 14-approximation that overcomes two main hurdles that hindered further progress so far. Moreover, based on a well-known 2-approximation for the metric traveling salesman problem (TSP), we show that our O(1)-approximation for MST interdiction implies an O(1)-approximation for a natural interdiction version of metric TSP

External-Memory Graph Algorithms

We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we call the “proximate neighbors” problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms. Time-forward processing. We present a general technique for evaluating circuits (or “circuit-like” computations) in external memory. We also usethis in a deterministic list ranking algorithm. Deterministic 3-coloring of a cycle. We give several optimal methods for 3-coloring a cycle, which can be used as a subroutine for finding large independent sets for list ranking. Our ideas go beyond a straightforward PRAM simulation, and may be of independent interest. External depth-first search. We discuss a method for performing depth first search and solving related problems efficiently in external memory. Our technique can be used in conjunction with ideas due to Ullman and Yannakakis in order to solve graph problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold. Our techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation

A Randomized Linear-Time Algorithm for Finding Minimum Spanning Trees

We present a randomized linear-time algorithm for finding a minimum spanning tree in a connected graph with edge weights. The algorithm is a modification of one proposed by Karger and uses random sampling in combination with a recently discovered linear-time algorithm for verifying a minimum spanning tree. Our computational model is a unit-cost random-access machine with the restriction that the only operations allowed on edge weights are binary comparisons. 1 Introduction We consider the problem of finding a minimum spanning tree in a connected graph with real-valued edge weights. This problem has a long and rich history; the first fully realized algorithm was devised by Boruvka in the 1920's [3]. An informative survey paper by Graham and Hell [9] describes the history of the problem up to 1985. In the last two decades faster and faster algorithms were found, the fastest being an algorithm of Gabow, Galil, and Spencer [7] (see also [8]), with a running time of O(m log fi(m; n)) on a ..

Algorithms for Fundamental Problems in Computer Networks.

Traditional studies of algorithms consider the sequential setting, where the whole input data is fed into a single device that computes the solution. Today, the network, such as the Internet, contains of a vast amount of information. The overhead of aggregating all the information into a single device is too expensive, so a distributed approach to solve the problem is often preferable. In this thesis, we aim to develop efficient algorithms for the following fundamental graph problems that arise in networks, in both sequential and distributed settings. Graph coloring is a basic symmetry breaking problem in distributed computing. Each node is to be assigned a color such that adjacent nodes are assigned different colors. Both the efficiency and the quality of coloring are important measures of an algorithm. One of our main contributions is providing tools for obtaining colorings of good quality whose existence are non-trivial. We also consider other optimization problems in the distributed setting. For example, we investigate efficient methods for identifying the connectivity as well as the bottleneck edges in a distributed network. Our approximation algorithm is almost-tight in the sense that the running time matches the known lower bound up to a poly-logarithmic factor. For another example, we model how the task allocation can be done in ant colonies, when the ants may have different capabilities in doing different tasks. The matching problems are one of the classic combinatorial optimization problems. We study the weighted matching problems in the sequential setting. We give a new scaling algorithm for finding the maximum weight perfect matching in general graphs, which improves the long-standing Gabow-Tarjan's algorithm (1991) and matches the running time of the best weighted bipartite perfect matching algorithm (Gabow and Tarjan, 1989). Furthermore, for the maximum weight matching problem in bipartite graphs, we give a faster scaling algorithm whose running time is faster than Gabow and Tarjan's weighted bipartite {it perfect} matching algorithm.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113540/1/hsinhao_1.pd

Modellierung und Architektur eines mobilen verteilten Systems zur Kompensation prospektiver Gedächtnisdefizite

This work describes the concept and model of structured interactive memory impulses for the compensation of deficits of the prospective memory and their trial in the mobile memory aid system MEMOS. For this purpose patients were equipped with a smartphone, the Personal Memory Assistant (PMA), that uses structured interactive memory impulses to remind them of upcoming tasks and provide situation-dependent guidance through these tasks. MEMOS is the first system world-wide that utilizes structured interactive memory impulses and a decoupled bidirectional communication between patient and caregiver.Context Memory dysfunction is one of the most common results of brain damages caused by strokes or craniocerebral injuries. Impairments of the prospective memory, which is responsible for planning and executing future tasks, have turned out to be particularly challenging for an autonomous life. The compensation of lost abilities by external memory aids that remind patients of prospective tasks is the only possibilityto effectively help affected patients.Methodology.This work and the implementation of MEMOS required the interdisciplinary solution of three main tasks: Analysis of neuropsychologicalrequirements: A patient-friendly memory aid can only be implemented as an easy-to-use electronic assistant that guides patients withsituation-dependent memory impulses through complex tasks. Model of structured interactive memory impulses and system architecture: MEMOS implements situation-dependent reminders using structured interactive memory impulses. For this purpose, complex tasks are split intosubtasks, for which memory impulses are generated and linked with each other. The MEMOS task model is an implementation of the structuredinteractive memory impulses as a machine-manageable structure that guarantees validity and integrity of individual tasks and entire day schedules. MEMOS comprises a mobile component, the PMA, for direct patient interaction and a base system that maintains and coordinates the structured interactive memory impulses. The PMA communicates with the base system using GPRS and can compensate connectivity loss for several hours. The base system is able to detect malfunctions and critical conditions and to automatically alert the responsible caregiver.Patient-friendly adaptation: Success of a memory aid depends on the patients’ acceptance. A survey among patients has revealed the central importance of the memory aid’s adaptation to the requirements andabilities of each individual patient, in addition to general usabilityaspects such as avoiding PMA operation errors, concealing error conditions and easy learnability.Relevance MEMOS was successfully tested in a clinical trial. The number of forgotten or failed tasks was significantly reduced. The model of structured interactive memory impulses has been validated and MEMOS was shown to work in a real-world environmentDiese Arbeit beschreibt die Konzeption und das Modell strukturierter interaktiver Erinnerungsimpulse zur Kompensation von Defiziten des prospektiven Erinnerns und deren Erprobung im mobilen Gedächtnishilfesystems MEMOS. Dazu wurden Patienten mit einem Smartphone, dem Personal Memory Assistant (PMA), ausgerüstet, und mittels strukturierter interaktiver Erinnerungsimpulse an bevorstehende Aufgaben erinnert und situationsabhängig durch diese Aufgaben geführt.MEMOS ist das weltweit erste System, das strukturierte interaktive Erinnerungsimpulse und eine entkoppelte bidirektionale Kommunikation zwischen Patient und Betreuer einsetzt.Kontext Gedächtnisstörungen sind eine der häufigsten Folgen von Hirnschäden nach Schlaganfällen oder Schädel-Hirn-Traumata. Störungen des prospektiven Gedächtnisses, welches verantwortlich für die Planung und Durchführung zukünftiger Aufgaben ist, sind besonders behindernd für ein autonomes Leben. Die Kompensation der ausgefallenen Funktionalität durch externe Gedächtnishilfen, die an bevorstehende Aufgaben erinnern,ist die einzige Möglichkeit, betroffenen Patienten effektiv zu helfen.Methode:Die Realisierung dieser Arbeit und die Implementierung von MEMOS erforderte die interdisziplinäre Bearbeitung von dreiAufgabenschwerpunkten. Analyse der neuropsychologischen Anforderungen: Eine patientengerechte Gedächtnishilfe kann nur in Form eines einfach zu nutzenden elektronischen Assistenten realisiert werden, der den Patienten mittels situationsabhängiger Erinnerungsimpulse durch komplexe Aufgaben führt. Modell der strukturierten interaktiven Erinnerungsimpulse und Systemarchitektur: Situationsabhängige Erinnerungen werden in MEMOS durch strukturierte interaktive Erinnerungsimpulse realisiert. Dazu werden Handlungsabläufe in einfache Teilschritte zerlegt, hierfür Erinnerungsimpulse erzeugt und miteinander verknüpft. Die Umsetzung in eine maschinell verwaltbare Struktur erfolgt im MEMOS-Taskmodell, das Validität und Integrität einzelner Aufgaben (Tasks) sowie kompletter Tagespläne sicher stellt. MEMOS besteht aus einer mobilen Komponente, dem PMA, für die direkte Patienteninteraktion und einem Basissystem für die Verwaltung und Koordination der strukturierten interaktiven Erinnerungsimpulse. Der PMA kommuniziert mit dem Basissystem überMobilfunk und ist in der Lage, auch längere Unterbrechungen zukompensieren. Das Basissystem erkennt Fehlfunktionen und kritische Zustände, wodurch automatisch der verantwortliche Betreuer alarmiert wird. Patientengerechte Anpassung: Der Erfolg einer Gedächtnishilfe hängt von der Akzeptanz durch den Patienten ab. Neben allgemeinenUsability-Aspekten, wie dem Verhindern von Fehlbedienungen, dem Verbergen von Fehlerzuständen und einer einfachen Erlernbarkeit, haben Befragungen die zentrale Bedeutung der individuellen Anpassung der Gedächtnishilfe an die Bedürfnisse und Fähigkeiten der einzelnen Patienten gezeigt.Relevanz MEMOS wurde erfolgreich im Einsatz mit Patienten getestet. Die Zahl vergessener oder gescheiterter Aufgaben wurde deutlich reduziert. Das Modell der strukturierten interaktiven Erinnerungsimpulse wurde validiert und die Praxistauglichkeit von MEMOS konnte gezeigt werden

Algorithmic Approaches to the Steiner Problem in Networks

Das Steinerproblem in Netzwerken ist das Problem, in einem gewichteten Graphen eine gegebene Menge von Knoten kostenminimal zu verbinden. Es ist ein klassisches NP-schweres Problem und ein fundamentales Problem bei der Netzwerkoptimierung mit vielen praktischen Anwendungen. Wir nehmen dieses Problem mit verschiedenen Mitteln in Angriff: Relaxationen, die die Zulässigkeitsbedingungen lockern, um eine optimale Lösung annähern zu können; Heuristiken, um gute, aber nicht garantiert optimale Lösungen zu finden; und Reduktionen, um die Probleminstanzen zu vereinfachen, ohne eine optimale Lösung zu zerstören. In allen Fällen untersuchen und verbessern wir bestehende Methoden, stellen neue vor und evaluieren sie experimentell. Wir integrieren diese Bausteine in einen exakten Algorithmus, der den Stand der Algorithmik für die optimale Lösung dieses Problems darstellt. Viele der vorgestellten Methoden können auch für verwandte Probleme von Nutzen sein