Applications of Relations and Graphs to Coalition Formation

A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory, social choice and bargaining theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. So, we can choose an un-dominated government. To achieve unique solutions, we additionally apply social choice rules. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.Graph Theory, RELVIEW, Relational Algebra, Dominance, Stable Government

Solving Hard Control Problems in Voting Systems via Integer Programming

Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control problems. Our ILP formulations are flexible in the sense that they can work with an arbitrary number of candidates and voters. Using the off-the-shelf solver Cplex, we show that our approaches can manipulate elections with a large number of voters and candidates efficiently

07431 Abstracts Collection -- Computational Issues in Social Choice

From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431 on ``Computational Issues in Social Choice\u27\u27 was held at the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their recent research, and ongoing work and open problems were discussed. The abstracts of the talks given during the seminar are collected in this paper. The first section summarises the seminar topics and goals in general. Links to full papers are provided where available

Entwurf funktionaler Implementierungen von Graphalgorithmen

Classic graph algorithms are usually presented and analysed in imperative programming languages. Imperative programming languages are well-suited for the description of a program flow, in which the order in which the operations are performed is important. One common example of such a description is the successive, typically destructive modification of objects. This kind of iteration often occurs in the context of graph algorithms that deal with a certain kind of optimisation. In functional programming, the order of execution is abstracted and problem solutions are described as compositions of intermediate solutions. Additionally, functional programming languages are referentially transparent and thus destructive updates of objects are discouraged. The development of purely functional graph algorithms begins with the decomposition of a given problem into simpler problems. In many cases the solutions of these partial problems can be used to solve different problems as well. What is more, this compositionality allows exchanging functions for more efficient or more comprehensible versions with little effort. An algebraic approach with a focus on relation algebra as defined by Tarski is used as an intermediate step in this dissertation. One advantage of this approach is the formality of the resulting specifications. Despite their formality, the resulting expressions are still readable, because the algebraic operations have intuitive interpretations. Another advantage is that the specification is executable, once the necessary operations are implemented. This dissertation presents the basics of the algebraic approach in the functional programming language Haskell. Using this foundation, some exemplary graph-theoretic problems are solved in the presented framework. Finally, optimisations of the presented implementations are discussed and pointers are provided to further problems that can be solved using the above methods.Klassische Graphalgorithmen werden üblicherweise in imperativen Programmiersprachen beschrieben und analysiert. Imperative Programmiersprachen eignen sich gut, um Programmabläufe zu beschreiben, in welchen die Reihenfolge der Operationen wichtig ist. Dies betrifft insbesondere die schrittweise, in der Regel destruktive Veränderung von Objekten, wie sie häufig im Falle von Optimierungsproblemen auf Graphen vorkommt. In der funktionalen Programmierung abstrahiert man von einer festen Berechnungsreihenfolge und beschreibt Problemlösungen als Kompositionen von Teillösungen. Ferner sind funktionale Programmiersprachen referentiell transparent, sodass destruktive Veränderungen nur bedingt möglich sind. Die Entwicklung rein funktionaler Graphalgorithmen setzt bei der Zerlegung der bestehenden Probleme in einfachere Probleme an. Oftmals können Lösungen dieser Teilprobleme auch in anderen Situationen eingesetzt werden. Darüber hinaus erlaubt es diese Kompositionalität, einzelne Funktionen mit wenig Aufwand durch effizientere oder verständlichere Fassungen auszutauschen. Als Zwischenschritt in der Entwicklung wird in dieser Dissertation ein algebraischer Ansatz basierend auf der Relationenalgebra im Sinne von Tarski verwendet. Ein Vorteil dieses Ansatzes ist die Formalität der entstehenden Spezifikationen. Trotz ihrer Formalität bleiben die entstehenden Ausdrücke oft leserlich, weil die algebraischen Operationen anschauliche Interpretationen zulassen. Ein weiterer Vorteil ist, dass Spezifikationen ausführbar werden, sobald bestimmte Basisoperationen implementiert sind. In dieser Dissertation werden Grundlagen einer Implementierung des algebraischen Ansatzes in der funktionalen Programmiersprache Haskell behandelt. Ausgehend hiervon werden exemplarisch einige Probleme der Graphentheorie gelöst. Schließlich werden Optimierungen der vorgestellten Implementierungen und weitere Probleme, welche mit den obigen Methoden lösbar sind, diskutiert

A deep exploration of the complexity border of strategic voting problems

Voting has found applications in a variety of areas. Unfortunately, in a voting activity there may exist strategic individuals who have incentives to attack the election by performing some strategic behavior. One possible way to address this issue is to use computational complexity as a barrier against the strategic behavior. The point is that if it is NP-hard to successfully perform a strategic behavior, the strategic individuals may give up their plan of attacking the election. This thesis is concerned with strategic behavior in restricted elections, in the sense that the given elections are subject to some combinatorial restrictions. The goal is to find out how the complexity of the strategic behavior changes from the very restricted case to the general case.Abstimmungen werden auf verschiedene Gebiete angewendet. Leider kann es bei einer Abstimmung einzelne Teilnehmer geben, die Vorteile daraus ziehen, die Wahl durch strategisches Verhalten zu manipulieren. Eine Möglichkeit diesem Problem zu begegnen ist es, die Berechnungskomplexität als Hindernis gegen strategisches Verhalten zu nutzen. Die Annahme ist, dass falls es NP-schwer ist, um strategisches Verhalten erfolgreich anzuwenden, der strategisch Handelnde vielleicht den Plan aufgibt die Abstimmung zu attackieren. Diese Arbeit befasst sich mit strategischem Vorgehen in eingeschränkten Abstimmungen in dem Sinne, dass die vorgegebenen Abstimmungen kombinatorischen Einschränkungen unterliegen. Ziel ist es herauszufinden, wie sich die Komplexität des strategischen Handelns von dem sehr eingeschränkten zu dem generellen Fall ändert