Subclasses of Normal Helly Circular-Arc Graphs

A Helly circular-arc model M = (C,A) is a circle C together with a Helly family \A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how do these classes of graphs relate with straight and round digraphs.Comment: 39 pages, 13 figures. A previous version of the paper (entitled Proper Helly Circular-Arc Graphs) appeared at WG'0

Essays on Stochastic Choice and Welfare

Motivated by the literature on preference elicitation and welfare analysis, Chapter I studies the properties of aggregators of choice datasets into preferences. Novel normative principles and their theoretical implications are provided. I analyse numerous approaches proposed by the literature in view of the introduced principles. I also propose and characterize two counting procedures that are foundational for the analysis. Motivated by the theoretical framework of the first chapter, in Chapter II, I propose a novel experimental design to test two normative principles: (1) Informational Responsiveness guarantees that no choice data is ignored; (2) Revealed Preference constrains the preference elicitation process to a particular reorganization of data. These principles are summarized by a method denoted as Counting Reveal Preference procedure. I show that approaches founded on this procedure provide more reliable results in terms of preference relation. Motivated by the literature on stochastic choice, Chapter III studies the relation between imperfect discrimination and the transitivity of preferences. I show that the degree of transitivity depends on the degree of discrimination between pairs of alternatives. I characterize the notions of Weak, Moderate and Strong stochastic transitivity. The results allow us to organize a wide range of stochastic models in accordance with Fechnerian models and imperfect discrimination

Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Inductive Characterizations of Finite Interval Orders and Semiorders

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