Related papers: Generalizing the Single-Crossing Property on Lines…

We generalize the classical single-crossing property to single-crossing property on trees and obtain new ways to construct Condorcet domains which are sets of linear orders which possess the property that every profile composed from those…

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation has no cycles. We observe that, without loss of generality, such domain can be assumed to…

We study the complexity of determining a winning committee under the Chamberlin--Courant voting rule when voters' preferences are single-crossing on a line, or, more generally, on a median graph (this class of graphs includes, e.g., trees…

We introduce and study the weakly single-crossing domain on trees which is a generalization of the well-studied single-crossing domain in social choice theory. We design a polynomial-time algorithm for recognizing preference profiles which…

We introduce two-crossing elections as a generalization of single-crossing elections, showing a number of new results. First, we show that two-crossing elections can be recognized in polynomial time, by reduction to the well-studied…

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced…

We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be…

In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…

We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…

The availability of large datasets composed of graphs creates an unprecedented need to invent novel tools in statistical learning for graph-valued random variables. To characterize the average of a sample of graphs, one can compute the…

An election over a finite set of candidates is called single-crossing if, as we sweep through the list of voters from left to right, the relative order of every pair of candidates changes at most once. Such elections have many attractive…

Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a constant. The purpose of this text is twofold: to provide an…

We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…

The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open…

We prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree…

Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge density. We study a stronger property, which requires that a…

We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for…

We uncover a new relation between Closeness centrality and the Condorcet principle. We define a Condorcet winner in a graph as a node that compared to any other node is closer to more nodes. In other words, if we assume that nodes vote on a…

We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an…