Related papers: Single-crossing Implementation
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs…
In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Constructive election control considers the problem of an adversary who seeks to sway the outcome of an electoral process in order to ensure that their favored candidate wins. We consider the computational problem of constructive election…
Let $S$ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of $S$ with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the…
Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…
We survey the design of elections that are resilient to attempted interference by third parties. For example, suppose votes have been cast in an election between two candidates, and then each vote is randomly changed with a small…
Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting…
An electoral spoiler is usually defined as a losing candidate whose removal would affect the outcome by changing the winner. So far, spoiler effects have been analyzed primarily for single-winner electoral systems. We consider this subject…
It is important to understand how the outcome of an election can be modified by an agent with control over the structure of the election. Electoral control has been studied for many election systems, but for all studied systems the winner…
Drawing graphs with the minimum number of crossings is a classical problem that has been studied extensively. Many restricted versions of the problem have been considered. For example, bipartite graphs can be drawn such that the two sets in…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
Approval-Based Committee (ABC) rules are an important tool for choosing a fair set of candidates when given the preferences of a collection of voters. Though finding a winning committee for many ABC rules is NP-hard, natural variations for…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most…
Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is…