Related papers: Revealed Preference Dimension via Matrix Sign Rank
A signed graph is a graph with edges marked positive and negative; it is unbalanced if some cycle has negative sign product. We introduce the concept of vector valued switching function in signed graphs, which extends the concept of…
We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player --- who is associated with a subset of vertices --- matches as many of…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
Metric dimension is a graph parameter motivated by problems in robot navigation, drug design, and image processing. In this paper, we answer several open extremal problems on metric dimension and pattern avoidance in graphs from (Geneson,…
How to efficiently represent a graph in computer memory is a fundamental data structuring question. In the present paper, we address this question from a combinatorial point of view. A representation of an $n$-vertex graph $G$ is called…
Preference learning is critical for aligning large language models (LLMs) with human values, with the quality of preference datasets playing a crucial role in this process. While existing metrics primarily assess data quality based on…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
Real-life tools for decision-making in many critical domains are based on ranking results. With the increasing awareness of algorithmic fairness, recent works have presented measures for fairness in ranking. Many of those definitions…
Let $G^{\sigma}$ be an oriented graph and $S(G^{\sigma})$ be its skew-adjacency matrix, where $G$ is called the underlying graph of $G^{\sigma}$. The skew-rank of $G^{\sigma}$, denoted by $sr(G^{\sigma})$, is the rank of $S(G^{\sigma})$.…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean an asymmetric and transitive binary relation, while a weak…
I develop a revealed preference framework to test whether an aggregate allocation of indivisible objects satisfies Pareto efficiency and individual rationality (PI) without observing individual preferences. Exploiting the type-based…
Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph…
The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to…
A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. The simplest case of another problem, stated by the same…
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…
A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a…
In this article, we introduce a geometric and a spectral preorder relation on the class of weighted graphs with a magnetic potential. The first preorder is expressed through the existence of a graph homomorphism respecting the magnetic…