相关论文: Lecture Notes on Evasiveness of Graph Properties

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing…

Given an undirected graph, each of the two end-vertices of an edge can own the edge. Call a vertex poor, if it owns at most one edge. We give a polynomial time algorithm for the problem of finding an assignment of owners to the edges which…

This note answers extremal questions like: what is the maximum number of edges in a graph of order n, which belongs to some hereditary property. The same question is answered also for the spectral radius and other similar parameters.

Lov\'asz (1967) showed that two graphs $G$ and $H$ are isomorphic if, and only if, they are homomorphism indistinguishable over all graphs, i.e., $G$ and $H$ admit the same number of number of homomorphisms from every graph $F$.…

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the…

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…

In this paper, we investigate some parity factors by using Lov\'asz's (g,f)-parity theorem. Let $m>0$ be an integer. Firstly, we obtain a sufficient and necessary condition for some graphs to have a parity factor with restricted minimum…

This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its…

In a celebrated work, Blais, Brody, and Matulef developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower…

We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…

These lecture notes cover advanced topics in linear regression, with an in-depth exploration of the existence, uniqueness, relations, computation, and non-asymptotic properties of the most prominent estimators in this setting. The covered…

The theta function of Lovasz is a graph parameter that can be computed up to arbitrary precision in polynomial time. It plays a key role in algorithms that approximate graph parameters such as maximum independent set, maximum clique and…

The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution…

Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…

Graph edges, along with their labels, can represent information of fundamental importance, such as links between web pages, friendship between users, the rating given by users to other users or items, and much more. We introduce LEAP, a…

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent…