Related papers: Depth First Exploration of a Configuration Model
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
A common technique to speed up shortest path queries in graphs is to use a bidirectional search, i.e., performing a forward search from the start and a backward search from the destination until a common vertex on a shortest path is found.…
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
We present a new technique for proving logarithmic upper bounds for diameters of evolving random graph models, which is based on defining a coupling between random graphs and variants of random recursive trees. The advantage of the…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…
We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of…
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of…
Graph generation is a fundamental problem in graph learning with broad applications across Web-scale systems, knowledge graphs, and scientific domains such as drug and material discovery. Recent approaches leverage diffusion models for…
Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…