Related papers: Random greedy triangle-packing beyond the 7/4 barr…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…
We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of…
Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…
A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been…
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
We study the influence minimization problem: given a graph $G$ and a seed set $S$, blocking at most $b$ nodes or $b$ edges such that the influence spread of the seed set is minimized. This is a pivotal yet underexplored aspect of network…
Consider the budget-constrained random graph process introduced by Frieze, Krivelevich and Michaeli, where each time an edge is offered through the (standard) random graph process we must irrevocably decide whether to "purchase" this edge…
We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)~N(s, 1) where s is an unknown quantity. A natural iterative way of estimating s is to perform the following procedure. At iteration t +…
Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…
This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graphs on $n$ vertices has at most $\lfloor n^2/4\rfloor$ edges. About half a century later Andr\'asfai studied dense triangle-free graphs and…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Sampling and interpolation have been extensively studied, in order to reconstruct or estimate the entire graph signal from the signal values on a subset of vertexes, of which most achievements are about continuous signals. While in a lot of…