Related papers: Edge and Pair Queries -- Random Graphs and Complex…
Nearest neighbor search plays a fundamental role in many disciplines such as multimedia information retrieval, data-mining, and machine learning. The graph-based search approaches show superior performance over other types of approaches in…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision…
The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
We consider random walks on edge coloured random graphs, where the colour of an edge reflects the cost of using it. In the simplest instance, the edges are coloured red or blue. Blue edges are free to use, whereas red edges incur a unit…
We introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using…
We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…
This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small…
Edge ideals of finite simple graphs are well-studied over polynomial rings. In this paper, we initiate the study of edge ideals over exterior algebras, specifically focusing on the depth and singular varieties of such ideals. We prove an…
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…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
In this paper, we study rare events in spherical and Gaussian random geometric graphs in high dimensions. In these models, the vertices correspond to points sampled uniformly at random on the $d$ dimensional unit sphere or correspond to $d$…
Edge ideals of finite simple graphs $G$ on $n$ vertices are the ideals $I(G)$ of the polynomial ring $S$ in $n$ variables generated by the quadratic monomials associated with the edges of $G$. In this paper, we consider the possible pairs…