A graph H is a minor of a second graph G if G can be transformed into H by two operations: 1) deleting nodes and/or edges, or 2) contracting edges. Coarse-grained reconfigurable array (CGRA) application mapping is closely related to the graph minor problem ...
Natural language processing has experienced significant improvements with the development of Transformer-based models, which employ self-attention mechanism and pre-training strategies. However, these models still present several obstacles. A notable issue ...
In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's aggregation functio ...
We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
Understanding the origins of militarized conflict is a complex, yet important undertaking. Existing research seeks to build this understanding by considering bi-lateral relationships between entity pairs (dyadic causes) and multi-lateral relationships amon ...
This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information.First, we consider two stochastic models called query-commit and price-of-information where the algo ...
The phenomenal growth of graph data from a wide variety of real-world applications has rendered graph querying to be a problem of paramount importance. Traditional techniques use structural as well as node similarities to find matches of a given query grap ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
It is shown that fora constant t is an element of N, every simple topological graph on n vertices has 0(n) edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of th ...
We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...
Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and ...
Institute of Electrical and Electronics Engineers2014
A topological graph G is a graph drawn in the plane with vertices represented by points and edges represented by continuous arcs connecting the vertices. If every edge is drawn as a straight-line segment, then G is called a geometric graph. A k-grid in a t ...
Fully numerical schemes are presented for high precision computations of the four-dimensional integrals arising in Galerkin surface integral equation formulations. More specifically, the focal point of this paper is the singular integrals for coincident, e ...
Institute of Electrical and Electronics Engineers2013
Relationships between entities in datasets are often of multiple types, which can naturally be modeled by a multi-layer graph; a common vertex set represents the entities and the edges on different layers capture different types of relationships between th ...
This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...
In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...
We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space iden ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conj ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
