Related papers: Directed Ear Anonymity
Let $H$ be a directed acyclic graph other than a rooted star. It is known that there are constants $c(H)$ and $C(H)$ such that the following holds for the complete directed graph $D_n$. There are at most $C\log n$ directed acyclic subgraphs…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the…
We investigate a communication setup where a source output is sent through a free noisy channel first and an additional codeword is sent through a noiseless but expensive channel later. With the help of the second message the decoder should…
A directed graph is called Eulerian, if it contains a tour that traverses every arc in the graph exactly once. We study the problem of Eulerian extension (EE) where a directed multigraph G and a weight function is given and it is asked…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
A graph has \emph{diameter} D if every pair of vertices are connected by a path of at most D edges. The Diameter-D Augmentation problem asks how to add the a number of edges to a graph in order to make the resulting graph have diameter D.…
We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor. We introduce a…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Circle graphs are intersection graphs of chords of a circle. In this paper, we present a new algorithm for the circle graph isomorphism problem running in time $O((n+m)\alpha(n+m))$ where $n$ is the number of vertices, $m$ is the number of…
Given a directed graph, the Minimal Feedback Arc Set (FAS) problem asks for a minimal set of arcs which, when removed, results in an acyclic graph. Equivalently, the FAS problem asks to find an ordering of the vertices that minimizes the…
A theoretical study is performed to analyze the directional response of different types of microphone array designs. 1-D (linear) and 2-D (planar) microphone array types are considered, and the delay and sum beamforming and conventional…
Graph pattern counting serves as a cornerstone of network analysis with extensive real-world applications. Its integration with local differential privacy (LDP) has gained growing attention for protecting sensitive graph information in…
For a dataset of label-count pairs, an anonymized histogram is the multiset of counts. Anonymized histograms appear in various potentially sensitive contexts such as password-frequency lists, degree distribution in social networks, and…
In a finite undirected simple graph, a {\it chordless cycle} is an induced subgraph which is a cycle. We propose two algorithms to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithms…
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…
Deep neural networks (DNNs) have been successfully applied to a wide variety of acoustic modeling tasks in recent years. These include the applications of DNNs either in a discriminative feature extraction or in a hybrid acoustic modeling…
An oriented graph is a directed graph without directed 2-cycles. Poljak and Turz\'{i}k (1986) proved that every connected oriented graph $G$ on $n$ vertices and $m$ arcs contains an acyclic subgraph with at least $\frac{m}{2}+\frac{n-1}{4}$…