Related papers: Testing a Graph-Theoretic Condition for Aggregatin…
We investigate the problem of detecting correlation between two Erd\H{o}s-R\'enyi graphs $G(n,p)$, formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative…
Interaction between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph is a well studied topic in graph theory. Perfect Graph Theorems are probably the most important results in this direction. Graph $G$ is called…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
We provide a combinatorial characterization of all testable properties of $k$-uniform hypergraphs ($k$-graphs for short). Here, a $k$-graph property $P$ is testable if there is a randomized algorithm which makes a bounded number of edge…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based…
This is a companion piece to my paper on "Example-Based Procedural Modeling Using Graph Grammars." This paper examines some of the theoretical issues in more detail. This paper discusses some more complex parts of the implementation, why…
Graphs are an essential part of many machine learning problems such as analysis of parse trees, social networks, knowledge graphs, transportation systems, and molecular structures. Applying machine learning in these areas typically involves…
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
Risk classification plays an important role in many regulations and standards. However, a general method that provides an optimal classification has not been proposed yet. Also, the criteria of optimality are not defined in these…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
Recent work on Graph Neural Networks has demonstrated that self-supervised pretraining can further enhance performance on downstream graph, link, and node classification tasks. However, the efficacy of pretraining tasks has not been fully…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…