Related papers: On the Existence of Balanced Chain Rule Task Sets

Distributed consensus has been intensively studied in recent years as a means to mitigate state differences among dynamic nodes on a graph. It has been successfully employed in various applications, e.g., formation control of multi-robots,…

Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…

The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…

Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…

A graph is circle if there is a family of chords in a circle such that two vertices are adjacent if the corresponding chords cross each other. There are diverse characterizations of circle graphs, many of them using the notions of local…

A graph $G=(V,E)$ is a geometric intersection graph if every node $v \in V$ is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…

Let $G$ be a simple graph of order $n$ with degree sequence $(d)=(d_1,d_2,\ldots,d_n)$ and conjugate degree sequence $(d^*)=(d_1^*,d_2^*,\ldots,d_n^*)$. In \cite{AkbariGhorbaniKoolenObudi2010,DasMojallalGutman2017} it was proven that…

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…

We study the joint minimization of communication and computation costs in distributed computing, where a master node coordinates $N$ workers to evaluate a function over a library of $n$ files. Assuming that the function is decomposed into…

Kirkpatrick et al. [ALT 2019] and Fallat et al. [JMLR 2023] introduced non-clashing teaching and proved that it is the most efficient batch machine teaching model satisfying the collusion-avoidance benchmark established in the seminal work…

Graphs can model complex relationships between objects, enabling a myriad of Web applications such as online page/article classification and social recommendation. While graph neural networks(GNNs) have emerged as a powerful tool for graph…

In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for…

Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering methods have…

A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…

Deduction is a recently introduced graph searching process in which searchers clear the vertex set of a graph with one move each, with each searcher's movement determined by which of its neighbors are protected by other searchers. In this…

A tree decomposition of a graph facilitates computations by grouping vertices into bags that are interconnected in an acyclic structure, hence their importance in a plethora of problems such as query evaluation over databases and inference…