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Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
Scene labeling task is to segment the image into meaningful regions and categorize them into classes of objects which comprised the image. Commonly used methods typically find the local features for each segment and label them using…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…
Many modern deep-learning techniques do not work without enormous datasets. At the same time, several fields demand methods working in scarcity of data. This problem is even more complex when the samples have varying structures, as in the…
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…
The analysis of large collections of image data is still a challenging problem due to the difficulty of capturing the true concepts in visual data. The similarity between images could be computed using different and possibly multimodal…
Choices made by individuals have widespread impacts--for instance, people choose between political candidates to vote for, between social media posts to share, and between brands to purchase--moreover, data on these choices are increasingly…
In many applications concerning statistical graphical models the data originate from several subpopulations that share similarities but have also significant differences. This raises the question of how to estimate several graphical models…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Series photo selection (SPS) is an important branch of the image aesthetics quality assessment, which focuses on finding the best one from a series of nearly identical photos. While a great progress has been observed, most of the existing…
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a spanning tree in which the distance between any two adjacent vertices of $G$…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…
Large, distributed data streams are now ubiquitous. High-accuracy sketches with low memory overhead have become the de facto method for analyzing this data. For instance, if we wish to group data by some label and report the largest counts…
Given an undirected graph $G=(V,E)$ with a set of vertices $V$ and a set of edges $E$, a graph coloring problem involves finding a partition of the vertices into different independent sets. In this paper we present a new framework that…
Image cropping is essential in image editing for obtaining a compositionally enhanced image. In display media, image cropping is a prospective technique for automatically creating media content. However, image cropping for media contents is…
One common task in image forensics is to detect spliced images, where multiple source images are composed to one output image. Most of the currently best performing splicing detectors leverage high-frequency artifacts. However, after an…