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Cutting out an object and estimating its opacity mask, known as image matting, is a key task in many image editing applications. Deep learning approaches have made significant progress by adapting the encoder-decoder architecture of…

Computer Vision and Pattern Recognition · Computer Science 2020-03-18 Marco Forte , François Pitié

Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…

Information Theory · Computer Science 2016-05-02 Abhishek Agarwal , Arya Mazumdar

The $k$-Strong Conflict-Free ($k$-SCF, in short) colouring problem seeks to find a colouring of the vertices of a hypergraph $H$ using minimum number of colours so that in every hyperedge $e$ of $H$, there are at least $\min\{|e|,k\}$…

Combinatorics · Mathematics 2021-06-08 S. M. Dhannya , N. S. Narayanaswamy

The first-fit coloring is a heuristic that assigns to each vertex, arriving in a specified order $\sigma$, the smallest available color. The problem Grundy Coloring asks how many colors are needed for the most adversarial vertex ordering…

Computational Complexity · Computer Science 2020-01-14 Pierre Aboulker , Édouard Bonnet , Eun Jung Kim , Florian Sikora

A $k$-improper edge coloring of a graph $G$ is a mapping $\alpha:E(G)\longrightarrow \mathbb{N}$ such that at most $k$ edges of $G$ with a common endpoint have the same color. An improper edge coloring of a graph $G$ is called an improper…

Combinatorics · Mathematics 2020-03-16 Carl Johan Casselgren , Petros A. Petrosyan

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…

Combinatorics · Mathematics 2025-06-11 Claudia Archetti , Martina Cerulli , Carmine Sorgente

In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…

Data Structures and Algorithms · Computer Science 2025-06-03 Allan Borodin , Christodoulos Karavasilis

In this paper, we present a fast exemplar-based image colorization approach using color embeddings named Color2Embed. Generally, due to the difficulty of obtaining input and ground truth image pairs, it is hard to train a exemplar-based…

Computer Vision and Pattern Recognition · Computer Science 2021-08-25 Hengyuan Zhao , Wenhao Wu , Yihao Liu , Dongliang He

In this paper, we revisit the online recoloring problem introduced recently by Azar et al. In online recoloring, there is a fixed set $V$ of $n$ vertices and an initial coloring $c_0: V\rightarrow [k]$ for some $k\in \mathbb{Z}^{>0}$. Under…

Data Structures and Algorithms · Computer Science 2024-08-13 Rajmohan Rajaraman , Omer Wasim

Image colorization is the process of colorizing grayscale images or recoloring an already-color image. This image manipulation can be used for grayscale satellite, medical and historical images making them more expressive. With the help of…

Computer Vision and Pattern Recognition · Computer Science 2023-09-27 Ahmed Samir Ragab , Shereen Aly Taie , Howida Youssry Abdelnaby

We study weighted edge coloring of graphs, where we are given an undirected edge-weighted general multi-graph $G := (V, E)$ with weights $w : E \rightarrow [0, 1]$. The goal is to find a proper weighted coloring of the edges with as few…

Data Structures and Algorithms · Computer Science 2021-01-01 Debarsho Sannyasi

First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…

Logic in Computer Science · Computer Science 2023-06-08 Paulius Dilkas , Vaishak Belle

An \emph{interval $t$-coloring} of a graph $G$ is a proper edge-coloring with colors $1,\dots,t$ such that the colors on the edges incident to every vertex of $G$ are colored by consecutive colors. A graph $G$ is called \emph{interval…

Combinatorics · Mathematics 2024-09-27 Petros A. Petrosyan , Hrant H. Khachatrian , Hovhannes G. Tananyan

For a graph $G$, we call an edge coloring of $G$ an \textit{improper} \textit{interval edge coloring} if for every $v\in V(G)$ the colors, which are integers, of the edges incident with $v$ form an integral interval. The \textit{interval…

Combinatorics · Mathematics 2024-08-09 Seunghun Lee

Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…

Data Structures and Algorithms · Computer Science 2024-05-29 Fabian Frei , Matthias Gehnen , Dennis Komm , Rastislav Královič , Richard Královič , Peter Rossmanith , Moritz Stocker

A {\em conflict-free coloring} of a graph {\em with respect to open} (resp., {\em closed}) {\em neighborhood} is a coloring of vertices such that for every vertex there is a color appearing exactly once in its open (resp., closed)…

Combinatorics · Mathematics 2022-10-11 Igor Fabrici , Borut Lužar , Simona Rindošová , Roman Soták

We introduce and explore a family of vertex-coloring problems which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of…

Discrete Mathematics · Computer Science 2018-11-19 David Orden , Jose Manuel Gimenez-Guzman , Ivan Marsa-Maestre , Enrique de la Hoz

An edge-coloring of a graph $G$ with consecutive integers $c_{1},\ldots,c_{t}$ is called an \emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of…

Combinatorics · Mathematics 2015-08-04 Petros A. Petrosyan , Hayk H. Tepanyan

In order to minimize the generalization error in neural networks, a novel technique to identify overfitting phenomena when training the learner is formally introduced. This enables support of a reliable and trustworthy early stopping…

Given a hypergraph $H$, the conflict-free colouring problem is to colour vertices of $H$ using minimum colours so that each hyperedge in $H$ sees a unique colour. We present a polynomial time reduction from the conflict-free colouring…

Data Structures and Algorithms · Computer Science 2020-01-02 S. M. Dhannya , N. S. Narayanaswamy