Related papers: Recycling Solutions for Vertex Coloring Heuristics
In vertex recoloring, we are given $n$ vertices with their initial coloring, and edges arrive in an online fashion. The algorithm must maintain a valid coloring by recoloring vertices, at a cost. The problem abstracts a scenario of job…
In the Edge Coloring problem, we are given an undirected graph $G$ with $n$ vertices and $m$ edges, and are tasked with finding the smallest positive integer $k$ so that the edges of $G$ can be assigned $k$ colors in such a way that no two…
We propose Generative Probabilistic Image Colorization, a diffusion-based generative process that trains a sequence of probabilistic models to reverse each step of noise corruption. Given a line-drawing image as input, our method suggests…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
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…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
A linearly ordered (LO) $k$-colouring of a hypergraph assigns to each vertex a colour from the set $\{0,1,\ldots,k-1\}$ in such a way that each hyperedge has a unique maximum element. Barto, Batistelli, and Berg conjectured that it is…
Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem,…
We propose the first deep learning approach for exemplar-based local colorization. Given a reference color image, our convolutional neural network directly maps a grayscale image to an output colorized image. Rather than using hand-crafted…
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only…
Given a graph $G$ and two graph homomorphisms $\alpha$ and $\beta$ from $G$ to a fixed graph $H$, the problem $H$-Recoloring asks whether there is a transformation from $\alpha$ to $\beta$ that changes the image of a single vertex at each…
The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
We present a deterministic distributed algorithm in the LOCAL model that finds a proper $(\Delta + 1)$-edge-coloring of an $n$-vertex graph of maximum degree $\Delta$ in $\mathrm{poly}(\Delta, \log n)$ rounds. This is the first nontrivial…
Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…
We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we…