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Lecture# Graph Coloring II

Description

This lecture delves into advanced concepts of graph coloring, focusing on the implications of planted coloring and the relation between planted and random graph coloring. The instructor explains the rigidity threshold and the frozen variables in the context of BP fixed points. The lecture also covers the equilibrium properties of random ensembles and the clustering of solutions. Various conjectures and claims are discussed regarding the contiguous nature of planted coloring to random coloring and the behavior of BP in different scenarios.

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In course

Instructors (2)

PHYS-642: Statistical physics for optimization & learning

This course covers the statistical physics approach to computer science problems, with an emphasis on heuristic & rigorous mathematical technics, ranging from graph theory and constraint satisfaction

Related concepts (202)

Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.

Hierarchical clustering

In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, , information retrieval, bioinformatics, data compression, computer graphics and machine learning.

BP

BP p.l.c. (formerly The British Petroleum Company p.l.c and BP Amoco p.l.c) is a British multinational oil and gas company headquartered in London, England. It is one of the oil and gas "supermajors" and one of the world's largest companies measured by revenues and profits. It is a vertically integrated company operating in all areas of the oil and gas industry, including exploration and extraction, refining, distribution and marketing, power generation, and trading.

Star cluster

Star clusters are large groups of stars held together by self-gravitation. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clustered groups of stars, generally containing fewer than a few hundred members, and are often very young.

Related lectures (473)

Statistical Physics of ClustersPHYS-467: Machine learning for physicists

Explores the statistical physics of clusters, focusing on complexity and equilibrium behavior.

Graph Coloring: Random vs SymmetricalPHYS-467: Machine learning for physicists

Compares random and symmetrical graph coloring in terms of cluster colorability and equilibrium.

Optimal Detection in Spinodal SystemsPHYS-467: Machine learning for physicists

Explores optimal detection in spinodal systems, discussing stability analysis and phase transitions.

Graph Coloring IIIPHYS-642: Statistical physics for optimization & learning

Explores properties of clusters and colorability threshold in graph coloring, including average connectivity and rigidity.

Graph Coloring: Theory and ApplicationsPHYS-512: Statistical physics of computation

Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.