graphs and dynamic programming

This repo is a work in progress

Discussion and problem solving on the topics of:

• Graph Algorithms
• Max Flow Networks
• Dynamic Programming and principle of optimality

For the purpose we will follow the notation introduced in the book "Digraphs: Theory, Algorithms, and Applications" by Jensen and Gutin.

Specifically we will discuss in details and will be writing python code for the following algorithms:

• Branch-and-bound

• Branch-and-cut

• Breadth-First-Search

• Depth-First-Search

• Backtracking

• Dijkstra's shortest path

• Bellman-Ford shortest path

• Floyd-Warshall shortest path

• Ford-Fulkerson / Edmonds-Karp max flow

• Push-relabel max flow

• Tarjan's strongly connected components

• Kruskal's min spanning forest

• Boruvka's min spanning forest

• Prim's min spanning tree

• reverse-delete min spanning tree

We will look into using open source python packages such as dynamic-programming and networkx.

Selected Topics in Machine Learning

• Reinforcement Learning and Game Theory

• Offline Reinforcement and Self-Supervised Learning

• NLP Concepts

• Transformers

• Large Language Models

• Bayesian Networks

• Probabilistic Machine Learning

• Optimization, Classification, Regression

• Causal Inference, Root Cause Analysis and Model Checking

• Deep Learning and Neural Networks

• Deep Learning for solving Image Processing problems and Generative Tasks

• Hypothesis Testing, Estimation of Treatment Effects and Generalized Synthetic Control

• Graphs and Dynamic Programming

• Dynamical Systems, State-Space Models, Chaos, Ergodicity

• Information Theory, Statistical Mechanics, Diffusion Models

• Queueing Networks, Queueing Theory, Reversible Stochastic Processes

• Spectral Analysis, Optimization in Spectral Domain, Spectral Domain Modeling

• Computability, Automata, Logic Systems, Formal Grammars and Theory of Parsing

• Thought Forming, Consciousness, Intelligent Machines, Inference, Logic Systems

Note

This repository uses git Large File Storage feature. In order to download locally the large files (> 1MB) which are maintained by git LFS you will need to install the Git extension for versioning large files: https://git-lfs.com/