algorithmic-theory.md

Algorithmic Theory

This document provides an overview of key areas in algorithm theory, including recommended resources for further study. Each section includes a visual representation and a self-assessment rating system.

Key Areas of Algorithm Theory

1. Algorithm Design and Analysis

• Topics: Time and space complexity, amortized analysis, probabilistic analysis, and randomized algorithms.
• Resources:
  • "Introduction to Algorithms" by Cormen, Leiserson, Rivest, and Stein (CLRS)
  • "Algorithm Design" by Jon Kleinberg and Éva Tardos
• My understanding: ⭐ / 5
• Visual:

2. Advanced Data Structures

• Topics: B-trees, Fibonacci heaps, van Emde Boas trees, and dynamic data structures.
• Resources:
  • "Data Structures and Network Algorithms" by Robert E. Tarjan
  • MIT OpenCourseWare: Advanced Data Structures
• My understanding: ⭐ / 5
• Visual:

3. Graph Algorithms

• Topics: Strongly connected components, network flow, matching in graphs, and planar graphs.
• Resources:
  • "Algorithms" by Robert Sedgewick and Kevin Wayne
  • Coursera: Algorithms Specialization by Stanford University
• My understanding: ⭐⭐ / 5
• Visual:

4. Computational Geometry

• Topics: Convex hulls, Voronoi diagrams, Delaunay triangulation, and range searching.
• Resources:
  • "Computational Geometry: Algorithms and Applications" by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars
  • Khan Academy: Computational Geometry
• My understanding: ⭐ / 5
• Visual:

5. Randomized Algorithms

• Topics: Monte Carlo methods, Las Vegas algorithms, and probabilistic analysis.
• Resources:
  • "Randomized Algorithms" by Rajeev Motwani and Prabhakar Raghavan
  • MIT's Randomized Algorithms course
• My understanding: ⭐ / 5
• Visual:

6. Approximation Algorithms

• Topics: Approximation schemes, greedy algorithms, and linear programming relaxation.
• Resources:
  • "Approximation Algorithms" by Vijay V. Vazirani
  • UC Berkeley: Approximation Algorithms
• My understanding: ⭐⭐⭐ / 5
• Visual:

7. Complexity Theory

• Topics: P vs NP problem, NP-completeness, and complexity classes.
• Resources:
  • "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak
  • Stanford University: CS254: Computational Complexity
• My understanding: ⭐ / 5
• Visual:

8. Parallel and Distributed Algorithms

• Topics: Parallel sorting, parallel graph algorithms, and distributed computing models.
• Resources:
  • "Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes" by F. Thomson Leighton
  • MIT's Distributed Algorithms course
• My understanding: ⭐ / 5
• Visual:

Additional Fundamental Skills

Algorithmic Game Theory

• Topics: Nash equilibria, auction algorithms, and mechanism design.
• Resources:
  • "Algorithmic Game Theory" by Noam Nisan, Tim Roughgarden, Éva Tardos, and Vijay V. Vazirani
  • Coursera: Game Theory
• My understanding: ⭐⭐⭐ / 5
• Visual:

Quantum Algorithms

• Topics: Quantum computing basics, Shor's algorithm, and Grover's algorithm.
• Resources:
  • "Quantum Computation and Quantum Information" by Michael A. Nielsen and Isaac L. Chuang
  • MIT OpenCourseWare: Quantum Computation
• My understanding: / 5
• Visual: