Algorithms Illuminated

Tim Roughgarden is a Professor of Computer Science at Columbia University. His research, teaching, and expository writings have been recognized by a Presidential Early Career Award for Scientists and Engineers, the ACM Grace Murray Hopper Award, the EATCS-SIGACT Gödel Prize, a Guggenheim Fellowship, the INFORMS Lancaster Prize, and a Tau Beta Pi Teaching Award. His other books include Twenty Lectures on Algorithmic Game Theory (2016) and Beyond the Worst-Case Analysis of Algorithms (2021).

'Algorithms Illuminated is academic gold for both students and instructors. The most incredible thing about this book is the way it reaches different types of learners. Beginning students love the approach of getting exposed to complex material slowly and methodically, with lots of intuition and illustrations; advanced students can focus their energy on the formal treatment, going back to the intuition as needed. I love this book because it makes very difficult concepts accessible to everyone.' Thomas Cook, US Military Academy at West Point

• Part I. The Basics: 1. Introduction; 2. Asymptotic notation; 3. Divide-and-Conquer algorithms; 4. The master method; 5. QuickSort; 6. Linear-time selection; Part II. Graph Algorithms and Data Structures: 7. Graphs: the Basics; 8. Graph search and its applications; 9. Dijkstra's shortest-path algorithm; 10. The heap data structure; 11. Search trees; 12. Hash tables and Bloom filters; Part III. Greedy Algorithms and Dynamic Programming; 13. Introduction to greedy algorithms; 14. Huffman codes; 15. Minimum spanning trees; 16. Introduction to dynamic programming; 17. Advanced dynamic programming; 18. Shortest paths revisited; Part IV. Algorithms for NP-Hard Problems; 19. What is NP-Hardness?; 20. Compromising on correctness: efficient inexact algorithms; 21. Compromising on speed: exact inefficient algorithms; 22. Proving problems NP-hard; 23. P, NP, and all that; 24. Case study: the FCC incentive auction; Appendix A. Quick review of proofs By induction; Appendix B. Quick review of discrete probability; Epilogue. A field guide to algorithm design; Hints and solutions.