Algorithms

• The Quiet Calculus of Probabilistic Commutativity · 2025-09-27

  A practical calculus for quantifying when non-commutative operations in distributed systems can be safely executed without heavyweight coordination.

• The Probabilistic Method and Randomized Algorithms: From Tail Bounds to Derandomization · 2025-05-30

  Master the probabilistic method — Paul Erdős's beautiful technique for proving existence non-constructively — alongside the tail bounds (Chernoff, Hoeffding, Azuma) that make randomized algorithms practical, and the modern methods for removing randomness.

• The Fast Fourier Transform: From Cooley-Tukey to Modern Signal Processing and Fast Multiplication · 2025-04-12

  Master the FFT from first principles: the Cooley-Tukey algorithm as recursive divide-and-conquer, the underlying group theory, modern variants for arbitrary sizes, and applications from polynomial multiplication to GPU signal processing.

• Bloom Filters and Probabilistic Data Structures: Trading Certainty for Speed · 2024-08-22

  Explore how Bloom filters, Count-Min sketches, and HyperLogLog sacrifice perfect accuracy for dramatic space and time savings—and learn when that trade-off makes sense.

• Reverse Indexing and Inverted Files: How Search Engines Fly · 2023-07-19

  Tokenization, postings lists, skip pointers, and WAND: a tour of the data structures that make full‑text search fast.

• Garbage Collection Algorithms: From Mark-and-Sweep to ZGC · 2022-11-22

  A comprehensive exploration of garbage collection algorithms, from classic mark-and-sweep to modern concurrent collectors like G1, Shenandoah, and ZGC. Learn how automatic memory management works and the trade-offs that shape collector design.

• Smoothed Analysis: Why Simplex Works in Practice and the Spielman-Teng Framework · 2019-11-19

  An exploration of smoothed analysis—Spielman and Teng's framework that explains why the simplex method and other algorithms transcend their worst-case bounds.

• Parameterized Complexity: FPT, the W-Hierarchy, Kernelization, and Bounded Search Trees · 2019-05-11

  An in-depth exploration of parameterized complexity theory—how structural parameters beyond input size can tame NP-hardness through FPT algorithms, kernelization, and the W-hierarchy.

• Network Flow: From Ford-Fulkerson to Push-Relabel and the Max-Flow Min-Cut Theorem · 2019-04-13

  A rigorous journey through the algorithms that solve maximum flow—Ford-Fulkerson, Edmonds-Karp, Dinic, and Push-Relabel—together with the duality that binds flows to cuts.

• Algorithm Design
• Algorithms
• Algorithms (4th ed.)
• Introduction to Algorithms (3rd ed.)
• Introduction to Parallel Computing (2nd ed.)
• The Art of Computer Programming, Vols. 1–4A