Algorithms

• The Hidden Backbone of Parallelism: How Prefix Sums Power Distributed Computation · 2025-09-21

  Discover how the humble prefix sum (scan) quietly powers GPUs, distributed clusters, and big data frameworks—an obscure but essential building block of parallel and distributed computation.

• 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.

• The PCP Theorem: Why Some Problems Are Hard Even to Approximate · 2025-03-30

  Unpack one of theoretical computer science's crown jewels: the PCP theorem, which shows that for many NP-hard problems, even finding an approximate solution is intractable — and how probabilistically checkable proofs revolutionized our understanding of hardness.

• Designing A Distributed Transaction Log With Raft Consensus: A Step By Step Implementation And Failure Testing In Go · 2023-10-06

  A comprehensive technical exploration of designing a distributed transaction log with raft consensus: a step by step implementation and failure testing in go, covering key concepts, practical implementations, and real-world applications.

• From Lru To Arc: A Technical Survey Of Cache Eviction Policies And Their Performance In Web Scale Distributed Caches · 2022-10-30

  A comprehensive technical exploration of cache eviction policies, from LRU to ARC, covering their performance in web-scale distributed caches, key concepts, practical implementations, and real-world applications.

• Optimizing Distributed Consensus: Comparing Fast Paxos, Epaxos, And Multi Paxos In Wan Deployments With Latency Benchmarks · 2021-08-20

  A comprehensive technical exploration of optimizing distributed consensus, comparing Fast Paxos, Epaxos, and Multi Paxos in WAN deployments with latency benchmarks, covering key concepts, practical implementations, and real-world applications.

• Integer Programming: Branch-and-Bound, Gomory Cuts, Lift-and-Project, and Solver Internals · 2020-02-23

  An inside look at integer programming algorithms—branch-and-bound, cutting planes, lift-and-project hierarchies—and how Gurobi and CPLEX solve NP-hard problems.

• Convex Optimization: Gradient Descent, Nesterov Acceleration, KKT Conditions, and the ML Stack · 2020-02-18

  A deep investigation of convex optimization—the engine of modern machine learning—from gradient descent and Nesterov momentum to KKT conditions and interior-point methods.

• Submodular Optimization: Diminishing Returns, the (1-1/e) Greedy Guarantee, and Machine Learning Applications · 2020-02-01

  A comprehensive study of submodular functions—the discrete analog of convexity—the greedy algorithm's optimal approximation, and applications in active learning and summarization.

• Matroid Theory: The Greedy Exchange Property, Matroid Intersection, and Applications in Spanning Trees and Matching · 2020-01-19

  A thorough exploration of matroid theory—the algebraic abstraction that explains why greedy algorithms work—matroid intersection, and their applications in combinatorial optimization.

• Fair Division: Cut-and-Choose, Selfridge-Conway, Brams-Taylor, and the Mathematics of Envy-Freeness · 2020-01-15

  A rigorous exploration of fair division—from cake-cutting protocols to envy-free allocations—and their application to cloud resource allocation and beyond.

• Mechanism Design: VCG Auctions, the Revelation Principle, and the Architecture of Truthfulness · 2019-12-23

  A deep exploration of mechanism design—the VCG mechanism, Myerson optimal auction, incentive compatibility, and how to design games where truth-telling is a dominant strategy.

• Algorithmic Game Theory: Nash Equilibrium Computation, PPAD-Completeness, and the Computational Lens on Strategy · 2019-11-23

  A rigorous look at algorithmic game theory—computing Nash equilibria, the PPAD complexity class, and how computational constraints reshape strategic reasoning.

• 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.

• Average-Case Complexity: Levin's Distributional Problems, AvgP, and Cryptographic Implications · 2019-10-20

  A deep examination of average-case complexity—Levin's theory of distributional NP-completeness, the class AvgP, and why cryptography needs hard-on-average problems.

• Descriptive Complexity: Fagin's Theorem, Logic, and an Alternative to Turing Machines · 2019-10-12

  An exploration of descriptive complexity—where computational classes are characterized by logical definability—and Fagin's theorem that NP equals existential second-order logic.

• Circuit Complexity: AC0, NC, P/poly, and the PARITY ∉ AC0 Proof · 2019-09-29

  A rigorous journey through circuit complexity classes—AC0, NC, P/poly—and the landmark result that PARITY cannot be computed by constant-depth polynomial-size circuits.

• Communication Complexity: Yao's Two-Party Model, the Rectangle Method, and Lower Bounds Galore · 2019-08-18

  A deep investigation of communication complexity—the mathematics of information exchange between parties—and its far-reaching implications for circuits, data structures, and streaming.

• Sublinear Algorithms: Property Testing, Query Complexity, and the Power of Random Sampling · 2019-07-07

  An exploration of sublinear-time algorithms—property testing, the regularity lemma connection, and how random sampling reveals global structure without reading the whole input.

• Streaming Algorithms: Misra-Gries, Count-Min Sketch, AMS, and the Power of Small Space · 2019-06-27

  A comprehensive tour of streaming algorithms—from frequency estimation sketches to frequency moments—and the space lower bounds that define what's possible.

• Online Algorithms: Competitive Analysis, Ski Rental, Paging, and the Primal-Dual Method · 2019-05-12

  A thorough examination of online algorithms—decisions without foresight—through the lens of competitive analysis, from ski rental and paging to the k-server problem.

• 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.

• NP-Completeness: The Cook-Levin Theorem, Polynomial Reductions, and the Hardest Problems in NP · 2019-05-03

  A deep dive into the theory of NP-completeness—from Turing machines and the Cook-Levin theorem to the taxonomy of NP-complete problems and the P versus NP question.