Theory
536 posts in category “Theory”.
Building A Simple Ray Tracer: Bvh Acceleration, Anti Aliasing, And Path Tracing
2025-09-20A comprehensive technical exploration of building a simple ray tracer: bvh acceleration, anti aliasing, and path tracing, covering key concepts, practical implementations, and real-world applications.
The Architecture Of A Log Structured Merge Tree (lsm) With Memory Bucketed Compaction
2025-09-07A comprehensive technical exploration of the architecture of a log structured merge tree (lsm) with memory bucketed compaction, covering key concepts, practical implementations, and real-world applications.
The Johnson-Lindenstrauss Lemma and the Geometry of High-Dimensional Data
2025-09-05Explore the surprising geometry of high-dimensional spaces: the Johnson-Lindenstrauss lemma showing that random projections preserve pairwise distances, the concentration phenomena that make it work, and its profound applications in nearest-neighbor search, compressed sensing, and machine learning.
Implementing The Dijkstra–scholten Algorithm For Termination Detection In Distributed Systems
2025-08-30A comprehensive technical exploration of implementing the dijkstra–scholten algorithm for termination detection in distributed systems, covering key concepts, practical implementations, and real-world applications.
Designing A Sharded Counter With Crdts For Eventually Consistent Analytics
2025-08-26A comprehensive technical exploration of designing a sharded counter with crdts for eventually consistent analytics, covering key concepts, practical implementations, and real-world applications.
Lattice-Based Cryptography: Learning With Errors and the Road to Fully Homomorphic Encryption
2025-08-24Enter the post-quantum world of lattice-based cryptography: the Learning With Errors (LWE) problem, its reduction from worst-case lattice problems, the construction of basic encryption from LWE, and the stunning breakthrough of fully homomorphic encryption that computes on encrypted data.
A Practical Introduction To Homomorphic Encryption: Bfv Scheme Implementation
2025-08-23A comprehensive technical exploration of a practical introduction to homomorphic encryption: bfv scheme implementation, covering key concepts, practical implementations, and real-world applications.
Building A Parallel Algorithm For Graph Coloring Using Openmp And Mpi
2025-08-12A comprehensive technical exploration of building a parallel algorithm for graph coloring using openmp and mpi, covering key concepts, practical implementations, and real-world applications.
Differential Privacy: Formal Guarantees, Composition Theorems, and the Engineering of Private Systems
2025-08-12Build differential privacy from first principles: the formal (ε, δ)-definition, the Laplace and Gaussian mechanisms, composition theorems (basic and advanced), the sparse vector technique, and how to engineer practical private data systems at scale.
Implementing A Distributed Lock Service Using Zookeeper (with Zab Protocol Analysis)
2025-08-10A comprehensive technical exploration of implementing a distributed lock service using zookeeper (with zab protocol analysis), covering key concepts, practical implementations, and real-world applications.
Kolmogorov Complexity and Algorithmic Information Theory: The Deepest Measure of Information
2025-07-30Dive into algorithmic information theory: Kolmogorov complexity as the ultimate measure of information content, its relationship to randomness (Martin-Löf tests), the incompressibility method for proving lower bounds, and the philosophical implications for science and mathematics.
The Design And Implementation Of A Database Index Using Fractal Trees (cache Oblivious B Trees)
2025-07-29A comprehensive technical exploration of the design and implementation of a database index using fractal trees (cache oblivious b trees), covering key concepts, practical implementations, and real-world applications.
Implementing A Simple Type System For A Programming Language: Hindley Milner Type Inference
2025-07-25A comprehensive technical exploration of implementing a simple type system for a programming language: hindley milner type inference, covering key concepts, practical implementations, and real-world applications.
A Deep Dive Into The Cuckoo Filter: Design, Implementation, And Performance Tuning
2025-07-21A comprehensive technical exploration of a deep dive into the cuckoo filter: design, implementation, and performance tuning, covering key concepts, practical implementations, and real-world applications.
Queueing Theory for Systems Engineers: From M/M/1 to Heavy-Tail Distributions and Tail-at-Scale
2025-07-18Master queueing theory as a practical tool for systems design: the M/M/1 model, Little's Law, Jackson networks, the dramatic impact of heavy-tailed service times on tail latency, and how to apply these insights to load balancers, microservices, and capacity planning.
Building A Distributed File System With Erasure Coding (reed Solomon Implementation)
2025-07-16A comprehensive technical exploration of building a distributed file system with erasure coding (reed solomon implementation), covering key concepts, practical implementations, and real-world applications.
The Science Of Clock Synchronization: Ntp, Ptp, And Hybrid Logical Clocks In Distributed Systems
2025-07-09A comprehensive technical exploration of the science of clock synchronization: ntp, ptp, and hybrid logical clocks in distributed systems, covering key concepts, practical implementations, and real-world applications.
Implementing A Convolutional Neural Network In Cuda: Kernels, Tiling, And Shared Memory
2025-07-07A comprehensive technical exploration of implementing a convolutional neural network in cuda: kernels, tiling, and shared memory, covering key concepts, practical implementations, and real-world applications.
Algebraic Topology in Distributed Computing: Wait-Free Solvability and Simplicial Complexes
2025-07-06Discover how algebraic topology — simplicial complexes, Sperner's lemma, and homology — provides the deepest known framework for understanding what concurrent and distributed tasks are fundamentally solvable, as developed in Herlihy and Shavit's 'The Art of Multiprocessor Programming'.
Writing A Tiny Elf Loader: Executable Linking And Relocation In Linux
2025-07-01A comprehensive technical exploration of writing a tiny elf loader: executable linking and relocation in linux, covering key concepts, practical implementations, and real-world applications.
Design And Implementation Of A Distributed Rate Limiter (token Bucket With Consistent Hashing)
2025-06-26A comprehensive technical exploration of design and implementation of a distributed rate limiter (token bucket with consistent hashing), covering key concepts, practical implementations, and real-world applications.
Memory Consistency Models: From Sequential Consistency to the C++11 Memory Model
2025-06-24A rigorous treatment of memory consistency models: Lamport's sequential consistency, the transition to relaxed models, the formal semantics of the C++11 memory model with its acquire-release and relaxed atomics, and how to reason about concurrent code that doesn't tear.
A Practical Guide To Implementing The Actor Model In Rust: Tokio And Custom Schedulers
2025-06-20A comprehensive technical exploration of a practical guide to implementing the actor model in rust: tokio and custom schedulers, covering key concepts, practical implementations, and real-world applications.
Implementing A Self Balancing Binary Search Tree: Red Black Tree Vs. Avl Tree Internals
2025-06-15A comprehensive technical exploration of implementing a self balancing binary search tree: red black tree vs. avl tree internals, covering key concepts, practical implementations, and real-world applications.