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🗺️ luk036.github.io

Educational Content on Algorithms, VLSI Design, and Programming

@luk036 👨‍💻 · 2026 📅

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📋 Agenda

.pull-left[

Part 1: Overview 🎯

• Site Structure & Navigation
• Technology Stack

Part 2: Mathematics & Theory 🧠

• Convex Optimization
• N-Sphere Sampling
• Geometry & Quorum Systems

Part 3: VLSI & Hardware 🔌

• Physical Design
• DFM Algorithms
• Approximate Computing
• Hardware Acceleration

] .pull-right[

Part 4: Programming & Tools 💻

• Modern C++
• Network Optimization
• Rust & Beyond

Part 5: Featured Topics 🌟

• In-Depth Highlights

Part 6: Packages & Navigation 📦

• Key Packages
• Running Slides Locally

]

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Part 1: Overview 🎯

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🌐 Site Overview

A static educational website hosted on GitHub Pages, covering three pillars:

.pull-left[ 🔬 Mathematics & Algorithms

• Convex optimization, ellipsoid method
• N-sphere sampling, LDS sequences
• Projective geometry, quorum systems
• Bayesian statistics and ML

💻 VLSI & Hardware Design

• Physical design automation
• DFM algorithms, clock skew
• Approximate computing, CSD
• CGRA, FPGA, LLVM/MLIR ] .pull-right[ 🛠️ Programming & Tools
• Modern C++ (17/20 features, patterns)
• Network optimization algorithms
• Python → Rust migration
• Documentation generation
• Git/CI workflows

By the numbers:

• 📁 18 topic directories
• 📄 100+ Remark.js slide decks
• 📐 KaTeX math rendering
• 🧩 Mermaid diagrams ]

---

🏗️ Technology Stack

.pull-left[ .mermaid[

graph LR
    A[Markdown\nContent] --> B[Remark.js\nSlide Engine]
    B --> C[HTML5 Slides]
    D[KaTeX\nMath] --> B
    E[Mermaid\nDiagrams] --> B
    F[Nord Theme\nCSS] --> C
    G[GitHub Pages] --> C
    style A fill:#4caf50
    style B fill:#2196f3
    style C fill:#ff9800
    style D fill:#9c27b0
    style E fill:#f44336
    style F fill:#00bcd4
    style G fill:#607d8b

] ] .pull-right[

• Remark.js — JavaScript slide engine rendering Markdown → HTML slides
• KaTeX — Fast $\LaTeX$ math rendering with ignoredTags for code blocks
• Mermaid — Flowcharts, architecture diagrams, state machines
• Nord Theme — Dark/light slide themes with consistent typography ]

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📁 Directory Structure

Content is organized into self-contained topic directories:

luk036.github.io/
├── cvx/              # Convex optimization & ellipsoid method
├── phys_des/         # VLSI physical design automation
├── algo4dfm/         # DFM algorithms & complexity theory
├── AxC/              # Approximate computing & CSD
├── cgra/             # CGRA, FPGA, LLVM/MLIR, HDL
├── proglang/         # Modern C++, Git/CI, docs, tools
├── net_optim/        # Graph algorithms & network flow
├── n_sphere/         # Low discrepancy sequences
├── cqs/              # Cyclic quorum systems
├── projgeom/         # Projective geometry
├── statistics/       # Bayesian optimization, RL
├── latch/            # Latch-based timing
├── rust_by_examples/ # Python → Rust migration
├── fun/              # Foundations (metric spaces, algebra)
├── flows/            # Development workflows
└── idea/             # Working notes, experiments

Each directory contains index.html + README.md (slide deck) + *-remark.html files.

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Part 2: Mathematics & Theory 🧠

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🔬 Mathematics & Theory

.font-sm.mb-xb[

Topic	Directory	Description
Convex Optimization	cvx/	CVXPY, KKT conditions, geometric programming, quasi-convex, LMI, ellipsoid method, cutting-plane, Krylov methods
N-Sphere Sampling	n_sphere/	Low discrepancy sequences (van der Corput, Halton), spherical point generation, CORDIC implementation
Projective Geometry	projgeom/	Cayley-Klein geometries, rational trigonometry, Python implementation
Cyclic Quorum Systems	cqs/	Difference covers, necklace generation, distributed systems
Statistics & ML	statistics/	Bayesian optimization, Gaussian processes, reinforcement learning
]

---

📐 Convex Optimization (cvx/)

.pull-left[ Core Topics:

• Convex programming fundamentals
• Geometric programming (posynomials)
• Quasi-convex programming (bisection)
• Linear Matrix Inequalities (LMI)
• Convex piecewise-linear fitting

Packages:

• ellalgo — Ellipsoid method, cutting-plane
• cvxpy — Python convex optimization ] .pull-right[ Key Algorithms:
• Ellipsoid method with deep/central/parallel cuts
• Cutting-plane with separation oracles
• Geometric program → convex transformations
• Spectral factorization for FIR filters
• Primal-dual interior point methods

Applications: EDA, filter design, circuit sizing ]

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🌐 N-Sphere Sampling (n_sphere/)

Low discrepancy sequences for generating points on spheres:

$$ \text{VdC}_b(n) = \sum_i d[i] \cdot b^{-i-1} $$

.pull-left[ Sphere<2,3> (unit 2-sphere in 3D):

• VdC₂ → cos ϕ, VdC₃ → θ
• CORDIC-free sqrt computation
• Hardware-friendly architecture ] .pull-right[ Sphere3([7,2,3]) (unit 3-sphere in 4D):
• VdC₇ → F₂⁻¹ LUT → CORDIC
• Spherical coordinates in 4D
• LDS hardware generators ]

Used in: quasi-Monte Carlo, particle filters, hardware test generation.

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Part 3: VLSI & Hardware 🔌

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💻 VLSI & Hardware Design

Topic	Directory	Description
Physical Design	phys_des/	Circuit partitioning, placement, routing, clock tree synthesis, timing closure
DFM Algorithms	algo4dfm/	Complexity theory, clock skew under PV, PSM, layout decomposition, delay padding
Approximate Computing	AxC/	Approximate arithmetic, CSD representation, multiplierless FIR/IIR filters
Hardware Acceleration	cgra/	CGRA architecture, FPGA, LLVM/MLIR, HDL generators, Yosys synthesis
Latch-Based Timing	latch/	Useful skew, max-plus algebra, timing optimization

---

🏭 Physical Design (phys_des/)

.pull-left[ Foundations:

• Circuit partitioning (FM, multi-level)
• Rectilinear geometry toolkit
• physdes C++/Python package

Placement & Routing:

• Global placement (min-max fairness)
• Steiner forest (2-approximation PD-SF)
• FPGA routing, global routing with keepouts ] .pull-right[ Clocking & Timing:
• DME algorithm for clock trees
• Arena-based tree with NodeIdx
• Linear vs Elmore delay models
• Timing closure (STA, setup/hold, ECO)
• Useful skew optimization

Packages: ckpttnpy, physdes, netlistx ]

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🛡️ DFM Algorithms (algo4dfm/)

.mermaid[

graph LR
    subgraph "Part I: Foundations"
        F1["DFM Introduction"]
        F2["Software Dev & Tools"]
        F3["Statistics & Correlation"]
        F4["Convex Optimization"]
    end
    subgraph "Part II: Core Algorithms"
        C1["Ellipsoid Method"]
        C2["Cutting-plane Method"]
        C3["Clock Skew Scheduling"]
        C4["Network Flow"]
        C5["Complexity Theory"]
    end
    subgraph "Part III: Advanced"
        A1["Phase Shifting Mask"]
        A2["Layout Decomposition"]
        A3["1D Layout Design"]
    end

]

Key topics: NP-completeness in EDA, yield-driven clock skew (EVEN, PROP, C-PROP), Hadlock's algorithm for planar MAX-CUT, delay padding via dual decomposition.

---

⚡ Approximate Computing (AxC/)

.pull-left[ Approximate Arithmetic:

• Survey of AxC techniques
• Approximate multipliers for neural nets
• Error tolerance analysis

Canonical Signed Digit (CSD):

• csdigit Python package
• CSD multiplier synthesis (LCSRe)
• Shift-add optimization ] .pull-right[ Digital Filters:
• Multiplierless FIR/IIR design
• Direct-form vs transpose-form
• Discrete optimization vs quantize-after

Root Finding:

• ginger package
• Polynomial root finding & reconstruction
• Leja ordering for numerical stability ]

---

🚀 Hardware Acceleration (cgra/)

.font-sm.mb-xs[

Topic	Description
CGRA	Coarse-grained reconfigurable arrays — architecture, compilation, challenges
FPGA	Principles, progression, COFFE2 modeling
Compilers	LLVM IR, MLIR multi-level infrastructure
HDL Generators	LDS hardware with CORDIC, van der Corput → unit sphere
Synthesis	Yosys flatten mode, hierarchical vs flat ABC
Approx Multipliers	Energy-efficient neural computing
Digital Design	Advanced digital system design
]

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Part 4: Programming & Tools 💻

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🛠️ Programming & Tools

Topic	Directory	Description
Programming Language	proglang/	Modern C++17/20, design patterns, Git/CI workflows, documentation generation, code quality, video processing, xTensor
Network Optimization	net_optim/	Graph algorithms, NCF, MCR, parametric SP, vertex cover (exact→GPU), TSP, DEC, Hadlock
Rust Migration	rust_by_examples/	Python → Rust migration guide, ownership, traits
Fundamentals	fun/	Metric spaces, vector spaces, Boolean algebra
Workflows	flows/	Development workflows, LaTeX, remote working

---

🖥️ Programming Languages (proglang/)

.pull-left[ C++ Features:

• C++17/20 (concepts, ranges, coroutines)
• Design patterns (Strategy, Visitor, CRTP)
• Performance tips (move semantics, inlining)
• Header-only → source-based refactoring

Documentation:

• Doxygen + KaTeX for equations
• Sphinx + matplotlib for figures
• Cross-language docs (C++/Python) ] .pull-right[ Tools & Quality:
• Git/GitHub CLI workflows
• CI automation (GitHub Actions)
• Common mistakes and lessons learned
• AI-assisted code validation
• Remove duplicate code patterns

Cross-Language:

• Python ⇄ C++ type systems
• Rust vs C++ comparison
• Cocotb HDL verification
• Video processing (FFmpeg)
• xTensor multi-dim arrays ]

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🌐 Network Optimization (net_optim/)

.pull-left[ Core Algorithms:

• Negative Cycle Finding (NCF) — Bellman-Ford, Howard
• Minimum Cycle Ratio (MCR) — Karp's algorithm
• Parametric shortest paths
• Discrete Exterior Calculus (DEC)

Approximations:

• Christofides TSP (3/2-approximation)
• Primal-dual for covering problems
• Hadlock's planar MAX-CUT ] .pull-right[ Vertex Cover Suite:
• Exact algorithms
• Randomized GPU (CUDA, cudarc)
• Python → C++ → Rust ports
• CUDA and Rust GPU implementations

Package: digraphx — Python graph algorithms ]

---

🦀 Rust & Beyond

• Rust Migration Guide — Python → Rust: ownership, borrowing, traits, patterns
• Porting physdes — C++ → Rust: geometry library with DME, Steiner routing, arena trees
• Porting netlistx — Python → Rust: EDA algorithms for covering, matching, graphs
• Rust Ellipsoid — Trait-based generic cutting-plane algorithms
• GPU Vertex Cover (Rust) — cudarc port for GPU-accelerated randomized algorithms

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Part 5: Featured Topics 🌟

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🎯 Convex Optimization

.pull-left[

• Introduction to CVXPY
• Quasi-convex programming via bisection
• Ellipsoid method and amazing oracles
• Geometric programming transformations
• Linear Matrix Inequalities (LMI)
• Convex fitting using B-splines ] .pull-right[ Key files: cvxprog-remark.html, quasicvx-remark.html, geomprog-remark.html, ellipsoid-remark.html, ellalgo-remark.html

📖 See: cvx/ ]

---

🎯 Physical Design Automation

.pull-left[

• Circuit partitioning (FM, multi-level, Gray code)
• Rectilinear geometry toolkit
• Global placement (min-max fairness)
• Steiner forest (2-approximation PD-SF)
• DME clock tree synthesis
• Timing closure (STA, ECO) ] .pull-right[ Key files: ckpttn-remark.html, nnsplace-remark.html, steiner-forest-remark.html, dme_algorithm-remark.html, timing-closure-remark.html

📖 See: phys_des/ ]

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🎯 DFM & Clock Skew

.pull-left[

• Complexity theory & NP-completeness in EDA
• Clock skew scheduling under process variations
• Useful skew optimization
• Multi-corner delay padding via dual decomposition
• Phase shifting mask algorithms
• Layout decomposition for multiple patterning ] .pull-right[ Key files: lec05a-remark.html, lec05b-remark.html, delay_padding-remark.html, lec08-remark.html, lec09-remark.html

📖 See: algo4dfm/ ]

---

🎯 Approximate Computing & CSD

.pull-left[

• Survey of approximate arithmetic circuits
• Approximate multipliers for neural computing
• Canonical Signed Digit (CSD) representation
• CSD multiplier: shift-add with LCSRe
• Multiplierless FIR filter design
• FIR vs IIR filter comparison ] .pull-right[ Key files: csd-remark.html, csd_multiplier-remark.html, csdigit-remark.html, multiplierless-remark.html, FIR-IIR-remark.html

📖 See: AxC/ ]

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Part 6: Packages & Navigation 📦

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📦 Key Packages

Package	Language	Description	Repo
ellalgo	Python	Ellipsoid method, cutting-plane, oracles	luk036/ellalgo
digraphx	Python	Graph algorithms, NCF, MCR, parametric SP	luk036/digraphx
ckpttnpy	Python	Multi-level hypergraph partitioning (FM)	luk036/ckpttnpy
physdes	Python/C++	Geometric operations, DME, Steiner routing	luk036/physdes-py
netlistx	Python	Covering, matching, independent set	luk036/netlistx
csdigit	Python	Canonical signed digit conversion	luk036/csdigit
projgeom	Python	Projective geometry, Cayley-Klein	luk036/projgeom-py

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🔗 Package Relationships

.mermaid[

graph LR
    ellalgo[ellalgo\nCutting-Plane] --> digraphx[digraphx\nGraph Algorithms]
    digraphx --> ckpttnpy[ckpttnpy\nPartitioning]
    ckpttnpy --> physdes[physdes\nGeometry]
    physdes --> netlistx[netlistx\nNetlist]
    csdigit[csdigit\nCSD] --> multiplierless[multiplierless\nFIR Filters]

    style ellalgo fill:#4caf50
    style digraphx fill:#2196f3
    style ckpttnpy fill:#ff9800
    style physdes fill:#9c27b0
    style netlistx fill:#f44336
    style csdigit fill:#00bcd4
    style multiplierless fill:#ff5722

]

---

🖥️ Running Slides Locally

Since slides use Remark.js with sourceUrl to load Markdown:

# Recommended: Python HTTP server
cd luk036.github.io
python -m http.server 8000
# Open: http://localhost:8000

⚠️ Opening index.html directly via file:// won't work for slides that load external .md files (CORS restriction). Self-contained *-remark.html files work via file://.

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🧭 Navigating the Site

.pull-left[ Starting points by topic:

.font-sm.mb-xs[

Topic	Start Here
Convex Opt	cvx/cvxprog-remark.html
N-Sphere	n_sphere/
Physical Design	phys_des/README.md
DFM	algo4dfm/lec00-remark.html
Approx Computing	AxC/AxC-remark.html
CGRA/FPGA	cgra/CGRA-remark.html
Programming	proglang/README.md
Network Opt	net_optim/quickstart.html
]
]
.pull-right[
Slide naming conventions:

• *-remark.html — Self-contained slides (inline pattern, works via file://)
• *-slides.md — External source markdown (loaded via sourceUrl)
• README.md — Course overview (also Remark.js slides)

All slide decks follow: flatten-remark.html reference style with Agenda, consistent CSS/script ordering, KaTeX callback pattern, and proper slide annotations. ]

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🙋 Questions?

Explore the site at luk036.github.io 🚀

Feel free to explore any topic above. Each directory contains Remark.js slide decks, code examples, and additional resources.

Slides built with Remark.js 🎉 | KaTeX | Mermaid | Nord Theme