luk036.github.io — A Guided Tour

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# 🗺️ luk036.github.io

### A Guided Tour of Educational Content on Algorithms, VLSI, and Programming

@luk036 👨‍💻 · 2026 📅 · 30 min

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### 📋 Agenda

**Part 1: Overview** 🎯
- What is luk036.github.io?
- Site Structure & Navigation
- Technology Stack

**Part 2: Mathematics & Theory** 🧠
- Convex Optimization (cvx/)
- N-Sphere Sampling (n_sphere/)
- Geometry & Quorum Systems

**Part 3: VLSI & Hardware** 🔌
- Physical Design (phys_des/)
- DFM Algorithms (algo4dfm/)
- Approximate Computing (AxC/)
- Hardware Acceleration (cgra/)

]
.pull-right[

**Part 4: Programming & Tools** 💻
- Modern C++ (proglang/)
- Network Optimization (net_optim/)
- Rust Migration (rust_by_examples/)

**Part 5: Key Packages** 📦
- ellalgo, digraphx, ckpttnpy
- csdigit, physdes, netlistx

**Part 6: How to Navigate** 🧭
- Running Slides Locally
- Finding Content
- Contributing

]

---

## Part 1: Overview 🎯

---

### 🌐 What is luk036.github.io?

A **static educational website** hosted on GitHub Pages, covering:

- 🔬 **Mathematics & Algorithms** — Convex optimization, geometry, statistics
- 💻 **VLSI & Hardware Design** — Physical design, DFM, approximate computing
- 🛠️ **Programming & Tools** — Modern C++, Rust, network optimization
]
.pull-right[
**By the numbers:**

- 📁 **18 topic directories**
- 📄 **100+ Remark.js slide decks**
- 📐 **KaTeX math rendering** throughout
- 🧩 **Mermaid diagrams** for architecture
- 🎨 **Nord theme** (dark/light slides)
]

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### 🏗️ Site Structure

All content is organized into **standalone topic directories**, each with its own `index.html` + `README.md` slide deck:

```text
luk036.github.io/
├── cvx/              # Convex optimization
├── phys_des/         # VLSI physical design
├── algo4dfm/         # DFM algorithms
├── AxC/              # Approximate computing
├── cgra/             # Hardware acceleration
├── proglang/         # Programming languages
├── net_optim/        # Network optimization
├── rust_by_examples/ # Rust migration
├── n_sphere/         # N-sphere sampling
├── projgeom/         # Projective geometry
├── cqs/              # Quorum systems
├── statistics/       # Statistics & ML
├── latch/            # Latch-based timing
└── ...
```

---

### 🛠️ Technology Stack

.mermaid[
<pre>
graph LR
    A[Markdown\nContent] --> B[Remark.js\nSlide Engine]
    B --> C[HTML Slides]
    D[KaTeX] --> B
    E[Mermaid] --> B
    F[Nord Theme\nCSS] --> 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
</pre>
]

- **Remark.js** — JavaScript slide engine, renders Markdown → HTML slides
- **KaTeX** — Fast math rendering ($\LaTeX$)
- **Mermaid** — Diagrams and flowcharts
- **Nord Theme** — Dark/light slide themes with consistent styling

---

## Part 2: Mathematics & Theory 🧠

---

### 🔬 Convex Optimization (cvx/)

| Topic | Description |
|-------|-------------|
| Convex Programming | KKT conditions, CVXPY |
| Geometric Programming | Posynomials, transformations |
| Quasi-convex Programming | Bisection method |
| Ellipsoid Method | Cutting-plane, oracles |
| ellalgo Package | Python implementation |

📖 See: [cvx/](https://luk036.github.io/cvx/)

**Key algorithms:** Ellipsoid method, cutting-plane, geometric programming transformations, LMI formulations, spectral factorization for FIR filters.

---

### 🌐 N-Sphere Sampling (n_sphere/)

**Low Discrepancy Sequences** for spherical point generation:

- **van der Corput** sequences in base $b$
- **Sphere<2,3>** — unit 2-sphere in 3D
- **Sphere3([7,2,3])** — unit 3-sphere in 4D
- **CORDIC** hardware implementation

Key equation — the van der Corput radical inverse:

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

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

---

### 📐 Other Math Topics

.pull-left[
**Cyclic Quorum Systems (cqs/)**
- Difference covers
- Necklace generation
- Distributed systems applications
]

.pull-right[
**Projective Geometry (projgeom/)**
- Cayley-Klein geometries
- Rational trigonometry
- Python implementation

**Statistics & ML (statistics/)**
- Bayesian optimization
- Reinforcement learning
]

---

## Part 3: VLSI & Hardware 🔌

---

### 🏭 Physical Design Automation (phys_des/)

.pull-left[
**Foundations:**
- Circuit partitioning (FM algorithm)
- Rectilinear geometry toolkit
- physdes Python/C++ package

**Placement & Routing:**
- Global placement (min-max fairness)
- Steiner forest (2-approximation)
- FPGA routing
]
.pull-right[
**Clocking & Timing:**
- DME algorithm for clock trees
- Arena-based tree implementation
- Timing closure (STA, ECO)

**Key packages:**
- `ckpttnpy` — Multi-level hypergraph partitioning
- `physdes` — Geometric operations
- `netlistx` — Graph algorithms
]

---

### 🛡️ DFM Algorithms (algo4dfm/)

Design-for-Manufacturability at advanced process nodes:

- **Complexity theory** — NP-completeness in EDA
- **Clock skew scheduling** — Yield-driven, statistical approaches (EVEN, PROP, C-PROP)
- **Phase shifting mask (PSM)** — Phase conflict graphs, Hadlock's algorithm
- **Layout decomposition** — Multiple patterning, 1D layout design
- **Delay padding** — Multi-corner optimization via dual decomposition

---

### ⚡ Approximate Computing (AxC/)

**Canonical Signed Digit (CSD):**
- csdigit Python package
- CSD multiplier synthesis
- LCSRe optimization
]
.pull-right[
**Digital Filters:**
- Multiplierless FIR design
- FIR vs IIR comparison
- Direct-form vs transpose-form

**Root Finding:**
- ginger package
- Polynomial root finding
]

---

### 🚀 Hardware Acceleration (cgra/)

.pull-left[
**Architecture:**
- CGRA — Coarse-grained reconfigurable arrays
- FPGA — Principles and progression
- Approximate multipliers for neural nets

**Compilers:**
- LLVM IR & MLIR infrastructure
- COFFE2 for FPGA modeling
]
.pull-right[
**HDL & Synthesis:**
- LDS hardware generators with CORDIC
- Yosys synthesis and flatten mode
- Advanced digital design

**Signal Processing:**
- Spectral factorization (FFT vs root-finding)
]

---

## Part 4: Programming & Tools 💻

---

### 🖥️ Programming Languages (proglang/)

.pull-left[
**Modern C++:**
- C++17/20 features
- Design patterns
- Performance tips
- Concepts and templates

**Documentation:**
- Doxygen + KaTeX for equations
- Sphinx + matplotlib for figures
- Cross-language docs (C++/Python)

**Git & CI:**
- GitHub CLI workflows
- CI automation
]
.pull-right[
**Code Quality:**
- Common mistakes and lessons
- AI-assisted validation
- Remove duplicate code patterns

**Cross-Language:**
- Python ⇄ C++ type systems
- Rust vs C++ comparison
- Cocotb HDL verification

**Video Processing:**
- FFmpeg-based automation
- xTensor C++ library
]

---

### 🌐 Network Optimization (net_optim/)

.font-sm.mb-xs[
| Algorithm | Description |
|-----------|-------------|
| **NCF** | Negative cycle finding (Bellman-Ford, Howard) |
| **MCR** | Minimum cycle ratio (Karp's algorithm) |
| **Parametric SP** | Shortest paths with variable weights |
| **Vertex Cover** | Exact to GPU-accelerated (CUDA, cudarc) |
| **Christofides TSP** | 3/2-approximation for metric TSP |
| **Hadlock's Algorithm** | Planar MAX-CUT via perfect matching |
| **Primal-Dual Cover** | Approximation with reverse-delete |
]

📦 **digraphx** — Python package: [luk036/digraphx](https://github.com/luk036/digraphx)

---

### 🦀 Rust & Beyond

.pull-left[
**Rust Migration (rust_by_examples/):**
- Python to Rust migration guide
- Ownership and borrowing
- Trait-based design patterns

**Related ports:**
- Porting physdes C++ → Rust
- Porting netlistx Python → Rust
- Rust trait architecture for ellipsoid method
- GPU-accelerated vertex cover in Rust (cudarc)
]
.pull-right[
**Fundamentals (fun/):**
- Metric spaces and topology
- Vector spaces and linear algebra
- Boolean algebra

**Workflows (flows/):**
- Development workflows
- LaTeX toolchains
- Remote working guide
]

---

## Part 5: Key Packages 📦

---

### 📦 Core Packages

| Package | Language | Description | Repo |
|---------|----------|-------------|------|
| `ellalgo` | Python | Ellipsoid method, cutting-plane | [luk036/ellalgo](https://github.com/luk036/ellalgo) |
| `digraphx` | Python | Graph algorithms, NCF, MCR | [luk036/digraphx](https://github.com/luk036/digraphx) |
| `ckpttnpy` | Python | Hypergraph partitioning (FM) | [luk036/ckpttnpy](https://github.com/luk036/ckpttnpy) |
| `physdes` | Python/C++ | Geometric operations, DME, routing | [luk036/physdes-py](https://github.com/luk036/physdes-py) |
| `netlistx` | Python | Covering, matching, graph algo | [luk036/netlistx](https://github.com/luk036/netlistx) |
| `csdigit` | Python | Canonical signed digit conversion | [luk036/csdigit](https://github.com/luk036/csdigit) |
| `projgeom` | Python | Projective geometry | [luk036/projgeom-py](https://github.com/luk036/projgeom-py) |

---

### 🔗 Package Relationships

.mermaid[
<pre>
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
</pre>
]

---

## Part 6: How to Navigate 🧭

---

### 🖥️ Running Slides Locally

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

```bash
# Option 1: Python HTTP server (recommended)
cd luk036.github.io
python -m http.server 8000
# Open: http://localhost:8000

# Option 2: VS Code Live Server extension
# Right-click index.html → Open with Live Server
```

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

---

### 🧭 Finding Content

.pull-left[
**Start at the root:**
- `luk036.github.io/` — Main course index
- Each directory has its own `index.html` + `README.md`

**Slide file naming:**
- `*-remark.html` — Self-contained slides (inline pattern)
- `*-slides.md` — External source markdown
- `README.md` — Course overview (also Remark.js slides)
]
.pull-right[
**Quick reference:**

.font-sm.mb-xs[
| Topic | Directory | Start Here |
|-------|-----------|------------|
| Convex Opt | `cvx/` | `cvxprog-remark.html` |
| Physical Design | `phys_des/` | `README.md` |
| DFM | `algo4dfm/` | `lec00-remark.html` |
| Approx Computing | `AxC/` | `AxC-remark.html` |
| Programming | `proglang/` | `README.md` |
| Network Opt | `net_optim/` | `quickstart.html` |
]

]

---

### 💡 Tips for Exploring

1. **Browse by topic** — Each directory is self-contained with its own `index.html`
2. **Follow the flow** — Start with `cvxprog-remark.html` for convex optimization, trace through to applications
3. **Cross-references** — Packages like `digraphx` appear in both `net_optim/` and `phys_des/`
4. **Search** — GitHub's file search works well for finding specific topics
5. **All slides have Agendas** — Every deck now starts with an agenda slide for easy navigation

---

### 🤝 Contributing

Content is organized as Remark.js Markdown + HTML:

```text
1. Edit the source .md file (or the textarea in -remark.html files)
2. Run a local server to preview: python -m http.server 8000
3. Ensure KaTeX math and Mermaid diagrams render correctly
4. Submit a PR on github.com/luk036/luk036.github.io
```

All `-remark.html` files follow the **flatten-remark.html** reference style:
- Consistent CSS/script ordering
- KaTeX callback pattern with `ignoredTags`
- Proper slide annotations (title, section, Q&A)
- Agenda slide after title

---

# 🙋 Q&A

### Questions? Explore the site at [luk036.github.io](https://luk036.github.io)

---

# 👏 Thank You

### Happy Learning! 🚀

**Resources:**
- 🌐 Site: [luk036.github.io](https://luk036.github.io)
- 🐙 GitHub: [github.com/luk036](https://github.com/luk036)
- 📖 Packages: ellalgo, digraphx, ckpttnpy, physdes, netlistx, csdigit

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