netlistx Python Package

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# netlistx Python Package 🥅

A Toolkit for Solving Optimization Problems in Graphs and Hypergraphs

@luk036 👨‍💻 · 2026 📅

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### 📋 Agenda

**Part 1: Introduction** 🎯
- What is netlistx? 🤔
- Graphs & Hypergraphs 🕸️

**Part 2: Optimization** 🔄
- Primal-Dual Method ✨
- Covering Problems 🛡️

**Part 3: Module 1 - Cover** 🧤
- min_vertex_cover 🖼️
- min_cycle_cover 🔄
- Usage Examples 📊

]
.pull-right[

**Part 4: Module 2 - Graph Algo** 🧠
- graph_algo Module 🤝
- Independent Set 🚫

**Part 5: Module 3 - Matching** 🔗
- Maximal Matching 🎯
- min_maximal_matching ⚙️

**Part 6: Module 4 - Netlist** 🔌
- Netlist Classes 🏗️
- Summary & Applications ✅

]

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## Part 1: Introduction 🎯

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### 🤔 What is netlistx?

- A **Python package** 🐍 providing tools for **working with netlists** 🔌.
- **Netlists** are representations of **electronic circuits** ⚡, specifically sets of classes and functions for netlists, representing electronic circuits.
- The main purpose is to provide **tools for creating 🛠️, manipulating 🔄, and analyzing 🔍 netlists**.
- Draws on **graph theory concepts** 📐.
- Uses the **NetworkX library** for graph objects.
- Can also be used for **various optimization problems** in computer science 💻 and operations research 📚 beyond just netlists.

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### 🕸️ Graphs & Hypergraphs

- **Graphs:** Represent connections between entities (nodes/vertices) using edges.
  - `netlistx` uses the **NetworkX library** for graph objects.
- **Hypergraphs:** A generalization of graphs where an edge can connect **more than two vertices** 🔗.
- **Weights:** Both vertices and edges can have associated weights ⚖️. This is often represented as a dictionary 📖 mapping the entity to its weight. Weights are crucial for optimization problems.
  - Often uses a **MutableMapping** (like a dictionary 📖) for weights.

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## Part 2: Optimization 🔄

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### ✨ Optimization & Primal-Dual

- Many problems in computer science 💻 and operations research 📚 can be modeled as graph or hypergraph optimization problems.
- `netlistx` implements algorithms for solving several types of problems, primarily focusing on **covering 🛡️ and matching 🤝**.
- A key technique used is the **primal-dual approximation method**.
  - This method iteratively builds a solution 🔄.
  - It often maintains a "gap" for each vertex or edge.
  - Helps ensure the solution is **within a certain factor of the optimal solution** ✅.
  - Algorithms are often **NP-hard** and difficult to solve exactly for large instances, making approximation methods valuable.

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## Part 3: Module 1 - Cover 🧤

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### 🧤 Module 1: `netlistx.cover`

- Focuses on **covering problems** 🛡️.
- Goal: Find a **minimal set of vertices or edges** that "**cover**" certain structures (like edges, vertices, cycles).
- Algorithms often return:
  - The set of elements forming the minimal cover.
  - The total weight or cost of that cover.
- Key functions include:
  - `pd_cover`: A general function that takes a `violate` function.
  - `min_vertex_cover`: Finds a minimum weighted vertex cover.
  - `min_hyper_vertex_cover`: Works on hypergraphs.
  - `min_cycle_cover`: Finds a minimum weighted set of vertices to cover all cycles.
  - `min_odd_cycle_cover`: Similar to `min_cycle_cover`, targets only odd cycles.
- These functions use the **primal-dual approximation algorithm**.

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### 🖼️ `min_vertex_cover` Example

- `netlistx.cover.min_vertex_cover(ugraph, weight, coverset)`
- **Parameters:**
  - `ugraph`: A **NetworkX graph** object.
  - `weight`: Dictionary mapping **each node to a weight** ⚖️.
  - `coverset`: Optional initial set of vertices already in the cover.
- **Returns:** A tuple
  - Set representing the **minimum weighted vertex cover**.
  - Integer or float representing the **weight of the minimum cover**.

.mermaid[
<pre>
graph LR
    A(("A\n w=2"))
    B(("B\n w=3"))
    C(("C\n w=1"))
    D(("D\n w=4"))
    E(("E\n w=2"))
    A --- B
    A --- C
    B --- D
    C --- D
    C --- E
    D --- E

style A fill:#c8e6c9,stroke:#2e7d32,stroke-width:3px,color:#2e3440
    style B fill:#fff3e0,stroke:#e65100,stroke-width:3px,color:#2e3440
    style C fill:#c8e6c9,stroke:#2e7d32,stroke-width:3px,color:#2e3440
    style D fill:#fff3e0,stroke:#e65100,stroke-width:3px,color:#2e3440
    style E fill:#c8e6c9,stroke:#2e7d32,stroke-width:3px,color:#2e3440
</pre>
]

_Example usage and diagram are provided in the source showing graph setup, weights, and the resulting cover._

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## Part 4: Module 2 - Graph Algo 🧠

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### 🧠 Module 2: `netlistx.graph_algo`

- Contains graph algorithms primarily focused on **optimization problems**.
- Also uses the **primal-dual approximation technique**.
- Key functions:
  - `min_minimal_independent_set`: Finds a minimum weighted maximal independent set in a graph.
    - An **independent set** is a set of vertices where **no two vertices are connected by an edge** 🚫.
    - A **maximal** independent set means you can't add any more vertices without breaking the rule.
  - `min_vertex_cover_fast`: Finds a minimum weighted vertex cover. This seems similar to the function in the `cover` module. It is noted as "fast" in its name and description.
- Useful for graph theory applications like **network design 🌐, scheduling ⏳, and resource allocation 📦**.

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### 🤝 `min_minimal_independent_set`

- `netlistx.graph_algo.min_minimal_independent_set(ugraph, weight, indset, dep)`
- **Parameters:**
  - `ugraph`: A **directed or undirected NetworkX graph**.
  - `weight`: Dictionary mapping **vertices to weights** ⚖️.
  - `indset`: Optional initial set of vertices in the independent set.
  - `dep`: Optional set of vertices that are already covered by the matching. (Note: description mentions 'matching' here, might be a slight mixup or dual concept to covering).
- **Returns:** A tuple
  - Set representing the **minimum maximal independent set** (`indset`).
  - Total primal cost (weight).

_Example usage and diagram are provided in the source._

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## Part 5: Module 3 - Matching 🔗

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### 🔗 Module 3: `min_maximal_matching`

- Implements an algorithm to find a **minimum weighted maximal matching in a hypergraph**.
- Purpose: Select a set of edges (called "nets" in this context) from a hypergraph.
- Goal: Minimize the total weight of the selected edges while ensuring that **no more edges can be added** without overlapping with already selected edges.
- Useful in optimization problems like **circuit design** or **resource allocation**.
- Also uses a **primal-dual approach**.
- Starts with an empty matching and iteratively adds edges.

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### ⚙️ `min_maximal_matching` Function

- `netlistx.algo.min_maximal_matching(hypergraph, weight, matchset, dep)`
- **Parameters:**
  - `hypergraph`: Representation of the hypergraph structure.
  - `weight`: Dictionary assigning **weight to each edge** ⚖️.
  - `matchset`: Optional set of pre-selected edges already in the matching.
  - `dep`: Optional set of vertices already covered by the matching.
- **Returns:** A tuple
  - Final set of **matched edges** (`matchset`).
  - Total weight of the selected matching.

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### 🕸️ Hypergraph Example

.mermaid[
<pre>
graph LR
    subgraph "Hypergraph Edges"
        E1("(e1\n w=2)")
        E2("(e2\n w=5)")
        E3("(e3\n w=3)")
    end
    subgraph "Vertices"
        V1(v1) --- E1
        V2(v2) --- E1
        V2 --- E2
        V3(v3) --- E2
        V3 --- E3
        V4(v4) --- E3
    end

style E1 fill:#c8e6c9,stroke:#2e7d32,stroke-width:3px,color:#2e3440
    style E2 fill:#ffcdd2,stroke:#c62828,stroke-width:3px,color:#2e3440
    style E3 fill:#c8e6c9,stroke:#2e7d32,stroke-width:3px,color:#2e3440
    style V1 fill:#e3f2fd,stroke:#1565c0,stroke-width:3px,color:#2e3440
    style V2 fill:#e3f2fd,stroke:#1565c0,stroke-width:3px,color:#2e3440
    style V3 fill:#e3f2fd,stroke:#1565c0,stroke-width:3px,color:#2e3440
    style V4 fill:#e3f2fd,stroke:#1565c0,stroke-width:3px,color:#2e3440
</pre>
]

_An example diagram of a hypergraph is provided._

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## Part 6: Module 4 - Netlist 🔌

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### 🔌 Module 4: `netlistx.netlist`

- This is the core module for working with **netlists** specifically.
- Defines classes and functions for **representing electronic circuits** ⚡.
- A netlist is represented as a **graph**.
- Takes **three inputs** when created:
  - List of modules (like chip instances).
  - List of nets (connections between modules/pins).
  - List of pins (connection points on modules).
- Allows getting information like the **number of modules, nets, and pins**.
- Includes helper functions for creating specific types of netlists, e.g., `create_random_hgraph`.
- Can **read netlists from JSON files**.

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### 🏗️ netlist: Key Classes & Functions

- Base representation is a **graph** (uses NetworkX).
- Includes simple graph classes like `SimpleGraph`, `ThinGraph`, `TinyGraph`.
- Provides utility functions for dictionary initialization (e.g., `all_edge_dict_factory`, `node_attr_dict_factory`).
- Functions to get netlist properties:
  - `get_max_degree()`: Max degree of nodes in the graph.
  - `get_module_weight(v)`: Weight of a given module.
  - `get_net_weight()`: Weight of a net.
  - `number_of_modules()`: Returns the count of modules.
  - `number_of_nets()`: Returns the count of nets.
  - `number_of_pins()`: Returns the count of edges (pins).
- Functions for creating test netlists: `create_drawf`, `create_inverter`, `create_inverter2`, `create_random_hgraph`, `create_test_netlist`.
- `read_json(filename)`: Reads a JSON file into a Netlist object.

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### ✅ Summary: What Can You Do with netlistx?

Based on the source, `netlistx` helps with:

- **Representing netlists** (electronic circuits) as graphs/hypergraphs.
- Solving various **covering problems** (vertex cover, cycle cover) in graphs and hypergraphs.
- Finding **independent sets** in graphs.
- Finding **maximal matchings** in hypergraphs.
- Using **primal-dual approximation algorithms** for efficient solutions.
- Creating and manipulating **netlist structures**.
- Handling **weighted graphs and hypergraphs**.

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### 👋 Conclusion

`netlistx` is a powerful library for tackling complex graph and hypergraph optimization problems, particularly those related to covering and matching, often leveraging primal-dual approximation for efficiency. While rooted in netlist applications, its algorithms have broader applicability in computer science and operations research.

**GitHub** 🐙: [netlistx](https://github.com/luk036/netlistx) 🔗

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# 🙋 Q&A

### Questions? Discussion? 💬

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# 👏 Thank You

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