Graph coloring for register allocation in Compiler Design - Mini Project: Build & Apply

Graph Coloring for Register Allocation

📖 Scenario: Imagine you are designing a simple compiler that needs to assign variables to a limited number of CPU registers. To avoid conflicts, variables that are used at the same time cannot share the same register. This problem can be solved using graph coloring.

🎯 Goal: Build a step-by-step understanding of how to represent variable conflicts as a graph and apply graph coloring to allocate registers without conflicts.

📋 What You'll Learn

Create a graph representing variable conflicts using an adjacency list

Define the number of available registers

Apply graph coloring to assign registers to variables

Complete the allocation by ensuring no two connected variables share the same register

💡 Why This Matters

🌍 Real World

Register allocation is a key step in compiler design to optimize CPU register usage and improve program speed.

💼 Career

Understanding graph coloring for register allocation is important for compiler engineers and systems programmers working on performance optimization.

1

Create the interference graph

Create a dictionary called interference_graph representing variable conflicts. Use these exact entries: 'a': ['b', 'c'], 'b': ['a', 'c', 'd'], 'c': ['a', 'b'], 'd': ['b'].

Compiler Design

# Create the interference graph dictionary
# Your code here

Need a hint?

Think of each variable as a node and list its neighbors that it conflicts with.

2

Define the number of registers

Create a variable called num_registers and set it to 3 to represent the available CPU registers.

Compiler Design

interference_graph = {
    'a': ['b', 'c'],
    'b': ['a', 'c', 'd'],
    'c': ['a', 'b'],
    'd': ['b']
}
# Define the number of registers
# Your code here

Need a hint?

Set a variable to the exact number 3 to represent registers.

3

Assign registers using graph coloring

Create a dictionary called register_allocation. Use a for loop with variable var iterating over interference_graph. For each var, assign the lowest register number from 1 to num_registers that is not used by its neighbors in register_allocation.

Compiler Design

interference_graph = {
    'a': ['b', 'c'],
    'b': ['a', 'c', 'd'],
    'c': ['a', 'b'],
    'd': ['b']
}
num_registers = 3
# Assign registers to variables
# Your code here

Need a hint?

Check neighbors' assigned registers and pick the first free register for each variable.

4

Complete the register allocation

Add a final line that creates a variable called allocation_complete and sets it to true if all variables in interference_graph have an assigned register in register_allocation.

Compiler Design

interference_graph = {
    'a': ['b', 'c'],
    'b': ['a', 'c', 'd'],
    'c': ['a', 'b'],
    'd': ['b']
}
num_registers = 3
register_allocation = {}
for var in interference_graph:
    used = {register_allocation.get(neigh) for neigh in interference_graph[var] if neigh in register_allocation}
    for reg in range(1, num_registers + 1):
        if reg not in used:
            register_allocation[var] = reg
            break
# Check if allocation is complete
# Your code here

Need a hint?

Use all() to check if every variable has a register assigned.