djgorillaz / maximum-independent-set-parallel

Maximum independent set problem - greedy and brute force parallel algorithms

Parallel algorithms for the maximum independent set problem

This program solves maximum independent set problem¹ using parallel algorithms (brute force and greedy).

Built With

• The Boost Graph Library
• Boost Thread

Problem

Given an undirected graph , find the maximum-cardinality subset such that no two vertices in is adjacent.

,

where,

Example

Maximal independent set is:

Algorithm

Brute force algorithm

For each subset (2^n) check adjacency matrix (n^2).

Complexity: O(n^2 * 2^n)

Amdahl's law:

where

• f - sequential part of algorithm;
• p - number of processors;
• Sp - theoretical speedup of the whole task.

Greedy algorithm (approximate solution)

Start from each vertex of graph and make recursive calls for adjacency vertices.

Complexity: O(n^2)

Amdahl's law: