â€œAn exhaustive search algorithm to solve the independent set problem in parallel.â€

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# â€œAn exhaustive search algorithm to solve the independent set problem in parallel.â€ - PowerPoint PPT Presentation

Parallel Computing I. Agarwal, Kshitij Ghosh , Aurodeep Elbahi , Reda. â€œAn exhaustive search algorithm to solve the independent set problem in parallel.â€. Project Mentor â€“ Prof. Alan Kaminsky. Independent set NP problem Set of vertices in a graph

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Presentation Transcript

Parallel Computing I

Agarwal, Kshitij

Ghosh, Aurodeep

Elbahi, Reda

“An exhaustive search algorithm to solve the independent set problem in parallel.”

Project Mentor – Prof. Alan Kaminsky

Independent set NP problem

• Set of vertices in a graph
• Property of the independent set of vertices is that no two vertices are adjacent
• If there is set of 5 vertices that are independent, then no two vertices in this set of 5 vertices can have a direct edge between them
Understanding Concepts

Independent set(contd.)

• Size of an independent set
• The number of vertices it contains, is the size of the vertices in the independent set.
Understanding Concepts

Independent set of size 9(Blue vertices)

Example of an independent set

Image Source: http://en.wikipedia.org/wiki/File:Independent_set_graph.svg

Generated the matrix using the random number generator

• Matrix stores the graph
• Generation of all possible subsets of a size k
• Finding all the independent sets of size k
Exhaustive search algorithm

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