The First (pleasantly) Parallel
Program
Kaustubh Gadkari
CS 475 FA08
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A Parallel Approach to Circuit Satisfiability: CS 475 FA08, Study notes of Computer Science
A parallel solution to the circuit satisfiability problem, a well-known np-complete problem in computer science. The author, kaustubh gadkari, explains how the problem's natural parallelism can be exploited to reduce the time complexity. Partitioning, agglomeration and mapping, and cyclic mapping. Students of computer science, particularly those taking cs 475 or similar courses, may find this document useful for understanding parallel algorithms and their applications.
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The First (pleasantly) Parallel
Program
Kaustubh Gadkari CS 475 FA
The Problem
โ For what combination of inputs, is the output 1?
Partitioning
โ Where is the parallelism? โ In this problem, the parallelism is natural. โ One task => one set of inputs. โ All tasks are independent. โ Therefore, all tasks can be performed in parallel.
Partitioning (contd.)
โ Pleasantly parallel!
- (^) No channels between tasks.
Cyclic Mapping
โ Assume p processes. โ Each process gets every p th piece of work.
- (^) For n pieces of work (0,1, .. ,n1) to be assigned to p processes (0,p, .. ,p1), the k th piece of work is assigned to process k modulo p.
Cyclic Mapping (contd.)
- For example, n = 20 and p = โ
- โ P0: 0, 6, 12,
- โ P1: 1, 7, 13,
- โ P2: 2, 8,
- โ P3: 3, 9,
- โ P4: 4, 10,
- โ P5: 5, 11,
Tasks
โ Login to bassi.nersc.gov. โ Try running the first pleasantly parallel program.