Experimental Design¶

This page defines the structured methodology used to evaluate process-based parallelism in matrix multiplication.

The goal is to systematically measure how execution time changes with varying problem size and degree of parallelism.

Experimental Parameters¶

Matrix Size (N)

Controls computational workload.

Values Tested: 1200, 1800, 2400
Purpose: Evaluate scaling behavior as problem size increases.
Number of Processes (PROCS)

Controls the degree of parallel execution.

Values Tested: 1, 4
Purpose: Measure impact of parallelization on runtime.

Total configurations tested: 6

Configuration	Matrix Size (N)	Processes (PROCS)	Status
1	1200	1	Complete
2	1200	4	Complete
3	1800	1	Complete
4	1800	4	Complete
5	2400	1	Complete
6	2400	4	Complete

Modify Parameters

Update #define N and #define PROCS in matrix_fork.c.
Compile
```
gcc -Wall matrix_fork.c -o matrix_fork
```
Execute (3 Runs)
```
./matrix_fork
```
Record Data

Capture execution time for each run and compute the average.
Maintain Environment Consistency

Ensure no other CPU-intensive processes are running.

Matrix Size (N)	PROCS	Run 1	Run 2	Run 3	Average (s)
1200	1	0.001	0.001	0.003	0.0016
1200	4	0.002	0.002	0.001	0.0016
1800	1	0.001	0.001	0.001	0.001
1800	4	0.003	0.003	0.003	0.003
2400	1	0.002	0.001	0.001	0.0013
2400	4	0.004	0.003	0.003	0.003

Performance Scaling

Compare execution time vs. PROCS
Compare execution time vs. N
Overhead Analysis

Evaluate process creation and synchronization overhead.
Efficiency Metrics

Compute:
- Speedup
- Efficiency
- Scalability
Statistical Analysis

Standard deviation and confidence interval calculations.

Small N

Overhead may outweigh parallel benefits.
Large N

Parallel execution should reduce runtime.
Optimal PROCS

Best performance expected when PROCS = 4 (CPU core count).
Diminishing Returns

Additional processes beyond available cores may reduce efficiency.