bharathaiys / Perfect-Square-Finder

A distributed system that uses the Actor model in the AKKA.NET framework to spawn a supervisor actor which in return spawns worker actors. Given 2 numbers N and k, each worker actor takes on a range of numbers and checks for the square of k consecutive numbers that add up to a perfect square.

Distributed-Operating-System-Principles (COP5615) Project 1

#Group members:

Name
Shaunak Sompura
Bharat Shankar

 Problem definition: Given N and k, find all k consecutive numbers starting at 1 and upto N such that the sum of squares is itself a perfect square.

Approach: The solution to this problem is achieved using the actor facility in F# and Akka.NET. Multiple child actors are spawned and assigned computational tasks using a single parent actor. This actor model decreases time taken to compute solution by carrying out tasks in parallel.

#Steps to run

1. Unzip the file and navigate inside the folder

2. Open Terminal

3. Run the following command: dotnet fsi --langversion:preview proj1.fsx 1000000 24

   Output: [Prints first number of the sequence that forms a perfect square]

    Real time: <real time> in ms
    CPU time: <cpu time> in ms
    Cores Used : <cores used in computation>
    (ratio of CPU time to Real Time)
   

#Size of work unit for each worker actor

• The work unit considered was k where a sequence of numbers of size k was given to each actor.
• The actor then squares each of those values of size k and adds it up.
• Another approach was to simultaneously square all the values from 1 to N by assigning it to actors and then sum up each sequence of size k parallelly.
• But this would take more time and space, since the boss would need to wait till all the squares are computed by workers and also needs space to store it.

• For an input of 1000000 it was found that dividing the work to 1000 actors where each actor received 1000 work units, used the most cores delivering the best performance.
• But when the input N<1000 we create only N actors and assigned 1 work unit for each actor.
• When 10,000 actors were spawned it was found to be more cumbersome to maintain this number of actors than perform the squaring.

For an input N=1000000 and k=24

No. of Actors	Work Unit Received by each actor	Cores used
1000	1000	4.84
10000	100	4.59
100000	10	4.08

#Result of running dotnet fsi proj1.fsx 1000000 4

There are no sequences of length k = 4 for n = 1000000

#Running time for n = 1000000 and k = 4

Real Time: 3800 ms
CPU Time: 18310 ms
Num of Cores: 8 Cores Used: 4.818421

#Largest Problem solved

N = 10^8 and k = 24

9

25

197

304

353

540

856

76

121

1301

2053

3112

3597

5448

8576

12981

20425

30908

35709

54032

84996

128601

202289

306060

353585

534964

841476

1273121

2002557

3029784

3500233

5295700

8329856

12602701

19823373

29991872

34648837

45863965

52422128

82457176

Real Time: 538246 ms 
CPU Time: 2844720 ms 
Num of Cores: 8 Cores Used: 5.285167

Note: Please refer Readme.pdf for screenshots