Monte Carlo Integration - Parallel Easier Than Sequential

A typical problem when introducing Monte Carlo Techniques is calculating the area of some two dimensional figure which lies inside another object whose size is known. The figure you see above is enclosed by a square of unit area and you start picking random points which lie in this square. All you have to do is count the total number of points you picked and how many were inside the figure. The area you are looking for is then just the ratio of the points inside the figure to the total number of points. (You have to multiply this by the area of the bounding box if it is not one.)
The borders of our figure are actually simple analytic funtions in every quadrant,

quadrant1 upper right circle with radius 0.5, center at (0.5, 0.5) y=-sqrt(-x*x+x)+0.5

quadrant2 lower right quadratic y=1.2*x*x-0.3

quadrant3 lower left ellipse y=-sqrt((1-x*x/0.25)*0.09)

quadrant4 upper left circle with radius 0.5, center at (0,0) y=sqrt(0.25-x*x)

If you write a sequential program to find the area of this figure you might do something like,

Create two randoms numbers x, y in the range -0.5 to 0.5
Check in which quadrant the point defined by x and y lies
If in quadrant one then use the border relation for this quadrant to find out if this point lies within the figure or not
If in quadrant two then ...
If in quadrant three then ...
If in quadrant four then ...
If insdie figure increase a variable by one

A more parallel approach would be,

Create two random numbers x, y in the range 0.0 to 0.5
Use the border relation of quadrant one to find out if this point is inside the figure or not.
If inside the figure increase a variable by one

This would determine the size of the part of the figure which lies in the first quadrant and it is simple enough to then move on to the second quadrant and so on. We will use this concept for our parallel program but we are going to use four different slave programs, one for each quadrant.

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Index: Getting started with PVM

quadrant1	upper right	circle with radius 0.5, center at (0.5, 0.5)	y=-sqrt(-x*x+x)+0.5
quadrant2	lower right	quadratic	y=1.2xx-0.3
quadrant3	lower left	ellipse	y=-sqrt((1-xx/0.25)0.09)
quadrant4	upper left	circle with radius 0.5, center at (0,0)	y=sqrt(0.25-x*x)