Term Project for Advanced Algorithms

Given two 2d point sets P and Q and a real number alpha in [0,1]. Let P = {p_i: i=1,2,...,m} and Q = {q_j: j=1,2,...,n}. Let r = radius of the largest circle such that if we consider the circles of radius r centered at points of P, then they do not intersect each other in their interiors. Let C_i be the circle of radius r and centered at point p_i. A point q_j of Q is said to match a point p_i of P if only the point q_j of Q lies inside C_i (and no other point inside C_i).

Let k = floor (alpha.min(m,n)). Q is said to match P if k points of Q are found to match with k points of P in the aforesaid manner. Find the match, if any.

Output should be a single image containing:

-- All points p_i in blue. -- Each point q_j in red if it matches some point p_i. Show this C_i in blue. -- All non-matched points of Q in yellow.

You have to save the output as an image in svg format: http://www.w3schools.com/svg/

HOW TO:

To run the program type following :$ bash setup.sh

INPUT FOR RANDOM NUMBERS: m (Number of points of P) n (Number of points of Q) alpha (as specified in question)

INPUT FROM FILE: The first line of input contains a two integer(m,n) and a double(a). Next line contains 4 space seperated positive doubles, minX maxX minY maxY. m is number of points in P set. n is number of points in Q set. a is alpha Next m lines contain 2 space seperated doubles px, py denoting a point in P set. Nest n lines contain 2 space seperated doubles qx, qy denoting a point in Q set.

OUTPUT: The svg image in gnuplot as required.

PROCESS: A randomized set of point-sets P and Q of the specified sizes will be generated. The range of the floating point co-ordinates is between 0 and 800.

Thereafter, the distance between the closest pair of points in P is evaluated in O(mlog(m)) time using the divide and conquer algorithm. The required common radius of the largest non-overlapping circles is half of this.