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Divide and Conquer is a well known algorithmic procedure for solving closest pair problems.In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. It is theoretically and practically observed that sometimes partitioning the problem space into more than two parts can give better performances. In this work we proposed that dividing the problem space into (n) number of parts can give better result.We organized the book as follows,in Chapter 2, we discussed DivideandConquer algorithm and ClosestPair problem. In Chapter 3, we reviewed previous works about Divideand Conquer algorithm to solve ClosestPair problem. In Chapter 4, we present detailed version of the Basic2 algorithm and give the correspondent proof of correctness as presented by Jose C. Pereira & Fernando G. Lobo (2010). In Chapter 5, some previous proofs are given where is proven that 2ary system is not the best choice for all the algorithms. The results in this chapter are based on [Kayk98]. In Chapter 6, a new procedure of divide and conquer rule is presented to solve the closest pair of points problem. In Chapter 7, we discussed future work and conclude our work.
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