On an optimality property of ternary trees

The concept of effort is defined for rooted trees. The class of rooted trees with minimal effort is determined. The asymptotic behaviour of the minimal effort is calculated. Various choices for the effort function are considered, as well as variations of the optimality criterion

Optimum Partition Parameter of Divide-and-Conquer Algorithm for Solving Closest-Pair Problem

Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an interesting topic in computer science. With divide and conquer algorithm we can solve closest pair problem. Here also the problem is partitioned into two parts until the problem is trivially solvable. But it is theoretically and practically observed that sometimes partitioning the problem space into more than two parts can give better performances. In this paper, a new proposal is given that dividing the problem space into (n) number of parts can give better result while divide and conquer algorithm is used for solving the closest pair of point's problem.Comment: arXiv admin note: substantial text overlap with arXiv:1010.590