A simple expected running time analysis for randomized “divide and conquer” algorithms

A simple expected running time analysis for randomized "divide and conquer" algorithms

There are many randomized “divide and conquer” algorithms, such as randomized Quicksort, whose operation involves partitioning a problem of size n uniformly at random into two subproblems of size k and n − k that are solved recursively. We present a simple combinatorial method for analyzing the expected running time of such algorithms, and prove that under very weak assumptions this expected ru...

Divide and Conquer for Linear Expected Time

Skeletons for Divide and Conquer Algorithms

Algorithmic skeletons intend to simplify parallel programming by providing recurring forms of program structure as predefined components. We present a fully distributed task parallel skeleton for a very general class of divide and conquer algorithms for MIMD machines with distributed memory. This approach is compared to a simple masterworker design. Based on experimental results for different e...

Divide and Conquer for Llyear Emecfed Time

Divide-and-conquer is one of the most frequently used methods for the design or” fast algorithms. The most common application of the technique involves breaking a problem of size N into two subproblems of size N/2, solving these subproblems, then doing work proportional to N to “marry” the partial answers into a solution for the entire problem; this scheme leads to algorithms of O(N log N) wors...

Space-efficient geometric divide-and-conquer algorithms

We develop a number of space-efficient tools including an approach to simulate divide-and-conquer space-efficiently, stably selecting and unselecting a subset from a sorted set, and computing the kth smallest element in one dimension from a multi-dimensional set that is sorted in another dimension. We then apply these tools to solve several geometric problems that have solutions using some form...