How to use Binary Search Trees part1(Data Structures and Algorithms)

Abstract: This paper presents a parallel solution based on the coarse-grained multicomputer (CGM) model using the four-splitting technique to solve the optimal binary search tree problem. The well-known sequential algorithm of Knuth solves this problem in O(n2) time and space, where n is the number of keys used to build the optimal binary search tree. To parallelize this algorithm on the CGM model, the irregular partitioning technique, consisting in subdividing the dependency graph into subgraphs (or blocks) of variable size, has been proposed to tackle the trade-off of minimizing the number of communication rounds and balancing the load of processors. This technique however induces a high latency time of processors (which accounts for most of the global communication time) because varying the blocks' sizes does not enable them to start evaluating some blocks as soon as the data they need are available. The four-splitting technique proposed in this paper solves this shortcoming by evaluating a block as a sequence of computation and communication steps of four subblocks.