synopsis cse

8/8/2019 Synopsis CSE

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SYNOPSISOF

TERM PAPER

Course: CSE2050 (DATA STRUCTURES)

Topic: Parallel Generation of Binary Search Trees

Submitted To:

Ms. Rajdeep Kaur

Submitted By:

Aashish Kumar

RB6801A03

B.Tech-ECE


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A binary tree is a special kind of tree, one that limits each node to

no more than two children. A binary search tree, or BST, is a binary tree

whose nodes are arranged such that for every node n, all of the nodes in

n's left subtree have a value less than n, and all nodes in n's right subtree

have a value greater than n. Binary Search tree is a binary tree in whicheach internal node x stores an element such that the element stored in

the left subtree of x are less than or equal to x and elements stored in the

right subtree of x are greater than or equal to x. This is called binary-

search-tree property.The basic operations on a binary search tree take

time proportional to the height of the tree. For a complete binary tree with

node n, such operations runs in (lg n) worst-case time. If the tree is a

linear chain of n nodes, however, the same operations takes (n) worst-

case time.

The height of the Binary Search Tree equals the number of linksfrom the root node to the deepest node.

We present a new parallel algorithm for generating binary trees; it

generates trees in A-order using A-sequences representation. This

algorithm is adaptive and cost-optimal and is executed on a shared

memory multiprocessor. We know of no other parallel algorithm in the

literature that generates trees in A-order. This parallel algorithm is

designed based on a presented sequential generation algorithm for A-sequences, with O(1) average time complexity.

Best-bound-first parallel branch-and-bound algorithms using as

many lists of live nodes as processors are discussed. In these algorithms

the distribution of the live nodes among the lists of live nodes becomes an

important task to achieve a good performance. We present three

distribution functions and we evaluate and compare them with the single

list branch-and-bound algorithms. As in best-bound-first parallel branch-and-bound algorithms the processors can unnecessarily branch active


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nodes, we establish a measure to evaluate the efficient work done by the

processors. This measure for best-bound-first algorithms is the percentage

of critical nodes branched in each iteration.

The parallelization of Branch and Bound algorithms has been very studied

when a single list of live nodes is used. Because this scheme is not suitable forno-shared memory multiprocessor architectures, we propose a scheme of

parallel Branch and Bound algorithms with as many lists of live nodes as

processors have. We study this scheme when a best bound first search is used.

In this scheme the distribution of live nodes among the lists becomes an

important task to achieve a good performance. We present three distribution

functions with different communication requirements, and we study theirs

performance, stablishing a measure of the efficient work made by the

processors. We evaluate the global performance of these algorithms and

compare these performances with the parallel algorithm that uses a single list of

live nodes.

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