TIME OPTIMAL n-SIZE MATCHING PARENTHESES AND BINARY TREE DECODING ALGORITHMS ON A p-PROCESSOR BSR

2002 ◽  
Vol 12 (03n04) ◽  
pp. 365-374 ◽  
Author(s):  
LIMIN XIANG ◽  
KAZUO USHIJIMA ◽  
JIANJUN ZHAO
Keyword(s):  
Binary Tree ◽  
Efficient Algorithms ◽  
Optimal Algorithms ◽  
Decoding Algorithms ◽  
Time Optimal ◽  
Crcw Pram

Time optimal algorithms on an n-processor BSR PRAM for many n-size problems can be found in the literature. They outpace those on EREW, CREW or CRCW PRAM for the same problems. When only p (1 < p < n) processors are available, efficient algorithms on a p-processor BSR for some n-size problems can not be obtained from those on an n-processor BSR, and they have to be reconsidered. In this paper, we discuss and give two algorithms on a p-processor BSR for the two n-size problems of matching parentheses and decoding a binary tree from its bit-string, respectively, and show that they are time optimal.

Time-Optimal algorithms of searching for pulsed-point sources for systems with several detectors

2017 ◽  
Vol 53 (3) ◽  
pp. 203-209 ◽  
Author(s):  
A. L. Reznik ◽  
A. V. Tuzikov ◽  
A. A. Soloview ◽  
A. V. Torgov
Keyword(s):  
Point Sources ◽  
Optimal Algorithms ◽  
Time Optimal

CONVEX POLYGON PROBLEMS ON MESHES WITH MULTIPLE BROADCASTING

1992 ◽  
Vol 02 (02n03) ◽  
pp. 249-256 ◽  
Author(s):  
D. BHAGAVATHI ◽  
S. OLARIU ◽  
J. L. SCHWING ◽  
J. ZHANG
Keyword(s):  
Convex Polygon ◽  
Optimal Algorithms ◽  
Time Optimal ◽  
Edge Intersect

We propose time-optimal algorithms for a number of convex polygon problems on meshes with multiple broadcasting. Specifically, we show that on a mesh with multiple broadcasting of size n × n, the task of deciding whether an n-gon is convex, deciding whether two convex n-gons edge-intersect, deciding whether one convex n-gon lies in the interior of another, as well as variants of the tasks of computing the intersection and union of two convex n-gons can be accomplished in Θ( log n) time. We also show that detecting whether two convex n-gons are separable takes O(1) time.

High-performance computing simulations of self-gravity in astronomical agglomerates

SIMULATION ◽  
2021 ◽  
pp. 003754972199876
Author(s):  
Néstor Rocchetti ◽  
Sergio Nesmachnow ◽  
Gonzalo Tancredi
Keyword(s):  
High Performance Computing ◽  
Binary Tree ◽  
High Performance ◽  
Efficient Algorithms ◽  
The Self ◽  
Numerical Accuracy ◽  
Self Gravity ◽  
Performance Computing

This article describes the advances in the design, implementation, and evaluation of efficient algorithms for self-gravity simulations in astronomical agglomerates. Three algorithms are presented and evaluated: the occupied cells method, and two variations of the Barnes–Hut method using an octal and a binary tree. Two scenarios are considered in the evaluation: two agglomerates orbiting each other and a collapsing cube. The results show that the proposed octal tree Barnes–Hut method allows improving the performance of the self-gravity calculation up to 100 times with respect to the occupied cells method, while having good numerical accuracy. The proposed algorithms are efficient and accurate methods for self-gravity simulations in astronomical agglomerates.

scholarly journals Time Optimal Algorithms for Black Hole Search in Rings

2010 ◽  
pp. 58-71 ◽  
Author(s):  
Balasingham Balamohan ◽  
Paola Flocchini ◽  
Ali Miri ◽  
Nicola Santoro
Keyword(s):  
Black Hole ◽  
Optimal Algorithms ◽  
Time Optimal

OPTIMAL PARALLEL ENCODING AND DECODING ALGORITHMS FOR TREES

1992 ◽  
Vol 03 (01) ◽  
pp. 1-10 ◽  
Author(s):  
STEPHAN OLARIU ◽  
JAMES L. SCHWING ◽  
JINGYUAN ZHANG
Keyword(s):  
Circuit Design ◽  
Integrated Circuit ◽  
Binary Tree ◽  
Integrated Circuit Design ◽  
Basic Step ◽  
Shape Information ◽  
Decoding Algorithms ◽  
Erew Pram ◽  
Pram Model ◽  
Parallel Encoding

Encoding the shape of a binary tree is a basic step in a number of algorithms in integrated circuit design, automated theorem proving, and game playing. We propose cost-optimal parallel algorithms to solve the binary tree encoding/decoding problem. Specifically, we encode the relevant shape information of an n-node binary tree in a 2n bitstring. Conversely, given an arbitrary 2n bitstring we reconstruct the shape of the corresponding binary tree, if such a tree exists. All our algorithms run in O (log n) time using O (n/log n) processors in the EREW-PRAM model of computation.

CONSTRUCTING RED-BLACK TREE SHAPES

2002 ◽  
Vol 13 (06) ◽  
pp. 837-863 ◽  
Author(s):  
ANDREA MANTLER ◽  
HELEN CAMERON
Keyword(s):  
Binary Tree ◽  
Insertion Sequence ◽  
Efficient Algorithms ◽  
Binary Trees ◽  
Tree Shape ◽  
Insertion Algorithm ◽  
Definition Of ◽  
Red Black Tree ◽  
Theoretical Analyses

Cormen et al. describe efficient algorithms for inserting nodes into and deleting nodes from red-black trees. If some binary trees satisfying the definition of red-black trees cannot be built by these algorithms, then theoretical analyses of red-black trees that consider all binary trees satisfying the definition of red-black trees may not accurately describe the behavior of red-black trees in practice. We show that any binary tree shape that satisfies the definition of red-black trees can be built using only the insertion algorithm, RB-INSERT, of Cormen et al. We first describe an algorithm, RB-SHAPE, which, given any red-black tree T, will construct an insertion sequence for T. When the constructed sequence of insertions is performed on the empty tree using RB-INSERT, the result is a red-black tree with the same shape as T. We then prove the correctness of algorithm RB-SHAPE.

Sign in / Sign up

Export Citation Format

Share Document