Non-Recursive Simulation on the Recursive Algorithm of Binary Tree Reverting to its Corresponding Forest in Intelligent Materials

2011 ◽  
Vol 63-64 ◽  
pp. 222-225
Author(s):  
Min Wang
Keyword(s):  
Binary Tree ◽  
Time Complexity ◽  
Recursive Algorithm ◽  
Space Complexity ◽  
Recursive Algorithms ◽  
Loop Structure ◽  
Simulation Algorithm ◽  
Intelligent Materials ◽  
Storage Structures ◽  
Design Ideas

By analyzing the storage structures of forest and binary tree, this paper introduced the design ideas of the non-recursive simulation on the recursive algorithm of binary tree reverting to its corresponding forest, gave the non-recursive simulation algorithm in C using stack structure and loop structure, and then analyzed and evaluated the recursive and non-recursive algorithms on the two aspects of time complexity and space complexity.

scholarly journals Efficient Nonrecursive Bit-Parallel Karatsuba Multiplier for a Special Class of Trinomials

VLSI Design ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yin Li ◽  
Yu Zhang ◽  
Xiaoli Guo
Keyword(s):  
Time Delay ◽  
Special Class ◽  
Time Complexity ◽  
Space Complexity ◽  
Polynomial Basis ◽  
Gate Delay ◽  
Complexity Bound ◽  
Parallel Multiplier ◽  
Highly Efficient ◽  
First Time

Recently, we present a novel Mastrovito form of nonrecursive Karatsuba multiplier for all trinomials. Specifically, we found that related Mastrovito matrix is very simple for equally spaced trinomial (EST) combined with classic Karatsuba algorithm (KA), which leads to a highly efficient Karatsuba multiplier. In this paper, we consider a new special class of irreducible trinomial, namely, xm+xm/3+1. Based on a three-term KA and shifted polynomial basis (SPB), a novel bit-parallel multiplier is derived with better space and time complexity. As a main contribution, the proposed multiplier costs about 2/3 circuit gates of the fastest multipliers, while its time delay matches our former result. To the best of our knowledge, this is the first time that the space complexity bound is reached without increasing the gate delay.

scholarly journals Cryptanalytic Performance Appraisal of Improved CCH2 Proxy Multisignature Scheme

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Raman Kumar ◽  
Nonika Singla
Keyword(s):  
Elliptic Curve ◽  
Performance Appraisal ◽  
Time Complexity ◽  
Space Complexity ◽  
Elliptic Curve Cryptosystem ◽  
Forgery Attack ◽  
Signature Schemes ◽  
Computational Overhead ◽  
Threshold Schemes

Many of the signature schemes are proposed in which thetout ofnthreshold schemes are deployed, but they still lack the property of security. In this paper, we have discussed implementation of improved CCH1 and improved CCH2 proxy multisignature scheme based on elliptic curve cryptosystem. We have represented time complexity, space complexity, and computational overhead of improved CCH1 and CCH2 proxy multisignature schemes. We have presented cryptanalysis of improved CCH2 proxy multisignature scheme and showed that improved CCH2 scheme suffered from various attacks, that is, forgery attack and framing attack.

Recursive Algorithm and its Practice in C Language Online Course Teaching

2021 ◽  
Vol 105 ◽  
pp. 341-347
Author(s):  
Ming Gu
Keyword(s):  
Recursive Algorithm ◽  
Online Course ◽  
Recursive Algorithms ◽  
Path Finding ◽  
Middle Point ◽  
Teaching Mode ◽  
C Language ◽  
Teachers And Students ◽  
Evaluation Of Learning ◽  
Core Issues

The recursive algorithm has two core issues which are the design of recursive parameter lists and exit condition. We summarized the types and characteristics of recursive algorithms, and extracted four types of representative recursive algorithms with different levels of difficulty. Pseudocodes of these algorithms are given and the core issues complexity of these algorithms is compared. The relatively complex and representative recursive algorithm of the maze path finding is described in detail. The description includes that the maze is expressed mathematically, using numbers from 0 to 9 to represent the path cost, using * to represent walls or obstacles, and abstracting the maze problem as a square maze represented by numbers and *. The maze path finding recursive algorithm has five steps which are the storage structure of the maze numbers and *, the consideration of the two core problems of the recursive algorithm, the recursive call in the four directions of the middle point and the printing of the maze path. The screenshot of the running result in C language is showed. Students are required to implement the maze path finding recursive algorithm in C language. Because the maze path finding recursive algorithm is interesting and challenging, it can stimulate students' enthusiasm and initiative in learning. In the current situation of online course teaching during the epidemic, considering the demand for C language programming ability, combining with the characteristics of higher vocational students and the difficulty of the maze path finding recursive algorithm, we designed and practiced the C Language online course teaching mode led by the recursive algorithms. The every step of the teaching mode is described in detail. From the feedback of students’ evaluation of teaching and teacher’s evaluation of learning, this teaching mode is praised by teachers and students.

An Efficient Algorithm for Automating Classification of Chemical Reactions into Classes in Ugi’s Reaction Scheme

2013 ◽  
pp. 285-296
Author(s):  
Sanjay Ram ◽  
Somnath Pal
Keyword(s):  
Chemical Reactions ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Symmetric Matrix ◽  
Reaction Scheme ◽  
Space Complexity ◽  
Average Case ◽  
Model Driven ◽  
Reaction Matrix

There are two approaches for classification of chemical reactions: Model-Driven and Data-Driven. In this paper, the authors develop an efficient algorithm based on a model-driven approach developed by Ugi and co-workers for classification of chemical reactions. The authors’ algorithm takes reaction matrix of a chemical reaction as input and generates its appropriate class as output. Reaction matrices being symmetric, matrix implementation of Ugi’s scheme using upper/lower tri-angular matrix is of O(n2) in terms of space complexity. Time complexity of similar matrix implementation is O(n4), both in worst case as well as in average case. The proposed algorithm uses two fixed size look-up tables in a novel way and requires constant space complexity. Time complexity both in worst and average cases of the algorithm is linear.

scholarly journals Some Stable Algorithms in Ruin Theory and Their Applications

1995 ◽  
Vol 25 (2) ◽  
pp. 153-175 ◽  
Author(s):  
David C.M. Dickson ◽  
Alfredo D. Egídio dos Reis ◽  
Howard R. Waters
Keyword(s):  
Risk Model ◽  
Recursive Algorithm ◽  
Recursive Algorithms ◽  
Classical Risk Model ◽  
Ruin Theory ◽  
Marginal Distributions ◽  
The Classical Risk Model ◽  
Stable Algorithms ◽  
Severity Of Ruin

AbstractIn this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions.

scholarly journals Approximation of bounds on mixed-level orthogonal arrays

2011 ◽  
Vol 43 (02) ◽  
pp. 399-421
Author(s):  
Ali Devin Sezer ◽  
Ferruh Özbudak
Keyword(s):  
Random Walk ◽  
Large Deviation ◽  
Recursive Algorithm ◽  
Markov Property ◽  
Orthogonal Arrays ◽  
Recursive Formula ◽  
Limit Problem ◽  
Simulation Algorithm ◽  
Bellman Equations ◽  
Combinatorial Representations

Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

scholarly journals Space and time complexity for infinite time Turing machines

2020 ◽  
Vol 30 (6) ◽  
pp. 1239-1255
Author(s):  
Merlin Carl
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Infinite Time ◽  
Space And Time ◽  
Open Questions ◽  
Separation Results ◽  
Ordinal Computability

Abstract We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in Section 7.2.2 of Carl (2019, Ordinal Computability: An Introduction to Infinitary Machines), which appear here as Lemma $6$ up to Corollary $9$.

Modified Ant Algorithm VLSI Planning on the Basis of the Composite Model of the Solution Space

2019 ◽  
pp. 49-63
Author(s):  
B.K. Lebedev ◽  
O.B. Lebedev ◽  
A.A. Zhiglaty
Keyword(s):  
Distinctive Feature ◽  
Binary Tree ◽  
Time Complexity ◽  
Solution Space ◽  
Composite Model ◽  
Ant Algorithm ◽  
Alternative States ◽  
Guillotine Cut ◽  
Search Graph ◽  
Evolutionary Memory

In this paper, the crystal plan is formed by the recursive use of a "guillotine cut". To set the plan means to set the structure of the binary tree of the cuts, i.e. sequence of binary cuts; for internal tree vertices, to indicate the type of the cut H or V; to number the leaves of the tree and indicate the orientation of the modules. The structure of the binary tree of the cuts can be set using the Polish expression on the base of the alphabet A = {M, TR}, where the set of letters M = {mi|i = 1, 2, ..., nМ} corresponds to the leaves of the section tree (regions), and the set R = {H, V} corresponds to the cuts. We propose a way and methods for solving the problems of planning VLSI based on a modified ant colony. The task of synthesizing the section tree of the plan with the choice of types of sections, identification and orientation of the modules in the work is reduced to the task of forming a modified Polish expression with the identification of elements on the composite model of the solution space, including many alternative vertices. To keep the collective evolutionary memory during the life of the ant population and to form the solution of the problem, we use the complete graph G = (X, U) with alternative vertex states. Each vertex may be in one of two alternative states, i.e., α or β, corresponding to the orientation of the module or the type of the cut. The task of synthesizing the Polish expression is formulated as the task of finding the least-cost route on the solution search graph G = (X, U). A distinctive feature is that when building a route, simultaneously with the choice of the vertex xi∈ X, the state of this vertex is selected. The time complexity of the algorithm is O(n2). Experiments have shown that for large dimensions, the time indicators of the developed algorithm exceed those of the compared algorithms with the best values of the objective function.

An Algorithm for Testing Isomorphism of Planer Graph Based on Distant Matrix

2012 ◽  
Vol 487 ◽  
pp. 317-321
Author(s):  
Yan Peng Wu ◽  
Shui Qiang Liu
Keyword(s):  
Graph Theory ◽  
Polynomial Time ◽  
Time Complexity ◽  
Graph Isomorphism ◽  
Distance Matrix ◽  
Space Complexity ◽  
The Subject ◽  
The Many

The testing for graph isomorphism is one of the many problems in the subject of graph theory. This thesis proposes an algorithm for testing isomorphism of planer graph of polynomial time via structuring characteristics of planer graph based on distance matrix. The algorithm, with a time complexity of O (n^4) and a space complexity of O (n^2), has a great application value.

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