scholarly journals Conversion of the Hamiltonian path problem into a wide bandwidth signal filtering problem

2020 ◽  
Author(s):  
William Icefield
Keyword(s):  
Filter Design ◽  
Hamiltonian Path ◽  
Numerical Differentiation ◽  
Angular Frequency ◽  
Divide And Conquer ◽  
Wide Bandwidth ◽  
Signal Filtering ◽  
Hamiltonian Path Problem ◽  
Problem Number ◽  
Filtering Problem

The (undirected) Hamiltonian path problem is reduced to a signal filtering problem - number of Hamiltonian paths becomes amplitude at zero frequency for sinusoidal signal f(t) that encodes a graph. Then a 'divide and conquer' strategy to filtering out wide bandwidth components of a signal is suggested - one filters out angular frequency 1/2 to 1, then 1/4 to 1/2, then 1/8 to 1/4 and so on. An actual implementation of this strategy involves careful extrapolation using numerical differentiation and local polynomial. This paper proves P=NP up to exactly proving that required filter design only necessitates number of samples that is polynomial of |V|, number of vertices in a graph, and that obtaining filter coefficients only take polynomial time complexity relative to |V|.

scholarly journals A successful algorithm for the undirected Hamiltonian path problem

1985 ◽  
Vol 10 (2) ◽  
pp. 179-195 ◽  
Author(s):  
Gerald L. Thompson ◽  
Sharad Singhal
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Path Problem

Expected Computation Time for Hamiltonian Path problem

1987 ◽  
Vol 16 (3) ◽  
pp. 486-502 ◽  
Author(s):  
Yuri Gurevich ◽  
Saharon Shelah
Keyword(s):  
Hamiltonian Path ◽  
Computation Time ◽  
Hamiltonian Path Problem

scholarly journals Network-BasedH∞Filter Design for Linear System with Random Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Ruixia Yan ◽  
Zhong Wu ◽  
Jinliang Liu
Keyword(s):  
Filter Design ◽  
Random Network ◽  
Sufficient Conditions ◽  
System Model ◽  
Linear Matrix ◽  
Communication Delays ◽  
Filter Parameter ◽  
Stochastic Characteristic ◽  
Random Communication Delays ◽  
Filtering Problem

This paper investigates the filtering problem for a class of network-based systems with random network-induced delays. The considered random delay between the sensor and the filter is assumed to be satisfying a certain stochastic characteristic. Considering the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. By using a properly constructed Lyapunov function, sufficient conditions for the existence of theH∞filters are presented in terms of linear matrix inequalities, which are dependent on the occurrence probability of both the random communication delays. The filter parameter is then characterized by the solution to a set of LMIs. A simulation example is employed to show the effectiveness of the proposed method.

scholarly journals New Sufficient Conditions for Hamiltonian Paths

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
M. Sohel Rahman ◽  
M. Kaykobad ◽  
Jesun Sahariar Firoz
Keyword(s):  
Hamiltonian Path ◽  
Sufficient Conditions ◽  
Hamiltonian Paths ◽  
Hamiltonian Path Problem

A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.

H∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

2020 ◽  
Vol 42 (8) ◽  
pp. 1559-1568
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Zakaria Chalh
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Filter Design ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Reduced Order ◽  
Arbitrary Switching ◽  
Discrete Switched Systems ◽  
Error System ◽  
Filtering Problem

This paper is concerned with the H∞ filtering problem for two-dimensional (2-D) discrete switched systems described by the second Fornasini and Marchesini (FM) model. The main purpose is to design a switched filter such that the resulting filtering error system under the arbitrary switching signal is asymptotically stable with a guaranteed H∞ performance level. By using the switched Lyapunov functions, a new sufficient condition is obtained to guarantee the asymptotic stability with a H∞ performance index for the filtering error system. Based on this condition, the full- and reduced-order H∞ filter design conditions are derived and formulated in terms of linear matrix inequalities (LMIs). Two illustrative examples are utilized to show the effectiveness and less conservativeness of the proposed method.

3D DNA Self-Assembly Algorithmic Model to Solve the Hamiltonian Path Problem

2021 ◽  
Vol 16 (5) ◽  
pp. 731-737
Author(s):  
Jingjing Ma
Keyword(s):  
Self Assembly ◽  
Dna Computing ◽  
Computing Time ◽  
Hamiltonian Path ◽  
Experimental Methods ◽  
Deterministic Algorithm ◽  
Assembly Algorithm ◽  
Hamiltonian Path Problem ◽  
Dna Tiles ◽  
Algorithmic Model

Self-assembly reveals the innate character of DNA computing, DNA self-assembly is regarded as the best way to make DNA computing transform into computer chip. This paper introduces a strategy of DNA 3D self-assembly algorithm to solve the Hamiltonian Path Problem. Firstly, I introduced a non-deterministic algorithm. Then, according to the algorithm I designed the types of DNA tiles which the computing process needs. Lastly, I demonstrated the self-assembly process and the experimental methods which can get the final result. The computing time is linear, and the number of the different tile types is constant.

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