Search computing model for the knapsack problem based on DNA origami

2019 ◽  
Vol 9 (6) ◽  
pp. 553-562 ◽  
Author(s):  
Jing Yang ◽  
Zhixiang Yin ◽  
Zhen Tang ◽  
Kaifeng Huang ◽  
Jianzhong Cui ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Knapsack Problem ◽  
Simulation Software ◽  
Dna Origami ◽  
Directed Path ◽  
Chain Reaction ◽  
Detection Techniques ◽  
Complete Problem ◽  
Computing Model ◽  
Np Complete

The knapsack problem is an import NP-complete problem in combinatorial optimization. In order to reduce the complexity of the problem, we provide a search computing model based on DNA origami to solve it. In this paper, we map the choice of each item to the directed path on the origami base of DNA. Then the solution of the problem is mapped to find a directed path to maximize the total value of items in the knapsack. Hybrid chain reaction and fluorescence detection techniques are used to generate solutions satisfying constraints. Lastly, we use Visual DSD simulation software to verify the validity of the model. Compared with other models through simulation, this model can automatically search the solution of the problem, and really reduce the complexity of the problem to linear.

DNA Computing Model for Satisfiability Problem Based on Hybridization Chain Reaction

2020 ◽  
pp. 2159010
Author(s):  
Zhixiang Yin ◽  
Jing Yang ◽  
Qiang Zhang ◽  
Zhen Tang ◽  
Guoqiang Wang ◽  
...  
Keyword(s):  
Dna Computing ◽  
Dna Origami ◽  
Satisfiability Problem ◽  
Hybridization Chain Reaction ◽  
Chain Reaction ◽  
Computing Device ◽  
Computing Model ◽  
Novel Method ◽  
Np Complete ◽  
The Given

Satisfiability problem is a famous nondeterministic polynomial-time complete (NP-complete) problem, which has always been a hotspot in artificial intelligence. In this paper, by combining the advantages of DNA origami with hybridization chain reaction, a computing model was proposed to solve the satisfiability problem. For each clause in the given formula, a DNA origami device was devised. The device corresponding to the clause was capable of searching for assignments that satisfied the clause. When all devices completed the search in parallel, the intersection of these satisfying assignments found must satisfy all the clauses. Therefore, whether the given formula is satisfiable or not was decided. The simulation results demonstrated that the proposed computing model was feasible. Our work showed the capability of DNA origami in architecting automatic computing device. The paper proposed a novel method for designing functional nanoscale devices based on DNA origami.

Surface- Based Computing Model of Maximum Independent Set Problem

2011 ◽  
Vol 328-330 ◽  
pp. 1729-1733
Author(s):  
Yan Yang ◽  
Zhi Xiang Yin
Keyword(s):  
Polynomial Time ◽  
Maximum Clique ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Complex Class ◽  
Independent Set Problem ◽  
Complete Problem ◽  
Computing Model ◽  
Np Complete ◽  
Maximum Independent Set Problem

About thirty years ago, the concept of the complexity of the problem was proposed. The most important complex class is P and NP class. Fruitful results of this concept are the existence of the so-called complex class complete problem. If the other issues of this class once solved in polynomial time, then the problem must exist polynomial time algorithms. Therefore, the complete problem is most difficult to solve, but because of their presence, we can choose any of them improved algorithm for a problem, so this kind of problem to get a good solution. DNA computing is a novel method that solving a class of intractable computational problems, in which the computing speeds up exponentially with the problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. Maximum Independent Set problem (MIS) is a well-known NP-complete problem. Maximum Clique and Minimum Vertex Covering problem is equivalent to Maximum Independent Set problem. In this paper, we explore solving Maximum Independent Set problem by transforming it into equivalent 0-1 programming problem, and utilizing the surface computing model of that. The proposed method demonstrates universal nature of NP-complete problem.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals On the restrictive channel thickness estimation

2007 ◽  
Vol 20 (3) ◽  
pp. 499-506
Author(s):  
Iskandar Karapetyan
Keyword(s):  
Positive Integer ◽  
Heuristic Algorithms ◽  
Clique Number ◽  
Directed Path ◽  
Channel Routing ◽  
Routing Problem ◽  
Thickness Estimation ◽  
Channel Thickness ◽  
Np Complete ◽  
Routing Method

Channel routing is an important phase of physical design of LSI and VLSI chips. The channel routing method was first proposed by Akihiro Hashimoto and James Stevens [1]. The method was extensively studied by many authors and applied to different technologies. At present there are known many effective heuristic algorithms for channel routing. A. LaPaugh [2] proved that the restrictive routing problem is NP-complete. In this paper we prove that for every positive integer k there is a restrictive channel C for which ?(C)>? (HG)+L(VG)+k, where ? (C) is the thickness of the channel, ?(HG) is clique number of the horizontal constraints graph HG and L(VG) is the length of the longest directed path in the vertical constraints graph VG.

scholarly journals Consecutive Colouring of Oriented Graphs

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marta Borowiecka-Olszewska ◽  
Ewa Drgas-Burchardt ◽  
Nahid Yelene Javier-Nol ◽  
Rita Zuazua
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Oriented Graphs ◽  
Complete Problem ◽  
Np Complete

AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r-regular oriented graphs, transitive tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.

scholarly journals Comparison of a PCR-based diagnostic assay for Mycoplasma pulmonis with traditional detection techniques

1994 ◽  
Vol 28 (3) ◽  
pp. 249-256 ◽  
Author(s):  
S. Sanchez ◽  
K. Tyler ◽  
N. Rozengurt ◽  
J. Lida
Keyword(s):  
Diagnostic Methods ◽  
Diagnostic Assay ◽  
Mycoplasma Pulmonis ◽  
Chain Reaction ◽  
Pcr Assay ◽  
Culture Techniques ◽  
Detection Techniques ◽  
Laboratory Rodent ◽  
Polymerase Chain ◽  
Diagnosis Of Infection

Current diagnosis of infection by Mycoplasma pulmonis, an important pathogen of laboratory rodent colonies worlwide, is based on serological, histopathological and culture techniques which can be slow and unreliable. A polymerase chain reaction (PCR) assay for M. pulmonis diagnosis was compared to current diagnostic methods. This PCR based technique allows a more specific, sensitive and rapid diagnosis of M. pulmonis from various tissues by comparison with culture and histopathology.

EFFICIENT ALGORITHMS FOR DEGENERATE PRIMER SEARCH

2007 ◽  
Vol 18 (04) ◽  
pp. 899-910 ◽  
Author(s):  
SUDHA BALLA ◽  
SANGUTHEVAR RAJASEKARAN ◽  
ION I. MANDOIU
Keyword(s):  
Dna Sequences ◽  
Multiplex Polymerase Chain Reaction ◽  
Efficient Algorithms ◽  
Degenerate Primer ◽  
Experimental Comparison ◽  
Chain Reaction ◽  
Degenerate Primers ◽  
Np Complete ◽  
Polymerase Chain ◽  
Input Strings

Degenerate primers are used to amplify a given set of genomic sequences using a technique called Multiplex Polymerase Chain Reaction (MP-PCR). The problem of minimizing the number of degenerate primers required to amplify a given set of DNA sequences, also known as the Degenerate Primer Design Problem (DPDP), has been extensively studied in the literature and proven to be NP-Complete. In this paper we present efficient algorithms for solving DPDP. For example, one of the algorithms we give in this paper is iterative and has a runtime of O(b|Σ|log|Σ|dn2mp) to select a set of p degenerate primers, each of given length l and degeneracy at most d, for n sequences each of length m in the input, the number of candidates retained in each iteration being b. Σ is the alphabet of the input strings. This is an improvement over the runtime of the best known prior algorithm, MIPS by Souvenir et al. [15], which has a runtime of O(bn3mp). We provide an experimental comparison of MIPS and our algorithms.

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