Application of DNA Nanoparticle Conjugation on the Hamiltonian Path Problem

2021 ◽  
Vol 16 (3) ◽  
pp. 501-505
Author(s):  
Jingjing Ma
Keyword(s):  
Graph Theory ◽  
Self Assembly ◽  
Dna Computing ◽  
Hamiltonian Path ◽  
Au Nanoparticle ◽  
Assembly Model ◽  
Hamiltonian Path Problem ◽  
Complete Problem ◽  
Np Complete ◽  
Nanoparticle Conjugation

A DNA computing algorithm is proposed in this paper. The algorithm uses the assembly of DNA/Au nanoparticle conjugation to solve an NP-complete problem in the Graph theory, the Hamiltonian Path problem. According to the algorithm, I designed the special DNA/Au nanoparticle conjugations which assembled based on a specific graph, then, a series of experimental techniques are utilized to get the final result. This biochemical algorithm can reduce the complexity of the Hamiltonian Path problem greatly, which will provide a practical way to the best use of DNA self-assembly model.

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.

scholarly journals The Property of Hamiltonian Connectedness in Toeplitz Graphs

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Tudor Zamfirescu
Keyword(s):  
Hamiltonian Path ◽  
Complete Problem ◽  
Hamiltonian Connected ◽  
The Family ◽  
Np Complete

A spanning path in a graph G is called a Hamiltonian path. To determine which graphs possess such paths is an NP-complete problem. A graph G is called Hamiltonian-connected if any two vertices of G are connected by a Hamiltonian path. We consider here the family of Toeplitz graphs. About them, it is known only for n=3 that Tnp,q is Hamiltonian-connected, while some particular cases of Tnp,q,r for p=1 and q=2,3,4 have also been investigated regarding Hamiltonian connectedness. Here, we prove that the nonbipartite Toeplitz graph Tn1,q,r is Hamiltonian-connected for all 1<q<r<n and n≥5r−2.

scholarly journals Hamiltonian Paths in Some Classes of Grid Graphs

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri
Keyword(s):  
Linear Time ◽  
Hamiltonian Path ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hamiltonian Paths ◽  
Grid Graphs ◽  
Hamiltonian Path Problem ◽  
Np Complete ◽  
Necessary And Sufficient ◽  
Linear Time Algorithms

The Hamiltonian path problem for general grid graphs is known to be NP-complete. In this paper, we give necessary and sufficient conditions for the existence of Hamiltonian paths inL-alphabet,C-alphabet,F-alphabet, andE-alphabet grid graphs. We also present linear-time algorithms for finding Hamiltonian paths in these graphs.

The Application of DNA Self-Assembly Model for Bin Packing Problem

2012 ◽  
Vol 3 (1) ◽  
pp. 1-15
Author(s):  
Yanfeng Wang ◽  
Xuewen Bai ◽  
Donghui Wei ◽  
Weili Lu ◽  
Guangzhao Cui
Keyword(s):  
Self Assembly ◽  
Bin Packing ◽  
Formal Model ◽  
Linear Time ◽  
Packing Problem ◽  
Assembly Model ◽  
Dna Tiles ◽  
Bin Packing Problem ◽  
Complete Problems ◽  
Np Complete

Bin Packing Problem (BPP) is a classical combinatorial optimization problem of graph theory, which has been proved to be NP-complete, and has high computational complexity. DNA self-assembly, a formal model of crystal growth, has been proposed as a mechanism for the bottom-up fabrication of autonomous DNA computing. In this paper, the authors propose a DNA self-assembly model for solving the BPP, this model consists of two units: grouping based on binary method and subtraction system. The great advantage of the model is that the number of DNA tile types used in the model is constant and it can solve any BPP within linear time. This work demonstrates the ability of DNA tiles to solve other NP-complete problems in the future.

scholarly journals As good as it gets: A scaling comparison of DNA computing, network biocomputing, and electronic computing approaches to an NP-complete problem

2021 ◽  
Author(s):  
Ayyappasamy Sudalaiyadum Perumal ◽  
Zihao Wang ◽  
Falco C M J M van Delft ◽  
Giulia Ippoliti ◽  
Lila Kari ◽  
...  
Keyword(s):  
Energy Efficient ◽  
Dna Computing ◽  
Computing Time ◽  
Real Life ◽  
Performance Criteria ◽  
Scaling Analysis ◽  
Complete Problem ◽  
Complete Problems ◽  
Electronic Computing ◽  
Np Complete

Abstract All known algorithms to solve Nondeterministic Polynomial (NP) Complete problems, relevant to many real-life applications, require the exploration of a space of potential solutions, which grows exponentially with the size of the problem. Since electronic computers can implement only limited parallelism, their use for solving NP-complete problems is impractical for very large instances, and consequently alternative massively parallel computing approaches were proposed to address this challenge. We present a scaling analysis of two such alternative computing approaches, DNA Computing (DNA-C) and Network Biocomputing with Agents (NB-C), compared with Electronic Computing (E-C). The Subset Sum Problem (SSP), a known NP-complete problem, was used as a computational benchmark, to compare the volume, the computing time, and the energy required for each type of computation, relative to the input size. Our analysis shows that the sequentiality of E-C translates in a very small volume compared to that required by DNA-C and NB-C, at the cost of the E-C computing time being outperformed first by DNA-C (linear run time), followed by NB-C. Finally, NB-C appears to be more energy-efficient than DNA-C for some types of input sets, while being less energy-efficient for others, with E-C being always an order of magnitude less energy efficient than DNA-C. This scaling study suggest that presently none of these computing approaches win, even theoretically, for all three key performance criteria, and that all require breakthroughs to overcome their limitations, with potential solutions including hybrid computing approaches.

scholarly journals Hamiltonian path problem solution using DNA computing

2020 ◽  
pp. 69-74
Author(s):  
Anna Sergeenko ◽  
Maria Yakunina ◽  
Oleg Granichin
Keyword(s):  
Branch And Bound ◽  
Dna Computing ◽  
Hamiltonian Path ◽  
Combinatorial Problem ◽  
Problem Solution ◽  
Branch And Bound Method ◽  
Popular Method ◽  
Time Consumption ◽  
Hamiltonian Path Problem ◽  
Classical Algorithm

In this article we study DNA computing, a method which is based on working with DNA molecules in a laboratory. That approach is implemented in solving one of the most popular combinatorial problem — the Hamiltonian path problem. Related to recent improvements in the biophysics methods, which are needed for DNA computing, we propose to change some steps in the classical algorithm to increase accuracy of this method. The branch-and-bound method, the most popular method which is realized on a computer, is also shown in this paper to compare its performance with the time consumption of DNA computing. The results of that comparison prove that it becomes inefficient to use the branch-and-bound method from the counted number of vertices because of its exponentially growing complexity, while DNA computing works parallel and has linearly growing time consumption.

DNA Codeword Design: Theory and Applications

2014 ◽  
Vol 24 (02) ◽  
pp. 1440001 ◽  
Author(s):  
Max H. Garzon
Keyword(s):  
Self Assembly ◽  
Dna Computing ◽  
Sphere Packing ◽  
Error Correcting Codes ◽  
Upper And Lower Bounds ◽  
Geometric Lattice ◽  
Euclidean Spaces ◽  
Large Sets ◽  
Codeword Design ◽  
Np Complete

This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. Major recent advances include the development of experimental techniques to search for such codes, as well as a theoretical framework to analyze this problem, despite the fact that it has been proven to be NP-complete using any single concrete metric space to model the Gibbs energy. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the key to finding such sets would lie in knowledge of the geometry of these spaces. A new general technique has been recently found to embed them in Euclidean spaces in a hybridization-affinity-preserving manner, i.e., in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This isometric embedding materializes long-held metaphors about codeword design in terms of sphere packing and error-correcting codes and leads to designs that are in some cases known to be provably nearly optimal for some oligo sizes. It also leads to upper and lower bounds on estimates of the size of optimal codes of size up to 32–mers, as well as to infinite families of solutions to CODEWORD DESIGN, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, this reduction suggests interesting new algorithms to find dense sphere packing solutions in high dimensional spheres using results for CODEWORD DESIGN previously obtained by experimental or theoretical molecular means, as well as a proof that finding these bounds exactly is NP-complete in general. Finally, some research problems and applications arising from these results are described that might be of interest for further research.

Nanopore Decoding for a Hamiltonian Path Problem

Nanoscale ◽  
2021 ◽  
Author(s):  
Sotaro Takiguchi ◽  
Ryuji Kawano
Keyword(s):  
Energy Consumption ◽  
Dna Computing ◽  
Hamiltonian Path ◽  
Low Energy ◽  
Massive Parallelism ◽  
Hamiltonian Path Problem ◽  
Low Energy Consumption ◽  
Mathematical Problems ◽  
Output Information

DNA computing has attracted attention as a tool for solving mathematical problems due to the potential for massive parallelism with low energy consumption. However, decoding the output information to a...

scholarly journals Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Sakander Hayat ◽  
Asad Khan ◽  
Suliman Khan ◽  
Jia-Bao Liu
Keyword(s):  
Computer Science ◽  
Connected Graph ◽  
Electrical Engineering ◽  
Convex Polytopes ◽  
Hamiltonian Path ◽  
Infinite Family ◽  
Complete Problem ◽  
Analytical Formulas ◽  
Np Complete ◽  
Hamilton Connected

A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.

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