A DNA Sticker Algorithm for Solving N-Queen Problem

Over the past few decades numerous attempts have been made to solve combinatorial optimization problems that are NP-complete or NP -hard. It has been evidenced that DNA computing can solve those problems which are currently intractable on even fastest electronic computers. This paper proposes a new DNA algorithm for solving N-Queen problem, a complex optimization problem. The algorithm not only shows whether or not a solution exists, but provides all possible solutions by massively parallel computations. The proposed algorithm can be easily extended to solve other optimization problems.

[1]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[2]  A Leier,et al.  Cryptography with DNA binary strands. , 2000, Bio Systems.

[3]  Erik Winfree.  DNA Computing by Self-Assembly , 2003 .

[4]  Ehud Shapiro,et al.  DNA molecule provides a computing machine with both data and fuel , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[5]  John S. Oliver.  Computation with DNA: Matrix multiplication , 1996, DNA Based Computers.

[6]  Jack Parker.  Computing with DNA , 2003, EMBO reports.

[7]  Kate Smith-Miles,et al.  Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research , 1999, INFORMS J. Comput..

[8]  Richard J. Lipton,et al.  Breaking DES using a molecular computer , 1995, DNA Based Computers.

[9]  Mitsunori Ogihara,et al.  Simulating Boolean circuits on a DNA computer , 1997, RECOMB '97.

[10]  A. Condon,et al.  Surface-based DNA computing operations: DESTROY and READOUT. , 1999, Bio Systems.

[11]  Clifford R. Johnson,et al.  Solution of a 20-Variable 3-SAT Problem on a DNA Computer , 2002, Science.

[12]  Jiahai Wang,et al.  A method to improve the transiently chaotic neural network , 2004, Neurocomputing.

[13]  Max H. Garzon,et al.  DNA implementation of nondeterminism , 1997, DNA Based Computers.

[14]  Niklaus Wirth,et al.  Algorithms + Data Structures = Programs , 1976 .

[15]  Rok Sosic,et al.  Efficient Local Search with Conflict Minimization: A Case Study of the n-Queens Problem , 1994, IEEE Trans. Knowl. Data Eng..

[16]  L F Landweber,et al.  Molecular computation: RNA solutions to chess problems , 2000, Proc. Natl. Acad. Sci. USA.

[17]  Niels Bohwerg.  Parallel Arithmetic with Splicing , 2000 .

[18]  Gheorghe Paun,et al.  Simple Splicing Systems , 1998, Discret. Appl. Math..

[19]  Jacek Mańdziuk,et al.  Neural networks for the N-Queens Problem : a review , 2002 .

[20]  Janardan Misra,et al.  Binary Arithmetic for DNA Computers , 2002, DNA.

[21]  M. Ganjtabesh,et al.  DNA algorithm for an unbounded fan-in Boolean circuit. , 2005, Bio Systems.

[22]  Lloyd M. Smith,et al.  DNA computing on surfaces , 2000, Nature.

[23]  Jing Liu,et al.  Evolutionary Agents for n-Queen Problems , 2005, ICNC.

[24]  Giancarlo Mauri,et al.  On the Universality of Post and Splicing Systems , 2000, MCU.

[25]  Grzegorz Rozenberg,et al.  Sticker Systems , 1998, Theor. Comput. Sci..

[26]  Abbas Nowzari-Dalini,et al.  DNA Simulation of Nand Boolean Circuits , 2004 .

[27]  Masaya Ohta,et al.  Chaotic neural networks with reinforced self-feedbacks and its application to N-Queen problem , 2002, Math. Comput. Simul..

[28]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[29]  Srinivasan Parthasarathy,et al.  Arithmetic and logic operations with DNA , 1997, DNA Based Computers.

[30]  Kelly D. Crawford,et al.  Solving the n-queens problem using genetic algorithms , 1992, SAC '92.

[31]  Erik Winfree,et al.  A Sticker-Based Model for DNA Computation , 1998, J. Comput. Biol..

[32]  Lloyd M Smith,et al.  Demonstration of a universal surface DNA computer. , 2004, Nucleic acids research.

[33]  Gheorghe Paun,et al.  DNA computing, sticker systems, and universality , 1998, Acta Informatica.

[34]  Rudolf Freund,et al.  DNA Computing Based on Splicing: The Existence of Universal Computers , 1999, Theory of Computing Systems.

[35]  Paul W. K. Rothemund,et al.  A DNA and restriction enzyme implementation of Turing machines , 1995, DNA Based Computers.

[36]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[37]  P D Kaplan,et al.  DNA solution of the maximal clique problem. , 1997, Science.

[38]  Piotr Wasiewicz,et al.  The Inference Based on Molecular Computing , 2000, Cybern. Syst..