Efficient DNA sticker algorithms for NP-complete graph problems

Zimmermann, Karl-Heinz

doi:10.1016/s0010-4655(02)00270-9

Cited by 44 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[5], Zimmermann proposed a sticker model to compute all k-cliques, independent k-sets, Hamiltonian paths, and Steiner trees with respect to a given edge or vertex set. The algorithms determine not merely the existence of a solution but yield all solutions (if any).…”

Section: Research Results Of Zimmermannmentioning

confidence: 99%

“…[5], the authors presented several algorithms for the problems by applying the sticker model. First, they presented an algorithm for the edge induced subgraph; then using this algorithm, they designed algorithms for the Hamiltonian path (or cycle) problem, Steiner number problem, the independent set problem and the maximal clique problem.…”

Section: Reviewmentioning

confidence: 99%

“…[5], Zimmermann also proposed vertexInducedGraphs sticker model which is not so important and has not been widely used in other hard NP-problems. We leave it out here, for details please see the original texts.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Sticker DNA computer model — Part II: Application

Dong

et al. 2004

Chin. Sci. Bull.

View full text Add to dashboard Cite

Sticker model is one of the basic models in the DNA computer models. This model is coded with single-double stranded DNA molecules. It has the following advantages that the operations require no strands extension and use no enzymes; What's more, the materials are reusable. Therefore, it arouses attention and interest of scientists in many fields. In this paper, we extend and improve the sticker model, which will be definitely beneficial to the construction of DNA computer. This paper is the second part of our series paper, which mainly focuses on the application of sticker model. It mainly consists of the following three sections: the matrix representation of sticker model is first presented; then a brief review of the past research on graph and combinatorial optimization, such as the minimal set covering problem, the vertex covering problem, Hamiltonian path or cycle problem, the maximal clique problem, the maximal independent problem and the Steiner spanning tree problem, is described; Finally a DNA algorithm for the graph isomorphic problem based on the sticker model is given.

show abstract

Section: Research Results Of Zimmermannmentioning

confidence: 99%

Section: Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Sticker DNA computer model — Part II: Application

Dong

et al. 2004

Chin. Sci. Bull.

View full text Add to dashboard Cite

show abstract

“…A stickers program basically filters out in parallel those solutions that satisfy the contraints. The stickers model is computationally complete and universal, and many NP complete problems can be described by stickers programs with polynomial runtime and exponential space [6,7,9,10]. Unlike other models of DNA computation, the stickers model has a random access memory that requires no strand extension.…”

Section: Introductionmentioning

confidence: 99%

Bioinspired Parallel Algorithms for Maximum Clique Problem on FPGA Architectures

Martínez-Pérez

Brandt

Wild

et al. 2008

J Sign Process Syst Sign Image Video Technol

Self Cite

View full text Add to dashboard Cite

The stickers model is a model of DNA computation that is computationally complete and universal. Many NP complete problems can be described by stickers programs that have polynomial runtime and are exponential in space. The stickers model can be viewed as a bit-vertically operating register machine. This makes it attractive for in silico implementation. This paper describes a stickers model for the maximum clique problem and its implementation by an FPGA architecture. The results show that the FPGA based algorithm is comparable with existing software algorithms for moderate problem sizes. More generally, the stickers model seems to be a well-suited programming model for dedicated hardware.

show abstract

“…DNA computing is attractive both theoretically and technically because of its intrinsic parallelism. DNA computing has been used to solve various computationally complex problems, such as the Hamiltonian problem [19], the SAT problem [20,21], the Steiner tree problem [22], the maximal clique problem [23], and the maximum independent set problem [24]. Because the problems solved by DNA computing are encoded by a DNA sequence, the design of DNA sequences is crucial for successful DNA computation.…”

mentioning

confidence: 99%

A membrane evolutionary algorithm for DNA sequence design in DNA computing

Xiao

Zhang

2012

Chin. Sci. Bull.

View full text Add to dashboard Cite

DNA sequence design has a crucial role in successful DNA computation, which has been proved to be an NP-hard (non-deterministic polynomial-time hard) problem. In this paper, a membrane evolutionary algorithm is proposed for the DNA sequence design problem. The results of computer experiments are reported, in which the new algorithm is validated and out-performs certain known evolutionary algorithms for the DNA sequence design problem.DNA computing, membrane computing, P system, DNA sequence design Citation:Xiao J H, Zhang X Y, Xu J. A membrane evolutionary algorithm for DNA sequence design in DNA computing. Chin Sci Bull, 2012Bull, , 57: 698706, doi: 10.1007 Membrane computing is an emergent branch of natural computing, first introduced by Paun [1]. This unconventional model of computation is a type of distributed parallel system, which is inspired by the structure and function of living cells. The devices of this model are called P systems.Roughly speaking, a P system consists of a cell-like membrane structure, in the compartments of which there are multisets of objects that evolve according to given rules in a synchronous, non-deterministic maximally parallel manner. Many different classes of such computing devices have already been investigated. Most of them are computationally universal, i.e., able to compute whatever a Turing machine can do [2][3][4], and are computationally efficient, i.e., able to trade space for time and in this way solve presumably intractable problems in a feasible time (e.g., [5][6][7][8][9]). Membrane computing is very attractive from a computational point of view because of its hierarchical structure and intrinsic parallelism. Evolutionary algorithms are robust optimization and search methods inspired by evolutionary processes occurring in natural selection and molecular genetics. They are approximation algorithms that seek a trade-off between solution quality and computational costs. The main features of evolutionary algorithms are the representation and evaluation of individuals, population dynamics, and evolutionary operators, such as selection, crossover, and mutation [10]. Evolutionary algorithms exhibit an intrinsic parallelism derived from dealing with multiple individuals, show remarkable adaptability and flexibility to various applications, and provide good search capabilities and robust results [11].Both P systems and evolutionary algorithms are natureinspired models and are used to solve complex problems; however, they are different with respect to the objects and rules used and in the computational strategies employed. While P systems represent a suitable formal framework for parallel-distributed computation, evolutionary algorithms are very effective for implementing different algorithms to solve numerous problems [11]. Thus, the possible interaction between P systems and evolutionary algorithms represents a fertile research field, as suggested by the list of 26 open problems in membrane computing [12]. The first attempt in this direction was by Nishida [13,14], who ...

show abstract

Efficient DNA sticker algorithms for NP-complete graph problems

Cited by 44 publications

References 7 publications

Sticker DNA computer model — Part II: Application

Sticker DNA computer model — Part II: Application

Bioinspired Parallel Algorithms for Maximum Clique Problem on FPGA Architectures

A membrane evolutionary algorithm for DNA sequence design in DNA computing

Contact Info

Product

Resources

About