Solving Vertex Cover Problem by Means of Tissue P Systems with Cell Separation

Tissue P systems is a computing model in the framework of membrane computing inspired from intercellular communication and cooperation between neurons. Many different variants of this model have been proposed. One of the most important models is known as tissue P systems with cell separation. This model has the ability of generating an exponential amount of workspace in linear time, thus it allows us to design cellular solutions to NP-complete problems in polynomial time. In this paper, we present a solution to the Vertex Cover problem via a family of such devices. This is the first solution to this problem in the framework of tissue P systems with cell separation.

Download Full-text

A Warning Propagation-Based Linear-Time-and-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

Integration of Constraint Programming, Artificial Intelligence, and Operations Research - Lecture Notes in Computer Science ◽

10.1007/978-3-319-93031-2_41 ◽

2018 ◽

pp. 567-584

Author(s):

Hong Xu ◽

Kexuan Sun ◽

Sven Koenig ◽

T. K. Satish Kumar

Keyword(s):

Linear Time ◽

Vertex Cover ◽

Time And Space ◽

Vertex Cover Problem ◽

Cover Problem ◽

Minimum Vertex Cover Problem

Download Full-text

Solving Vertex Cover Problem by Tissue P Systems with Cell Division

Applied Mathematics & Information Sciences ◽

10.12785/amis/080141 ◽

2014 ◽

Vol 8 (1) ◽

pp. 333-337 ◽

Cited By ~ 9

Author(s):

Tao Song ◽

Hongjiang Zheng ◽

Juanjuan He

Keyword(s):

Cell Division ◽

Vertex Cover ◽

P Systems ◽

Vertex Cover Problem ◽

Cover Problem

Download Full-text

Semi-Uniform Solution for Common Algorithmic Problem by P System in the Minimally Parallel Mode

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.568-570.802 ◽

2014 ◽

Vol 568-570 ◽

pp. 802-806

Author(s):

Yun Yun Niu ◽

Zhi Gao Wang

Keyword(s):

Linear Time ◽

P Systems ◽

P System ◽

Algorithmic Problem ◽

Complete Problems ◽

Active Membranes ◽

Uniform Solution ◽

Parallel Mode ◽

The Common ◽

Np Complete

It is known that the Common Algorithmic Problem (CAP) has a nice property that several other NP-complete problems can be reduced to it in linear time. In the literature, the decision version of this problem can be efficiently solved with a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes that do not use polarizations and present a semi-uniform solution to CAP in the minimally parallel mode.

Download Full-text

A Uniform Solution for Vertex Cover Problem by Using Time-Free Tissue P Systems

Communications in Computer and Information Science - Bio-Inspired Computing -- Theories and Applications ◽

10.1007/978-3-662-49014-3_28 ◽

2015 ◽

pp. 306-314 ◽

Cited By ~ 1

Author(s):

Yunyun Niu ◽

Zhigao Wang ◽

Jianhua Xiao

Keyword(s):

Vertex Cover ◽

P Systems ◽

Vertex Cover Problem ◽

Uniform Solution ◽

Cover Problem

Download Full-text

Research of the Minimum Vertex-Cover Solutions on the Tree and Lattice Structures

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.989-994.4926 ◽

2014 ◽

Vol 989-994 ◽

pp. 4926-4929

Author(s):

Yun Jia Zhang ◽

Wei Wei ◽

Ting Wang

Keyword(s):

Lattice Structure ◽

Fundamental Problem ◽

Vertex Cover ◽

Solution Space ◽

Theoretical Computer Science ◽

Vertex Cover Problem ◽

Complete Problems ◽

Cover Problem ◽

Minimum Vertex Cover Problem ◽

Arbitrary Lattice

We focus the solution space of a most fundamental problem - Minimum Vertex-Cover problem - in theoretical computer science. After some rigorous analysis, we provide the formation mechanism of minimum vertex-cover solutions on the tree and give the organization of these solutions on arbitrary lattice structure. By the results, we can easily calculate the solution numbers on these structures and have better understanding of the hardness of Minimum Vertex-Cover problem. The proposed study and algorithm can make a new way on detecting the essential difficulty of NP-complete problems and designing efficient algorithms on solving them.

Download Full-text

A linear-time approximation algorithm for the weighted vertex cover problem

Journal of Algorithms ◽

10.1016/0196-6774(81)90020-1 ◽

1981 ◽

Vol 2 (2) ◽

pp. 198-203 ◽

Cited By ~ 249

Author(s):

R Bar-Yehuda ◽

S Even

Keyword(s):

Approximation Algorithm ◽

Linear Time ◽

Vertex Cover ◽

Time Approximation ◽

Vertex Cover Problem ◽

Weighted Vertex ◽

Cover Problem

Download Full-text

Solving Vertex Cover Problem Using DNA Tile Assembly Model

Journal of Applied Mathematics ◽

10.1155/2013/407816 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Zhihua Chen ◽

Tao Song ◽

Yufang Huang ◽

Xiaolong Shi

Keyword(s):

Biological Function ◽

Linear Time ◽

Vertex Cover ◽

Assembly Model ◽

Dna Tiles ◽

Vertex Cover Problem ◽

Tile Assembly ◽

Cover Problem ◽

Tile Systems ◽

Assembly Models

DNA tile assembly models are a class of mathematically distributed and parallel biocomputing models in DNA tiles. In previous works, tile assembly models have been proved be Turing-universal; that is, the system can do what Turing machine can do. In this paper, we use tile systems to solve computational hard problem. Mathematically, we construct three tile subsystems, which can be combined together to solve vertex cover problem. As a result, each of the proposed tile subsystems consists ofΘ(1) types of tiles, and the assembly process is executed in a parallel way (like DNA’s biological function in cells); thus the systems can generate the solution of the problem in linear time with respect to the size of the graph.

Download Full-text