Solving Vertex Cover Problem by Tissue P Systems with Cell Division

Abstract

Abstract:Tissue P systems are a class of distributed and parallel computing models investigated in membrane computing, which are inspired from the structure and functioning of communication cells in tissues. Such systems with cell division (corresponding to the mitosis behavior of living cells) can theoretically generate exponential working space in linear time, therefore providing a possible way to solve computational hard problems in feasible time by a space-time trade-off. In this work, we construct a family of tissue P systems with cell division to solve the vertex cover problems, and achieve a linear time solution (with respect to the size of the problems). Furthermore, we prove that the systems are constructed in a uniform manner and work in a confluent way.

A Review of Membrane Computing Models for Complex Ecosystems and a Case Study on a Complex Giant Panda System

“…In some studies, spiking-like P systems are used as a computing device to solve several arithmetic problems; for instance, the addition of n natural numbers and the product of two arbitrary natural numbers with a given length of binary bits [24,25]. Of course, apart from providing automatic design and arithmetic operations, P systems are applied to hard problems such as vertex cover [26,27], quadratic assignment [28], graph coloring problems [29][30][31], and non-semilinear sets [32,33]. Besides, they have been applied to solve image processing problems [34][35][36][37][38][39], complex optimization problems [40][41][42], complex market interactions [43], and intelligent control problems for robots [44][45][46].…”

An Improved Apriori Algorithm Based on an Evolution-Communication Tissue-Like P System with Promoters and Inhibitors

“…The coupled membrane algorithm combines the traditional algorithm with some structural characters of P systems, such as dividing the whole system into several relatively independent computing units, where the computing units can communicate with each other, the computing units can be dynamically rebuilt, and rules can be executed in parallel [12][13][14][15][16]. The direct membrane algorithm designs the algorithm based on the structure, the objects, and the rules of P systems directly [17][18][19][20][21]. The final goal of membrane computing is to build biocomputers and the direct membrane algorithm can be transplanted to the biocomputers directly, which is more meaningful from this perspective.…”

“…However, the direct membrane algorithm needs to transform the whole traditional algorithm into P system, which is complex and difficult. Up to date, a few simple studies on the direct membrane algorithm focus on the arithmetic operations, the logic operations, the generation of graphic language, and clustering [17][18][19][20][21].…”