Solving a weak NP-complete problem in polynomial time by using mutual mobile membrane systems

2011 ◽  
Vol 48 (7-8) ◽  
pp. 409-415 ◽  
Author(s):  
Bogdan Aman ◽  
Gabriel Ciobanu
Keyword(s):  
Polynomial Time ◽  
Membrane Systems ◽  
Complete Problem ◽  
Np Complete

EFFICIENT APPROACH FOR WEB SERVICES SELECTION WITH MULTI-QoS CONSTRAINTS

2008 ◽  
Vol 17 (03) ◽  
pp. 349-371 ◽  
Author(s):  
TAO HUANG ◽  
LEI LI ◽  
JUN WEI
Keyword(s):  
Web Services ◽  
Polynomial Time ◽  
High Performance ◽  
Feasible Solution ◽  
Search Space ◽  
User Preference ◽  
Composite Service ◽  
Efficient Approach ◽  
Complete Problem ◽  
Np Complete

With the increasing number of Web Services with similar or identical functionality, the non-functional properties of a Web Service will become more and more important. Hence, a choice needs to be made to determine which services are to participate in a given composite service. In general, multi-QoS constrained Web Services composition, with or without optimization, is a NP-complete problem on computational complexity that cannot be exactly solved in polynomial time. A lot of heuristics and approximation algorithms with polynomial- and pseudo-polynomial-time complexities have been designed to deal with this problem. However, these approaches suffer from excessive computational complexities that cannot be used for service composition in runtime. In this paper, we propose a efficient approach for multi-QoS constrained Web Services selection. Firstly, a user preference model was proposed to collect the user's preference. And then, a correlation model of candidate services are established in order to reduce the search space. Based on these two model, a heuristic algorithm is then proposed to find a feasible solution for multi-QoS constrained Web Services selection with high performance and high precision. The experimental results show that the proposed approach can achieve the expecting goal.

scholarly journals Polynomial time solution to NP-complete problem Hamiltonian cycle (P=NP Proof)

2021 ◽  
Author(s):  
Yasaman KalantarMotamedi
Keyword(s):  
Computer Science ◽  
Polynomial Time ◽  
Hamiltonian Cycle ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Rigorous Proof ◽  
Complete Problem ◽  
Time Solution ◽  
Np Complete

P vs NP is one of the open and most important mathematics/computer science questions that has not been answered since it was raised in 1971 despite its importance and a quest for a solution since 2000. P vs NP is a class of problems that no polynomial time algorithm exists for any. If any of the problems in the class gets solved in polynomial time, all can be solved as the problems are translatable to each other. One of the famous problems of this kind is Hamiltonian cycle. Here we propose a polynomial time algorithm with rigorous proof that it always finds a solution if there exists one. It is expected that this solution would address all problems in the class and have a major impact in diverse fields including computer science, engineering, biology, and cryptography.

scholarly journals Acyclic colourings of graphs with bounded degree

2010 ◽  
Vol Vol. 12 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Mieczyslaw Borowiecki ◽  
Anna Fiedorowicz ◽  
Katarzyna Jesse-Jozefczyk ◽  
Elzbieta Sidorowicz
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Cubic Graph ◽  
Bounded Degree ◽  
Complete Problem ◽  
International Audience ◽  
Np Complete

Graphs and Algorithms International audience A k-colouring of a graph G is called acyclic if for every two distinct colours i and j, the subgraph induced in G by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, there are no bichromatic alternating cycles. In 1999 Boiron et al. conjectured that a graph G with maximum degree at most 3 has an acyclic 2-colouring such that the set of vertices in each colour induces a subgraph with maximum degree at most 2. In this paper we prove this conjecture and show that such a colouring of a cubic graph can be determined in polynomial time. We also prove that it is an NP-complete problem to decide if a graph with maximum degree 4 has the above mentioned colouring.

scholarly journals Graphs with no induced wheel and no induced antiwheel

2015 ◽  
Vol 9 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Frédéric Maffray
Keyword(s):  
Polynomial Time ◽  
Simple Structure ◽  
Complete Problem ◽  
Complementary Graph ◽  
Np Complete ◽  
Chordless Cycle

A wheel is a graph that consists of a chordless cycle of length at least 4 plus a vertex with at least three neighbors on the cycle. An antiwheel is the complementary graph of a wheel. It was shown recently that detecting induced wheels is an NP-complete problem. In contrast, it is shown here that graphs that contain no wheel and no antiwheel have a very simple structure and consequently can be recognized in polynomial time.

scholarly journals Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Bosheng Song ◽  
Linqiang Pan ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Polynomial Time ◽  
Efficient Solution ◽  
Efficient Solutions ◽  
Affirmative Answer ◽  
P Systems ◽  
Membrane Systems ◽  
Complete Problems ◽  
Np Complete ◽  
Np Problem ◽  
Computing Models

Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

scholarly journals 3-Colorability of Pseudo-Triangulations

2015 ◽  
Vol 25 (04) ◽  
pp. 283-298
Author(s):  
Oswin Aichholzer ◽  
Franz Aurenhammer ◽  
Thomas Hackl ◽  
Clemens Huemer ◽  
Alexander Pilz ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Plane Graphs ◽  
Np Completeness ◽  
Complete Problem ◽  
Polynomial Time Algorithms ◽  
Complexity Results ◽  
The Family ◽  
General Plane ◽  
Np Complete

Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-triangulations, which are a generalization of triangulations, and prove NP-completeness for this class. This result also holds if we bound their face degree to four, or exclusively consider pointed pseudo-triangulations with maximum face degree five. In contrast to these completeness results, we show that pointed pseudo-triangulations with maximum face degree four are always 3-colorable. An according 3-coloring can be found in linear time. Some complexity results relating to the rank of pseudo-triangulations are also given.

scholarly journals Some algorithmic results for finding compatible spanning circuits in edge-colored graphs

2020 ◽  
Vol 40 (4) ◽  
pp. 1008-1019
Author(s):  
Zhiwei Guo ◽  
Hajo Broersma ◽  
Ruonan Li ◽  
Shenggui Zhang
Keyword(s):  
Polynomial Time ◽  
Sufficient Conditions ◽  
Complete Graphs ◽  
Hamilton Cycles ◽  
Colored Graph ◽  
Colored Graphs ◽  
Complete Problem ◽  
Polynomial Time Algorithms ◽  
Np Complete ◽  
Euler Tours

Abstract A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have been considered in previous literature. More recently, sufficient conditions for the existence of more general compatible spanning circuits in specific edge-colored graphs have been established. In this paper, we consider the existence of (more general) compatible spanning circuits from an algorithmic perspective. We first show that determining whether an edge-colored connected graph contains a compatible spanning circuit is an NP-complete problem. Next, we describe two polynomial-time algorithms for finding compatible spanning circuits in edge-colored complete graphs. These results in some sense give partial support to a conjecture on the existence of compatible Hamilton cycles in edge-colored complete graphs due to Bollobás and Erdős from the 1970s.

ALL SEPARATING TRIANGLES IN A PLANE GRAPH CAN BE OPTIMALLY "BROKEN" IN POLYNOMIAL TIME

2000 ◽  
Vol 11 (03) ◽  
pp. 405-421 ◽  
Author(s):  
ANNA ACCORNERO ◽  
MASSIMO ANCONA ◽  
SONIA VARINI
Keyword(s):  
Planar Graph ◽  
Polynomial Time ◽  
Efficient Algorithm ◽  
Plane Graph ◽  
Covering Problem ◽  
Graph Covering ◽  
Complete Problem ◽  
Arbitrary Plane ◽  
Np Complete

Lai and Leinwand have shown that an arbitrary plane (i.e., embedded planar) graph G can be transformed, by adding crossover vertices, into a new plane graph G′ admitting a rectangular dual. Moreover, they conjectured that finding a minimum set of such crossover vertices is an NP-complete problem. In this paper it is shown that the above problem can be resolved in polynomial time by reducing it to a graph covering problem, and an efficient algorithm for finding minimum set of edges on which to insert the crossover vertices is also presented.

scholarly journals P Systems with Evolutional Communication and Division Rules

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 327
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Membrane Computing ◽  
P Systems ◽  
Membrane Systems ◽  
Sat Problem ◽  
Complete Problem ◽  
Intractable Problems ◽  
Np Complete ◽  
The One

A widely studied field in the framework of membrane computing is computational complexity theory. While some types of P systems are only capable of efficiently solving problems from the class P, adding one or more syntactic or semantic ingredients to these membrane systems can give them the ability to efficiently solve presumably intractable problems. These ingredients are called to form a frontier of efficiency, in the sense that passing from the first type of P systems to the second type leads to passing from non-efficiency to the presumed efficiency. In this work, a solution to the SAT problem, a well-known NP-complete problem, is obtained by means of a family of recognizer P systems with evolutional symport/antiport rules of length at most (2,1) and division rules where the environment plays a passive role; that is, P systems from CDEC^(2,1). This result is comparable to the one obtained in the tissue-like counterpart, and gives a glance of a parallelism and the non-evolutionary membrane systems with symport/antiport rules.

scholarly journals On the Nash equilibrium in the inspector problem

2014 ◽  
Vol 55 ◽  
Author(s):  
Martynas Sabaliauskas ◽  
Jonas Mockus
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Explicit Solution ◽  
Security Systems ◽  
Bimatrix Game ◽  
Complete Problem ◽  
Elimination Algorithm ◽  
Np Complete ◽  
Special Case

Inspector problem represents an economic duel of inspector and law violator and is formulated as a bimatrix game. In general, bimatrix game is NP-complete problem. The inspector problem is a special case where the equilibrium can be found in polynomial time. In this paper, a generalized version of the Inspector Problem is described with the aim to represent broader family of applied problems, including the optimization of security systems. The explicit solution is provided and the Modified Strategy Elimination algorithm is introduced.

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