EDGE-DELETION GRAPH PROBLEMS WITH FIRST-ORDER EXPRESSIBLE SUBGRAPH PROPERTIES

1991 ◽  
Vol 02 (02) ◽  
pp. 83-99
Author(s):  
V. ARVIND ◽  
S. BISWAS
Keyword(s):  
Normal Form ◽  
Polynomial Time ◽  
Edge Deletion ◽  
Present Evidence ◽  
First Order ◽  
Graph Problems ◽  
Polynomial Time Algorithms ◽  
Complete Problems ◽  
Np Complete ◽  
New Perspective

In this paper edge-deletion problems are studied with a new perspective. In general an edge-deletion problem is of the form: Given a graph G, does it have a subgraph H obtained by deleting zero or more edges such that H satisfies a polynomial-time verifiable property? This paper restricts attention to first-order expressible properties. If the property is expressed by π, which in prenex normal form is Q(Φ) where Q is the quantifier-prefix, then we prove results on the quantifier structure that characterize the complexity of the edge-deletion problem. In particular we give polynomial-time algorithms for problems for which Q is ‘simple’ and in other cases we encode certain NP-complete problems as edge-deletion problems, essentially using the quantifier structure of π. We also present evidence that Q alone cannot capture the complexity of the edge-deletion problem.

scholarly journals POLYNOMIAL TIME ALGORITHMS FOR SOLVING NP-COMPLETE PROBLEMS

2020 ◽  
Vol 3 (441) ◽  
pp. 97-101
Author(s):  
B. Sinchev ◽  
◽  
A. B. Sinchev ◽  
Zh. Akzhanova ◽  
Y. Issekeshev ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithms ◽  
Complete Problems ◽  
Np Complete

scholarly journals Polynomial Time Algorithms for Variants of Graph Matching on Partial k-Trees

2016 ◽  
Vol 41 (3) ◽  
pp. 163-181
Author(s):  
Takayuki Nagoya
Keyword(s):  
Polynomial Time ◽  
Graph Matching ◽  
Graph Isomorphism ◽  
Exact Algorithms ◽  
Polynomial Time Algorithms ◽  
Np Complete

AbstractIn this paper, we deal with two variants of graph matching, the graph isomorphism with restriction and the prefix set of graph isomorphism. The former problem is known to be NP-complete, whereas the latter problem is known to be GI-complete. We propose polynomial time exact algorithms for these problems on partial k-trees.

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.

COMPUTING JORDAN NORMAL FORMS EXACTLY FOR COMMUTING MATRICES IN POLYNOMIAL TIME

1994 ◽  
Vol 05 (03n04) ◽  
pp. 293-302 ◽  
Author(s):  
JIN-YI CAI
Keyword(s):  
Normal Form ◽  
Polynomial Time ◽  
Normal Forms ◽  
Transformation Matrix ◽  
Rational Matrix ◽  
Jordan Normal Form ◽  
Polynomial Time Algorithms ◽  
Commuting Matrices

Given a rational matrix A, and a set of rational matrices B, C,… which commute with A, we give polynomial time algorithms to compute exactly the Jordan Normal Form of A, as well as the transformed matrices of B, C,…. We also obtain the transformation matrix and its inverse exactly in polynomial time.

scholarly journals Hamiltonian Cycle in K1,r-Free Split Graphs — A Dichotomy

2021 ◽  
pp. 1-32
Author(s):  
P. Renjith ◽  
N. Sadagopan
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Optimization Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Np Hard ◽  
Polynomial Time Algorithms ◽  
Split Graphs ◽  
Np Complete ◽  
Cycle Path

For an optimization problem known to be NP-Hard, the dichotomy study investigates the reduction instances to determine the line separating polynomial-time solvable vs NP-Hard instances (easy vs hard instances). In this paper, we investigate the well-studied Hamiltonian cycle problem (HCYCLE), and present an interesting dichotomy result on split graphs. T. Akiyama et al. (1980) have shown that HCYCLE is NP-complete on planar bipartite graphs with maximum degree [Formula: see text]. We use this result to show that HCYCLE is NP-complete for [Formula: see text]-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in [Formula: see text]-free and [Formula: see text]-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path problem and other variants of Hamiltonian cycle (path) problems.

Cellular Solutions to Some Numerical NP-Complete Problems

2011 ◽  
pp. 115-149 ◽  
Author(s):  
Andrés Cordón-Franco ◽  
Miguel A. Gutiérrez-Naranjo ◽  
Mario J. Pérez-Jiménez ◽  
Agustín Riscos-Núñez
Keyword(s):  
Polynomial Time ◽  
Efficient Solutions ◽  
Cellular Systems ◽  
P Systems ◽  
Knapsack Problems ◽  
Simulation Tool ◽  
Working Space ◽  
Complete Problems ◽  
Subset Sum ◽  
Np Complete

This chapter is devoted to the study of numerical NP-complete problems in the framework of cellular systems with membranes, also called P systems (Pun, 1998). The chapter presents efficient solutions to the subset sum and the knapsack problems. These solutions are obtained via families of P systems with the capability of generating an exponential working space in polynomial time. A simulation tool for P systems, written in Prolog, is also described. As an illustration of the use of this tool, the chapter includes a session in the Prolog simulator implementing an algorithm to solve one of the above problems.

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