A depth first search algorithm to generate the family of maximal independent sets of a graph lexicographically

Computing ◽  
1981 ◽  
Vol 27 (4) ◽  
pp. 349-366 ◽  
Author(s):  
E. Loukakis ◽  
C. Tsouros
Keyword(s):  
Search Algorithm ◽  
Independent Sets ◽  
Depth First Search ◽  
The Family ◽  
Maximal Independent Sets

scholarly journals CheAPS: a Checker of Asynchronous Parameterized Systems

10.29007/d336 ◽  
2018 ◽  
Author(s):  
Igor Konnov
Keyword(s):  
Search Algorithm ◽  
Fixed Number ◽  
Depth First Search ◽  
Parameterized Systems ◽  
Full Version ◽  
The Family ◽  
Fixed Set ◽  
Finite State ◽  
State Models ◽  
Finite State Models

We present CheAPS, the checker of asynchronous parameterized communicating systems. It is a set of tools for verification of parameterized families F = M_n of finite-state models against LTL specification S. Each model M_n from a family F is composed of a fixed number of control processes and n processes from a fixed set of prototypes. Given a description of a family CheAPS generates finite-state models M_n and checks if one of such models can be used as an invariant of the family. As soon as an invariant is detected it is model checked by Spin to verify it against a specification S. If Spin completes the verification successfully, then all the models of F satisfy S.We are going to demonstrate an application of CheAPS to several examples: Chandy-Lamport snapshot algorithm, Awerbuch distributed depth-first search algorithm, Milner's scheduler, and the model of RSVP protocol, where invariants were detected successfully on that models by our tools. The project homepage is http://lvk.cs.msu.su/\~konnov/cheaps/. It is available under BSD-like license.The full version of the abstract is uploaded.

Trees without twin-leaves with smallest number of maximal independent sets

2020 ◽  
Vol 30 (1) ◽  
pp. 53-67 ◽  
Author(s):  
Dmitriy S. Taletskii ◽  
Dmitriy S. Malyshev
Keyword(s):  
Independent Sets ◽  
Adjacent Vertex ◽  
Maximal Independent Sets

AbstractFor any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets.

On graphs with the third largest number of maximal independent sets

2009 ◽  
Vol 109 (4) ◽  
pp. 248-253 ◽  
Author(s):  
Hongbo Hua ◽  
Yaoping Hou
Keyword(s):  
Independent Sets ◽  
The Third ◽  
Maximal Independent Sets

scholarly journals Maximal independent sets on a grid graph

2017 ◽  
Vol 340 (12) ◽  
pp. 2762-2768 ◽  
Author(s):  
Seungsang Oh
Keyword(s):  
Independent Sets ◽  
Grid Graph ◽  
Maximal Independent Sets

scholarly journals Autosetting soliton pulsation in a fiber laser by improved depth-first search algorithm

2021 ◽  
Author(s):  
Pei-Zhu Zheng ◽  
Ti-Jian Li ◽  
Handing Xia ◽  
Mengjun Feng ◽  
Meng Liu ◽  
...  
Keyword(s):  
Fiber Laser ◽  
Search Algorithm ◽  
Depth First Search

Combinatorial aspects of the Löwenstein avoidance rule. Part I: the independence polynomial

2021 ◽  
Vol 77 (6) ◽  
Author(s):  
Montauban Moreira de Oliveira Jr ◽  
Jean-Guillaume Eon
Keyword(s):  
Propositional Calculus ◽  
Independent Sets ◽  
Companion Paper ◽  
Theoretical Interpretation ◽  
Vector Method ◽  
Independence Polynomial ◽  
Calculation Technique ◽  
Independence Polynomials ◽  
Maximal Independent Sets

According to Löwenstein's rule, Al–O–Al bridges are forbidden in the aluminosilicate framework of zeolites. A graph-theoretical interpretation of the rule, based on the concept of independent sets, was proposed earlier. It was shown that one can apply the vector method to the associated periodic net and define a maximal Al/(Al+Si) ratio for any aluminosilicate framework following the rule; this ratio was called the independence ratio of the net. According to this method, the determination of the independence ratio of a periodic net requires finding a subgroup of the translation group of the net for which the quotient graph and a fundamental transversal have the same independence ratio. This article and a companion paper deal with practical issues regarding the calculation of the independence ratio of mainly 2-periodic nets and the determination of site distributions realizing this ratio. The first paper describes a calculation technique based on propositional calculus and introduces a multivariate polynomial, called the independence polynomial. This polynomial can be calculated in an automatic way and provides the list of all maximal independent sets of the graph, hence also the value of its independence ratio. Some properties of this polynomial are discussed; the independence polynomials of some simple graphs, such as short paths or cycles, are determined as examples of calculation techniques. The method is also applied to the determination of the independence ratio of the 2-periodic net dhc.

Local Structure When All Maximal Independent Sets Have Equal Weight

1998 ◽  
Vol 11 (4) ◽  
pp. 644-654 ◽  
Author(s):  
Yair Caro ◽  
M. N. Ellingham ◽  
J. E. Ramey
Keyword(s):  
Local Structure ◽  
Independent Sets ◽  
Equal Weight ◽  
Maximal Independent Sets

scholarly journals Maximal independent sets in minimum colorings

2011 ◽  
Vol 311 (13) ◽  
pp. 1158-1163 ◽  
Author(s):  
S. Arumugam ◽  
Teresa W. Haynes ◽  
Michael A. Henning ◽  
Yared Nigussie
Keyword(s):  
Independent Sets ◽  
Maximal Independent Sets
Sign in / Sign up

Export Citation Format

Share Document