#### DMCA

## The All-Ones Problem for Binomial Trees, Butterfly and Benes Networks

### Citations

1716 | Graph Theory with Applications
- Bondy, Murty
- 1985
(Show Context)
Citation Context ...this chapter, we consider connected, simple, undirected graphs only. One can deal with disconnected graphs, component by component. For all notations and terminology used in this chapter, we refer to =-=[2]-=-. An equivalent version of the all-ones problem was proposed by Peled [8], where it was called the Lamp Lighting problem. The rule of the all-ones problem is called σ+ rule on graphs, which means that... |

92 | Topological structure and analysis of interconnection networks - Xu - 2001 |

24 |
The σ -game and cellular automata,
- Sutner
- 1990
(Show Context)
Citation Context ...INDIA. R. Prabha Department of Mathematics, Ethiraj College for women, Chennai- 600 008, INDIA. E-mail: prabha75@gmail.com Abstract The all-ones problem is an NP-complete problem introduced by Sutner =-=[11]-=-, with wide applications in linear cellular automata. In this paper, we solve the all-ones problem for some of the widely studied architectures like binomial trees, butterfly, and benes networks. Keyw... |

15 |
σ -game, σ+-game and two-dimensional additive cellular automata,
- Barua, Ramakrishnan
- 1996
(Show Context)
Citation Context ...ly its neighbours but also its own light. If a button lights only its neighbours but not its own light, this rule on graphs is called σ rule. There have been many publications on the All-Ones Problem =-=[1, 6, 12]-=-. Using linear algebra, Sutner [13] proved that it is always possible to light every lamp in any graph by σ+ rule. A graph-theoretic proof was given by Erikisson et al. [7]. In [9] Sutner proved that ... |

11 |
Additive automata on graphs,
- Sutner
- 1988
(Show Context)
Citation Context ...Ones Problem [1, 6, 12]. Using linear algebra, Sutner [13] proved that it is always possible to light every lamp in any graph by σ+ rule. A graph-theoretic proof was given by Erikisson et al. [7]. In =-=[9]-=- Sutner proved that the Minimum all-ones problem is 1 2 Paul Manuel, Indra Rajasingh, Bharathi Rajan and R. Prabha NP-complete in general. Li et al. [3] have proved that the problem is NP-complete eve... |

8 | Universal configurations in light-flipping games
- Dodis, Winkler
- 2001
(Show Context)
Citation Context ...ly its neighbours but also its own light. If a button lights only its neighbours but not its own light, this rule on graphs is called σ rule. There have been many publications on the All-Ones Problem =-=[1, 6, 12]-=-. Using linear algebra, Sutner [13] proved that it is always possible to light every lamp in any graph by σ+ rule. A graph-theoretic proof was given by Erikisson et al. [7]. In [9] Sutner proved that ... |

6 |
Note on the lamp lighting problem, in:
- Eriksson, Eriksson, et al.
- 2000
(Show Context)
Citation Context ...the All-Ones Problem [1, 6, 12]. Using linear algebra, Sutner [13] proved that it is always possible to light every lamp in any graph by σ+ rule. A graph-theoretic proof was given by Erikisson et al. =-=[7]-=-. In [9] Sutner proved that the Minimum all-ones problem is 1 2 Paul Manuel, Indra Rajasingh, Bharathi Rajan and R. Prabha NP-complete in general. Li et al. [3] have proved that the problem is NP-comp... |

5 |
The minimum all-ones problem for trees,
- Chen, Li, et al.
- 2004
(Show Context)
Citation Context ...is 1 2 Paul Manuel, Indra Rajasingh, Bharathi Rajan and R. Prabha NP-complete in general. Li et al. [3] have proved that the problem is NP-complete even when restricted to bipartite graphs. Li et al. =-=[5]-=- have given a linear time algorithm for finding optimal solutions for trees. 2 Notations Let G = (V,E) be a simple, connected graph. Let |V | = n and |E| = m. The open neighbourhood of a vertex v is {... |

5 |
σ-automata and Chebyshev-polynomials, Theoret
- Sutner
(Show Context)
Citation Context ... If a button lights only its neighbours but not its own light, this rule on graphs is called σ rule. There have been many publications on the All-Ones Problem [1, 6, 12]. Using linear algebra, Sutner =-=[13]-=- proved that it is always possible to light every lamp in any graph by σ+ rule. A graph-theoretic proof was given by Erikisson et al. [7]. In [9] Sutner proved that the Minimum all-ones problem is 1 2... |

3 |
Problem 10197
- Peled
(Show Context)
Citation Context ...can deal with disconnected graphs, component by component. For all notations and terminology used in this chapter, we refer to [2]. An equivalent version of the all-ones problem was proposed by Peled =-=[8]-=-, where it was called the Lamp Lighting problem. The rule of the all-ones problem is called σ+ rule on graphs, which means that a button lights not only its neighbours but also its own light. If a but... |

3 | Problem 88-8 - Sutner |

2 |
Connected odd dominating sets in graphs, Discuss
- Caro, Klostermeyer, et al.
- 2005
(Show Context)
Citation Context ...od of a vertex v is {v} ∪ N(v) and is denoted by N [v]. The degree of a vertex v in G is the number of neighbours of v in G. The all-ones problem is equivalent to the following dominating set problem =-=[4]-=- from a graph-theoretic point of view. A set S of vertices is independent if no two vertices in S are adjacent in G. A clique is a graph where all the vertices are mutually adjacent. A maximal clique ... |

2 | The general sigma all-ones problem for trees - Li, Wang, et al. |

1 | On the complexity of dominating set problems related to the minimum all-ones problem, Theor
- Broersma, Li
(Show Context)
Citation Context ...tic proof was given by Erikisson et al. [7]. In [9] Sutner proved that the Minimum all-ones problem is 1 2 Paul Manuel, Indra Rajasingh, Bharathi Rajan and R. Prabha NP-complete in general. Li et al. =-=[3]-=- have proved that the problem is NP-complete even when restricted to bipartite graphs. Li et al. [5] have given a linear time algorithm for finding optimal solutions for trees. 2 Notations Let G = (V,... |