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## Disjoint identifying-codes for arbitrary graphs (2005)

Venue: | In Proc. International Symposium on Information Theory (ISIT |

Citations: | 3 - 0 self |

### Citations

2646 |
The Theory of Error-correcting Codes
- MacWilliams, Sloane
- 1977
(Show Context)
Citation Context ...here H(p) = −p log p − (1 − p) log(1 − p) is the binary entropy function and all logarithms have the same base. Example 1 demonstrates an application of Theorems 1 and 2 to modified Hadamard matrices =-=[13]-=-, and Example 2 generalizes this to a family of graphs that asymptotically reach the bounds in this paper. Before proving Theorem 2, we adapt the following bound on the size of an identifying code fro... |

1960 | The Probabilistic Method
- Alon, Spencer
- 1992
(Show Context)
Citation Context ...mpletes the proof. June 6, 2005 DRAFT 5sIV. LOWER BOUNDS ON κ The main results in this section, Theorems 4 and 5, provide lower bounds on κ based on the symmetric form of the Lovăsz Local Lemma (LLL) =-=[14]-=-, a powerful probabilistic tool for proving the existence of an event. We restate this form of LLL for completeness. Lemma 3 Consider a set of events E = {E1 . . . En} such that Pr[Ei] ≤ p for all i. ... |

73 | Approximating the domatic number
- Feige, Halldórsson, et al.
- 2000
(Show Context)
Citation Context ...types. By cycling resources through disjoint dominating sets in a system graph, one can improve the robustness of the system with respect to connection failures. On the theoretical size, Feige et al. =-=[9]-=- have applied the Lovăsz Local Lemma (LLL) to approximate the domatic number of an arbitrary graph as (1 − o(1)) where bmin and bmax are the minimum and maximum vertex neighborhood ball sizes respecti... |

54 | Robust location detection in emergency sensor networks
- Ray, Ungrangsi, et al.
- 2003
(Show Context)
Citation Context ...ral point can uniquely determine the faulty processor. Several bounds on the minimum size of an identifying code were also presented in [1] and studied further in [7, 8] and many subsequent works. In =-=[3, 4]-=- identifying codes of radius r = 1 were suggested for use in indoor location detection and thereafter refined for purposes of robustness. 2) Domatic number: One well-known generalization of our work i... |

42 | Robust location detection with sensor networks
- Ray, Starobinski, et al.
- 2004
(Show Context)
Citation Context ...ral point can uniquely determine the faulty processor. Several bounds on the minimum size of an identifying code were also presented in [1] and studied further in [7, 8] and many subsequent works. In =-=[3, 4]-=- identifying codes of radius r = 1 were suggested for use in indoor location detection and thereafter refined for purposes of robustness. 2) Domatic number: One well-known generalization of our work i... |

38 | Coding theory framework for target location in distributed sensor networks - Chakrabarty, Iyengar, et al. - 2001 |

20 | On locating-dominating codes in binary Hamming spaces
- Honkala, Laihonen, et al.
(Show Context)
Citation Context ...lescing the various reports, the central point can uniquely determine the faulty processor. Several bounds on the minimum size of an identifying code were also presented in [1] and studied further in =-=[7, 8]-=- and many subsequent works. In [3, 4] identifying codes of radius r = 1 were suggested for use in indoor location detection and thereafter refined for purposes of robustness. 2) Domatic number: One we... |

14 |
Fault-tolerant locating-dominating sets
- Slater
(Show Context)
Citation Context ...r of a unique subset of vertices in S. As such, these sets are codes that identify all vertices not in the set, a subtle but important difference from standard identifying codes. It has been shown in =-=[11]-=- that whenever there is an identifying code of size s in a graph, there is also a locating-dominating set of size at most s. B. Technical definitions Given an directed graph G with vertices V and edge... |

13 | An implementation of indoor location detection systems based on identifying codes - Ungrangsi, Trachtenberg, et al. - 2004 |

12 |
Bounds on identifying codes
- Blass, Honkala, et al.
(Show Context)
Citation Context ...lescing the various reports, the central point can uniquely determine the faulty processor. Several bounds on the minimum size of an identifying code were also presented in [1] and studied further in =-=[7, 8]-=- and many subsequent works. In [3, 4] identifying codes of radius r = 1 were suggested for use in indoor location detection and thereafter refined for purposes of robustness. 2) Domatic number: One we... |

11 |
A new class of codes for identification of vertices in graphs
- Karpovsky, Chakrabarty, et al.
- 1998
(Show Context)
Citation Context ...sium on Information on Information Theory 2005. I. INTRODUCTION Identifying codes have been proposed and implemented for a variety of applications, including fault diagnosis of multiprocessor systems =-=[1]-=- and location detection in harsh environments [2–6]. The latter application is designed for implementation in a network of battery-powered microprocessors (more generally, “sensors”). Specifically, in... |

2 | Location detection in emergency sensor networks using robust identifying codes - Ungrangsi - 2003 |