An improved lower bound for (1,

نویسندگان

  • Florent Foucaud
  • Tero Laihonen
  • Aline Parreau
چکیده

We call a subset C of vertices of a graph G a (1,≤ l)-identifying code if for all subsets X of vertices with size at most l, the sets {c ∈ C|∃u ∈ X, d(u, c) ≤ 1} are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a (1,≤ 2)-identifying code in the king grid with density 3 7 and that there are no such identifying codes with density smaller than 5 12 . Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any (1,≤ 2)-identifying code of the king grid has density at least 47 111 .

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Improved Cramer-Rao Inequality for Randomly Censored Data

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...

متن کامل

An improved approach for ranking the candidates in a voting system based on efficiency intervals

This paper proposes improvements and revisions to a recent approach in a voting system, and provides an effective approach with a stronger discriminate power. For this purpose, the advantage of a linear transformation is utilized to redene a previously used concept of virtual worst candidate, by incorporating the existing weight restrictions. Then, the best score of this virtual candidate is us...

متن کامل

The Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics

In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...

متن کامل

An improved infeasible‎ ‎interior-point method for symmetric cone linear complementarity‎ ‎problem

We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...

متن کامل

A New Lower Bound for Completion Time Distribution Function of Stochastic PERT Networks

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

متن کامل

A New Lower Bound for Completion Time Distribution Function of Stochastic PERT Networks

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017