Disjoint identifying-codes for arbitrary graphs

IEEE Trans. Inform. Theory

Trachtenberg²

2008

The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. Initially introduced in 1998, this problem has demonstrated its fundamental nature through a wide variety of applications, such as fault diagnosis, location detection, and environmental monitoring, in addition to deep connections to information theory, superimposed and covering codes, and tilings. This work establishes efficient reductions between the identifying code problem and the well-known setcovering problem, resulting in a tight hardness of approximation result and novel, provably tight polynomial-time approximations. The main results are also extended to r-robust identifying codes and analogous set (2r + 1)-multicover problems. Finally, empirical support is provided for the effectiveness of the proposed approximations, including good constructions for well-known topologies such as infinite two-dimensional grids. Index TermsIdentifying codes, robust identifying codes, hardness of approximation, set cover, test cover, distributed algorithms.

Section: Localized Robust Identifying Code and Its Approximationmentioning

confidence: 99%

“…This localization is possible when the identifying codes are required to produce only non-empty identifying sets 5 . In this section and henceforth we introduce this requirement, and call the resulting codes -localized identifying codes.…”

Section: Localized Robust Identifying Code and Its Approximationmentioning

confidence: 99%

Identifying Codes and Covering Problems

IEEE Trans. Inform. Theory

Trachtenberg²

2008

“…Identifying codes have since been extended and applied to location detection in hostile environments [6,7], to energy balancing of such systems [8], and to dynamic location detection agents [9]. In the first example, a coverage area is quantized into a finite number of clusters.…”

Section: ) Applicationsmentioning

confidence: 99%

“…It was observed in [7,8] that an r-robust identifying code can be built in a localized manner, where each vertex only considers its two-hop neighborhood. The resulting localized identifying codes are the subject of this section, and the approximation algorithm we derive is critical to the distributed algorithm of the next section.…”

Section: B Robust Identifying Code and Its Approximationmentioning

confidence: 99%

Localization and identification in networks using robust identifying codes

2008 Information Theory and Applications Workshop

2008

Abstract-Many practical problems in networks such as fault detection and diagnosis, location detection, environmental monitoring, etc, require to identify specific nodes or links based on a set of observations, which size is a subject of optimization. In this paper we focus on a combinatorial approach to these problems, which is closely related to coding techniques, and specifically to identifying codes. The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. In this paper we show efficient reductions between the identifying code problem and well-known covering problems, resulting in a tight hardness of approximation result and provable good centralized and distributed approximations. We further provide empirical and theoretical results on identifying codes in random networks and efficient constructions of these codes in infinite grids.

“…It was observed in [6,21] that an r-robust identifying code can be built in a localized manner, where …”

Section: Localized Robust Identifying Code and Its Approximationmentioning

confidence: 99%

Joint monitoring and routing in wireless sensor networks using robust identifying codes

2007 Fourth International Conference on Broadband Communications, Networks and Systems (BROADNETS '07)

Trachtenberg

Cohen

et al. 2007

Abstract-Wireless Sensor Networks (WSNs) provide an important means of monitoring the physical world, but their limitations present challenges to fundamental network services such as routing. In this work we utilize an abstraction of WSNs based on the theory of identifying codes. This abstraction has been useful in recent literature for a number of important monitoring problems, such as localization and contamination detection. In our case, we use it to provide a joint infrastructure for efficient and robust monitoring and routing in WSNs. Specifically, we make use of efficient and distributed algorithm for generating robust identifying codes, an NP-hard problem, with a logarithmic performance guarantee based on a reduction to the set kmulticover problem. We also show how this same identifyingcode infrastructure provides a natural labeling that can be used for near-optimal routing with very small routing tables. We provide experimental results for various topologies that illustrate the superior performance of our approximation algorithms over previous identifying code heuristics.