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On the Maximum Number of Linearly Independent Cycles and Paths in a Network

Gopalan, Abishek and Ramasubramanian, Srinivasan (2014) On the Maximum Number of Linearly Independent Cycles and Paths in a Network. In: IEEE-ACM TRANSACTIONS ON NETWORKING, 22 (5). pp. 1373-1388.

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Official URL: http://dx.doi.org/ 10.1109/TNET.2013.2291208


Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the ``link rank'' of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

Item Type: Journal Article
Additional Information: Copyrights for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 14 Dec 2014 10:57
Last Modified: 14 Dec 2014 10:57
URI: http://eprints.iisc.ac.in/id/eprint/50447

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