Degree of Redundancy of Linear Systems Using Implicit Set Covering

Author

Arellano, John D. ; Hicks, Illya V.

Author_Institution

Dept. of Comput. & Appl. Math., Rice Univ., Houston, TX, USA

Volume

11

Issue

1

fYear

2014

fDate

Jan. 2014

Firstpage

274

Lastpage

279

Abstract

In this paper, we present a set covering problem (SCP) formulation to compute the degree of redundancy of linear systems. Computing the degree of redundancy of a linear system allows for the evaluation of the quality of the sensor network. The formulation is equivalent to solving the linear matroid cogirth problem, finding the cardinality of the smallest cocircuit of a matroid. We also discuss existing methods developed to solve the matroid cogirth problem and the SCP. Computational results are provided to validate a branch-and-cut algorithm that addresses the SCP formulation.

Keywords

combinatorial mathematics; linear systems; matrix algebra; sensors; tree searching; SCP formulation; branch-and-cut algorithm; degree of redundancy; implicit set covering problem; linear matroid cogirth problem; linear systems; matroid cocircuit; sensor network quality; Greedy algorithms; Linear matrix inequalities; Linear programming; Linear systems; Redundancy; Vectors; Matroids; NP-hard; cogirth; degree of redundancy; girth; linear matroid; sensor networks; set covering problem;

fLanguage

English

Journal_Title

Automation Science and Engineering, IEEE Transactions on

Publisher

ieee

ISSN

1545-5955

Type

jour

DOI

10.1109/TASE.2013.2271703

Filename

6558498