@inproceedings{0d6356704e43419da7d6b834142291d4,

title = "Minimum ratio cover of matrix columns by extreme rays of its induced cone",

abstract = "Given a matrix S ∈ ℝ m x n and a subset of columns R, we study the problem of finding a cover of R with extreme rays of the cone F = {v ∈ ℝ n | Sv = 0, v ≥ 0}, where an extreme ray v covers a column k if v k > 0. In order to measure how proportional a cover is, we introduce two different minimization problems, namely the minimum global ratio cover (MGRC) and the minimum local ratio cover (MLRC) problems. In both cases, we apply the notion of the ratio of a vector v, which is given by max i v i/min j | vj > 0 v j. We show that these two problems are NP-hard, even in the case in which |R| = 1. We introduce a mixed integer programming formulation for the MGRC problem, which is solvable in polynomial time if all columns should be covered, and introduce a branch-and-cut algorithm for the MLRC problem. Finally, we present computational experiments on data obtained from real metabolic networks.",

keywords = "Extreme rays, elementary modes, metabolic networks",

author = "Freire, {A. S.} and V. Acu{\~n}a and P. Crescenzi and Ferreira, {C. E.} and V. Lacroix and Milreu, {P. V.} and E. Moreno and Sagot, {M. F.}",

year = "2012",

doi = "10.1007/978-3-642-32147-4_16",

language = "English",

isbn = "9783642321467",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "165--177",

booktitle = "Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers",

note = "null ; Conference date: 19-04-2012 Through 21-04-2012",

}