Sparse solutions of sparse linear systems: Fixed-parameter tractability and an application of complex group testing
Paper in proceeding, 2012

A vector with at most k nonzeros is called k-sparse. We show that enumerating the support vectors of k-sparse solutions to a system Ax=b of r-sparse linear equations (i.e., where the rows of A are r-sparse) is fixed-parameter tractable (FPT) in the combined parameter r,k. For r=2 the problem is simple. For 0,1-matrices A we can also compute a kernel. For systems of linear inequalities we get an FPT result in the combined parameter d,k, where d is the total number of minimal solutions. This is achieved by interpreting the problem as a case of group testing in the complex model. The problems stem from the reconstruction of chemical mixtures by observable reaction products.

sparse vector


hitting set

group testing

problem kernel

linear system

parameterized algorithm


Peter Damaschke

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 7112 94-105
978-364228049-8 (ISBN)


Basic sciences

Areas of Advance

Life Science Engineering (2010-2018)

Subject Categories

Computer Science



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