Fixed-parameter tractability of error correction in graphical linear systems
Paper in proceedings, 2013

In an overdetermined and feasible system of linear equations Ax=b, let vector b be corrupted, in the way that at most k entries are off their true values. Assume that we can check in the restricted system given by any minimal dependent set of rows, the correctness of all corresponding values in b. Furthermore, A has only coefficients 0 and 1, with at most two 1s in each row. We wish to recover the correct values in b and x as much as possible. The problem arises in a certain chemical mixture inference application in molecular biology, where every observable reaction product stems from at most two candidate substances. After formalization we prove that the problem is NP-hard but fixed-parameter tractable in k. The FPT result relies on the small girth of certain graphs.

girth

sparse system of linear equations

parameterized algorithm

even cycle matroid

error correction

Author

Peter Damaschke

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

Ömer Egecioglu

Leonid Molokov

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

7th International Workshop on Algorithms and Computation WALCOM 2013, Lecture Notes in Computer Science

Vol. 7748 245-256

Roots

Basic sciences

Subject Categories

Bioinformatics (Computational Biology)

Computer Science

Discrete Mathematics

Areas of Advance

Life Science Engineering (2010-2018)

ISBN

978-3-642-36064-0

More information

Created

10/6/2017