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

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

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

Vol. 7748 245-256

Basic sciences

Bioinformatics (Computational Biology)

Computer Science

Discrete Mathematics

Life Science Engineering (2010-2018)

978-3-642-36064-0