Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
A group testing problem for hypergraphs of bounded rank
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
Note: A competitive algorithm in searching for many edges in a hypergraph
Discrete Applied Mathematics
Exact Transcriptome Reconstruction from Short Sequence Reads
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Shared Peptides in Mass Spectrometry Based Protein Quantification
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
A Top-Down Approach to Search-Trees: Improved Algorithmics for 3-Hitting Set
Algorithmica - Including a Special Section on Genetic and Evolutionary Computation; Guest Editors: Benjamin Doerr, Frank Neumann and Ingo Wegener
Parameterized algorithms for d-Hitting Set: The weighted case
Theoretical Computer Science
On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations
IEEE Transactions on Information Theory
Error propagation in sparse linear systems with peptide-protein incidence matrices
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
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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 an O(rkr) 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 interpeting 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.