An improved exact algorithm and an NP-completeness proof for sparse matrix bipartitioning

The genomic scaffold filling problem has attracted a lot of attention recently. The problem is on filling an incomplete sequence (scaffold) [Formula: see text] into [Formula: see text], with respect to a complete reference genome [Formula: see text], such that the number of common/shared adjacencies between [Formula: see text] and [Formula: see text] is maximized. The problem is NP-complete, and admits a constant-factor approximation. However, the sequence input [Formula: see text] is not quite practical and does not fit most of the real datasets (where a scaffold is more often given as a list of contigs). In this paper, we revisit the genomic scaffold filling problem by considering this important case when a scaffold [Formula: see text] is given, the missing genes can only be inserted in between the contigs, and the objective is to maximize the number of common adjacencies between [Formula: see text] and the filled genome [Formula: see text]. For this problem, we present a simple NP-completeness proof, we then present a factor-2 approximation algorithm.

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Reconstructing polyatomic structures from discrete X-rays: NP-completeness proof for three atoms

Theoretical Computer Science ◽

10.1016/s0304-3975(99)00325-4 ◽

2001 ◽

Vol 259 (1-2) ◽

pp. 81-98 ◽

Cited By ~ 29

Author(s):

Marek Chrobak ◽

Christoph Dürr

Keyword(s):

X Rays ◽

Completeness Proof ◽

Np Completeness

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The Impact of Missing and Error-Prone Auxiliary Information on Sparse-Matrix Sub-Population Parameter Estimates

Methodology ◽

10.1027/1614-2241/a000095 ◽

2015 ◽

Vol 11 (3) ◽

pp. 89-99 ◽

Cited By ~ 1

Author(s):

Leslie Rutkowski ◽

Yan Zhou

Keyword(s):

Sparse Matrix ◽

Small Body ◽

Auxiliary Information ◽

Poor Quality ◽

Quality Data ◽

Estimation Methods ◽

Parameter Estimates ◽

Population Parameter ◽

Conditioning Model ◽

The Impact

Abstract. Given a consistent interest in comparing achievement across sub-populations in international assessments such as TIMSS, PIRLS, and PISA, it is critical that sub-population achievement is estimated reliably and with sufficient precision. As such, we systematically examine the limitations to current estimation methods used by these programs. Using a simulation study along with empirical results from the 2007 cycle of TIMSS, we show that a combination of missing and misclassified data in the conditioning model induces biases in sub-population achievement estimates, the magnitude and degree to which can be readily explained by data quality. Importantly, estimated biases in sub-population achievement are limited to the conditioning variable with poor-quality data while other sub-population achievement estimates are unaffected. Findings are generally in line with theory on missing and error-prone covariates. The current research adds to a small body of literature that has noted some of the limitations to sub-population estimation.

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