Border Length Minimization Problem on a Square Array

Border Length Minimization Problem on a Square Array

Protein/peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and high-throughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having low serum titers, and locate antibody signatures. Improving the yield of microarray fabrication involves solving a hard combinatorial optimization problem ca...

Border Length Minimization in DNA Array Design

Optimal design of DNA arrays for very large-scale immobilized polymer synthesis (VLSIPS) [3] seeks to minimize effects of unintended illumination during mask exposure steps. Hannenhalli et al. [6] formulate this requirement as the Border Minimization Problem and give an algorithm for placement of probes at array sites under the assumption that the array synthesis is synchronous, i.e., nucleotid...

Hardness and Approximation of The Asynchronous Border Minimization Problem

We study a combinatorial problem arising from the microarrays synthesis. The objective of the BMP is to place a set of sequences in the array and to find an embedding of these sequences into a common supersequence such that the sum of the “border length” is minimized. A variant of the problem, called P-BMP, is that the placement is given and the concern is simply to find the embedding. Approxim...

Border Array on Bounded Alphabet

In this article we present an on-line linear time algorithm, to check if an integer array f is a border array of some string x built on a bounded size alphabet, which is simplest that the one given in [2]. Furthermore if f is a border array we are able to build, on-line and in linear time, a string x on a minimal size alphabet for which f is the border array.

On A Square Packing Problem