Hardness and Approximation of The Asynchronous Border Minimization Problem

Details Hardness and Approximation of The Asynchronous Border Minimization Problem Hardness and Approximation of The Asynchronous Border Minimization Problem

2010-11-04

arxiv.org/abs/1011.1202v1

Computer Science

Data Structures and Algorithms

Scientific paper

We study a combinatorial problem arising from microarrays synthesis. The synthesis is done by a light-directed chemical process. The objective is to minimize unintended illumination that may contaminate the quality of experiments. Unintended illumination is measured by a notion called border length and the problem is called Border Minimization Problem (BMP). The objective of the BMP is to place a set of probe sequences in the array and find an embedding (deposition of nucleotides/residues to the array cells) such that the sum of 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. Approximation algorithms have been previously proposed for the problem but it is unknown whether the problem is NP-hard or not. In this paper, we give a thorough study of different variations of BMP by giving NP-hardness proofs and improved approximation algorithms. We show that P-BMP, 1D-BMP, and BMP are all NP-hard. Contrast with the previous result that 1D-P-BMP is polynomial time solvable, the interesting implications include (i) the array dimension (1D or 2D) differentiates the complexity of P-BMP; (ii) for 1D array, whether placement is given differentiates the complexity of BMP; (iii) BMP is NP-hard regardless of the dimension of the array. Another contribution of the paper is improving the approximation for BMP from $O(n^{1/2} \log^2 n)$ to $O(n^{1/4} \log^2 n)$, where $n$ is the total number of sequences.

Affiliated with

Also associated with

No associations

Rating

Hardness and Approximation of The Asynchronous Border Minimization Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hardness and Approximation of The Asynchronous Border Minimization Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hardness and Approximation of The Asynchronous Border Minimization Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-146454