Abstract
We study the border minimization problem (BMP), which arises in microarray synthesis to place and embed probes in the array. The synthesis is based on a light-directed chemical process in which unintended illumination may contaminate the quality of the experiments. Border length is a measure of the amount of unintended illumination and the objective of BMP is to find a placement and embedding of probes such that the border length is minimized. The problem is believed to be NP-hard. In this paper we show that BMP admits an \(O(\sqrt{n}\log^2{n})\)-approximation, where n is the number of probes to be synthesized. In the case where the placement is given in advance, we show that the problem is O(log2 n)-approximable. We also study a related problem called agreement maximization problem (AMP). In contrast to BMP, we show that AMP admits a constant approximation even when placement is not given in advance.
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Li, C.Y., Wong, P.W.H., Xin, Q., Yung, F.C.C. (2008). Approximating Border Length for DNA Microarray Synthesis. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_36
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DOI: https://doi.org/10.1007/978-3-540-79228-4_36
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