Rectangle Cover Problem

The rectangle cover problem is known to be NP-hard and approximation algorithms with small performance ratios for this problem are unknown ([6,7]). We explore the specifics of oligonucleotide masks and devise an efficient algorithm which finds a (provably) optimal rectangle cover for all masks we tested at Affymetrix. 

The solution to the general problem of determining the area under a curve arises directly from differential calculus, the concept of limits, and the infinitesimal. Seventeenth century mathematicians began to think of the area, not as a whole, but as made up of a series of rectangles, of width Ax, placed side by side, and which, together, cover the interval [a,b (see Figure 6.2). 

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