Improved Approximability Result for Test Set with Small Redundancy

Details Improved Approximability Result for Test Set with Small Redundancy Improved Approximability Result for Test Set with Small Redundancy

2007-05-17

arxiv.org/abs/0705.2503v4

Computer Science

Data Structures and Algorithms

7 pages

Scientific paper

Test set with redundancy is one of the focuses in recent bioinformatics research. Set cover greedy algorithm (SGA for short) is a commonly used algorithm for test set with redundancy. This paper proves that the approximation ratio of SGA can be $(2-\frac{1}{2r})\ln n+{3/2}\ln r+O(\ln\ln n)$ by using the potential function technique. This result is better than the approximation ratio $2\ln n$ which directly derives from set multicover, when $r=o(\frac{\ln n}{\ln\ln n})$, and is an extension of the approximability results for plain test set.

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