Deeper Approximability Results of Redundant Test Set in Bioinformatics

Redundant test set is one of focuses in recent bioinformatics research. The author investigates the phenomenon of ”differentiation repetition” of (redundant) test set and utilizes derandomization method to give deeper approximability results of redundant test set conditionally better than directly derived from set cover. Set cover greedy algorithm (SGA for short) is a common used algorithm for (redundant) test set. This paper proves approximation ratio of SGA for odd redundancy r ≥ 3 can be (2 − 1 2(r+1) ) lnn + 2 ln r + 1, approximation ratio of SGA for redundancy 2 can be 5 3 lnn + 1 3 lnm∗ + 1 3 ln lnn + 1, and approximation ratio of SGA for even redundancy r ≥ 4 can be (2 − 1 2r ) lnn + 1 r lnm∗ + 2 ln(r − 1) + 1, where m∗ is the size of the optimal test set in the optimal solution.