Non-approximability of Weighted Multiple Sequence Alignment
We consider a weighted generalization of multiple sequence alignment with sum-of-pair score. Multiple sequence alignment without weights is known to be NP-complete and can be approximated within a constant factor, but it is unknown whether it has a polynomial time approximation scheme. Weighted multiple sequence alignment can be approximated within a factor of O(log2n) where n is the number of sequences.
We prove that weighted multiple sequence alignment is MAX SNP-hard and establish a numerical lower bound on its approximability, namely 324/323 - €. This lower bound is obtained already for the simple binary weighted case where the weights are restricted to 0 and 1. Furthermore, we show that weighted multiple sequence alignment and its restriction to binary weights can be approximated exactly to the same degree.
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