The computational complexity of calculating partition functions of optimal medians with Hamming distance

TL;DR

This paper proves that computing the partition function of optimal medians with Hamming distance is P-complete, with implications for bioinformatics and evolutionary scenario analysis, extending to binary trees and various models.

Contribution

It establishes the P-completeness of calculating partition functions for optimal medians under Hamming distance, including applications in bioinformatics.

Findings

P-completeness for several weight functions

Application to bioinformatics with factorial weight functions

Extension to binary trees and biological sequence models

Abstract

In this paper, we show that calculating the partition function of optimal medians of binary strings with Hamming distance is \#P-complete for several weight functions. The case when the weight function is the factorial function has application in bioinformatics. In that case, the partition function counts the most parsimonious evolutionary scenarios on a star tree under several models in bioinformatics. The results are extended to binary trees and we show that it is also \#P-complete to calculate the most parsimonious evolutionary scenarios on an arbitrary binary tree under the substitution model of biological sequences and under the Single Cut-or-Join model for genome rearrangements.