Computing linear extensions for Boolean lattices with algebraic constraints
Year: 2020
Type: preprint
Abstract: In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multi-variate polynomials, and only a small subset of these linear extensions, determined implicitly by the evaluation map, are of interest. This seemingly novel problem arises in the study of global dynamics of gene regulatory networks in which case the poset is a Boolean lattice. We provide an algorithm for solving this problem using linear programming for arbitrary partial orders of linear polynomials.
This algorithm exploits this additional algebraic structure inherited from the polynomials to efficiently compute the admissible linear extensions. The biologically relevant problem involves multi-linear polynomials and we provide a construction for embedding it into an instance of the linear problem.
Source: arXiv (Cornell University)
Authors: Shane Kepley, Konstantin Mischaikow, Lun Zhang
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3033750364