An Implicit Cover Problem in Wild Population Study

TL;DR

This paper investigates an implicit set cover problem arising in biological studies of wild populations, focusing on Mendelian constraints, and provides theoretical results on how well it can be approximated.

Contribution

It introduces a new implicit cover problem specific to biological population analysis and establishes its approximability bounds.

Findings

Proves approximability results for the implicit cover problem.

Links the problem to Mendelian inheritance constraints.

Provides theoretical bounds on solution quality.

Abstract

In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly For example, the well-known minimum feedback arc set problem is such a problem. In this paper, we consider such a cover problem that arises in the study of wild populations in biology in which the sets are defined implicitly via the Mendelian constraints and prove approximability results for this problem.