Partial order alignment by adjacencies and breakpoints

TL;DR

This paper investigates the computational complexity of aligning two partial orders to maximize adjacencies and minimize breakpoints, revealing the problem's APX-hardness even under specific order restrictions.

Contribution

It proves that linearizing two partial orders for optimal adjacency and breakpoint metrics is APX-hard, even with simplified order types.

Findings

The problem is APX-hard for general partial orders.

Hardness persists when one order is linear and the other is an interval order.

The problem remains hard for weak orders.

Abstract

Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if both partial orders are weak orders.