Parameterized Complexity of Asynchronous Border Minimization

TL;DR

This paper analyzes the parameterized complexity of the Border Minimization Problem in microarrays, identifying conditions under which it is fixed-parameter tractable and providing hardness results.

Contribution

It establishes new fixed-parameter tractability results for BMP and P-BMP under various parameter combinations and complements these with hardness proofs.

Findings

BMP and P-BMP are in FPT for certain parameter sets

The paper provides hardness results for other parameter combinations

Identifies parameters influencing the computational complexity of BMP and P-BMP

Abstract

Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given placement (P-BMP). In this paper we investigate the parameterized complexity of natural variants of BMP and P-BMP under several natural parameters. We show that BMP and P-BMP are in FPT under the following two combinations of parameters: 1) the size of the alphabet (c), the maximum length of a sequence (string) in the input (l) and the number of rows of the microarray (r); and, 2) the size of the alphabet and the size of the border length (o). Furthermore, P-BMP is in FPT when parameterized by c and l. We complement our tractability results with corresponding hardness results.