Interval scheduling maximizing minimum coverage

Abstract

In the classical interval scheduling type of problems, a set of n jobs, characterized by their start and end time, need to be executed by a set of machines, under various constraints. In this paper we study a new variant in which the jobs need to be assigned to at most k identical machines, such that the minimum number of machines that are busy at the same time is maximized. This is relevant in the context of genome sequencing and haplotyping, specifically when a set of DNA reads aligned to a genome needs to be pruned so that no more than k reads overlap, while maintaining as much read coverage as possible across the entire genome. We show that the problem can be solved in time min O(n 2 log k/ log n), O(nk log k) by using max-flows. We also give an O(n log n)-time approximation algorithm with approximation ratio ρ = k k/2 .

Selecting Reads for Haplotype Assembly

“…We are currently comparing our heuristic approach to the flow-based algorithm proposed by Mäkinen et al (2015). Our algorithm was designed to also work well when combining different types of reads (such as PacBio and Illumina mate pairs), which we plan to evaluate systematically in the future.…”

“…properties is an open research question and little literature on it exists. Mäkinen et al (2015) propose to maximize the minimum coverage by means of a flow-based approach. In the following, we introduce a heuristic algorithm that we show to work well in practice.…”