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Related Experiment Video

Updated: Apr 23, 2026

Hybrid De Novo Genome Assembly for the Generation of Complete Genomes of Urinary Bacteria using Short- and Long-read Sequencing Technologies

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On the complexity of Minimum Path Cover with Subpath Constraints for multi-assembly.

Romeo Rizzi, Alexandru I Tomescu, Veli Mäkinen

BMC Bioinformatics

|September 26, 2014

Summary

This study addresses complex multi-assembly problems in genomics by extending the Minimum Path Cover (MPC) problem. We show long-read constraints are efficiently solvable, while paired-end read constraints are NP-hard but fixed-parameter tractable.

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Last Updated: Apr 23, 2026

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Rapid Assembly of Multi-Gene Constructs using Modular Golden Gate Cloning

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Published on: February 5, 2021

Area of Science:

Computational Biology
Bioinformatics
Graph Theory

Background:

Next-Generation Sequencing (NGS) technologies enable multi-assembly analyses of complex biological data like RNA-Seq and viral quasi-species.
The Minimum Path Cover (MPC) problem on directed acyclic graphs is a foundational model for many multi-assembly methods.
Classical MPC is polynomial-time solvable due to graph acyclicity.

Purpose of the Study:

To investigate two generalizations of the MPC problem incorporating constraints from long reads (subpaths) and paired-end reads (pairs of subpaths).
To develop efficient algorithms for these generalized MPC problems in the context of multi-assembly challenges.

Main Methods:

For long reads, a reduction to the classical MPC problem is employed, including a weighted variant solved via min-cost circulation.
For paired-end reads, the problem is shown to be NP-hard, but fixed-parameter tractable (FPT) with respect to the number of constraints.
Improvements to the time complexity of the classical minimum weight MPC problem are also presented.

Main Results:

The generalized MPC problem with subpath constraints (long reads) is solved in polynomial time.
The generalized MPC problem with pairs of subpath constraints (paired-end reads) is NP-hard but FPT.
The study reveals a computational dichotomy between handling long reads and paired-end reads in multi-assembly.

Conclusions:

The developed methods provide efficient solutions for specific multi-assembly problems arising from NGS data.
The findings offer insights into the computational complexity of integrating different read types in genome assembly.
This work contributes to advancing algorithms for reconstructing complex biological sequences.