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An Optimal O(nm) Algorithm for Enumerating All Walks Common to All Closed Edge-covering Walks of a Graph

Authors:

Nidia Obscura Acosta,

Alexandru I. TomescuAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 15, Issue 4

Article No.: 48, Pages 1 - 17

https://doi.org/10.1145/3341731

Published: 29 July 2019 Publication History

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Abstract

In this article, we consider the following problem. Given a directed graph G, output all walks of G that are sub-walks of all closed edge-covering walks of G. This problem was first considered by Tomescu and Medvedev (RECOMB 2016), who characterized these walks through the notion of omnitig. Omnitigs were shown to be relevant for the genome assembly problem from bioinformatics, where a genome sequence must be assembled from a set of reads from a sequencing experiment. Tomescu and Medvedev (RECOMB 2016) also proposed an algorithm for listing all maximal omnitigs, by launching an exhaustive visit from every edge.

In this article, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Ω(nm). We implement this algorithm and show that it is 9--12 times faster in practice than the one of Tomescu and Medvedev (RECOMB 2016).

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Cited By

Obscura Acosta NTomescu A(2024)Simplicity in Eulerian circuitsInformation Processing Letters10.1016/j.ipl.2023.106421183:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.ipl.2023.106421
Cairo MRizzi RTomescu AZirondelli E(2023)Genome Assembly, from Practice to Theory: Safe, Complete and Linear-TimeACM Transactions on Algorithms10.1145/363217620:1(1-26)Online publication date: 8-Nov-2023
https://dl.acm.org/doi/10.1145/3632176
Dias FCáceres MWilliams LMumey BTomescu A(2023)A safety framework for flow decomposition problems via integer linear programmingBioinformatics10.1093/bioinformatics/btad64039:11Online publication date: 20-Oct-2023
https://doi.org/10.1093/bioinformatics/btad640
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Index Terms

An Optimal O(nm) Algorithm for Enumerating All Walks Common to All Closed Edge-covering Walks of a Graph
1. Applied computing
  1. Life and medical sciences
    1. Bioinformatics
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 15, Issue 4

October 2019

297 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3351875

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 July 2019

Accepted: 01 June 2019

Revised: 01 June 2019

Received: 01 January 2019

Published in TALG Volume 15, Issue 4

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Cited By

Obscura Acosta NTomescu A(2024)Simplicity in Eulerian circuitsInformation Processing Letters10.1016/j.ipl.2023.106421183:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.ipl.2023.106421
Cairo MRizzi RTomescu AZirondelli E(2023)Genome Assembly, from Practice to Theory: Safe, Complete and Linear-TimeACM Transactions on Algorithms10.1145/363217620:1(1-26)Online publication date: 8-Nov-2023
https://dl.acm.org/doi/10.1145/3632176
Dias FCáceres MWilliams LMumey BTomescu A(2023)A safety framework for flow decomposition problems via integer linear programmingBioinformatics10.1093/bioinformatics/btad64039:11Online publication date: 20-Oct-2023
https://doi.org/10.1093/bioinformatics/btad640
Khan SKortelainen MCáceres MWilliams LTomescu A(2022)Improving RNA Assembly via Safety and Completeness in Flow DecompositionsJournal of Computational Biology10.1089/cmb.2022.026129:12(1270-1287)Online publication date: 1-Dec-2022
https://doi.org/10.1089/cmb.2022.0261
Cairo MKhan SRizzi RSchmidt STomescu A(2022)Safety in s-t Paths, Trails and WalksAlgorithmica10.1007/s00453-021-00877-w84:3(719-741)Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1007/s00453-021-00877-w
Khan SKortelainen MCáceres MWilliams LTomescu A(2022)Safety and Completeness in Flow Decompositions for RNA AssemblyResearch in Computational Molecular Biology10.1007/978-3-031-04749-7_11(177-192)Online publication date: 29-Apr-2022
https://doi.org/10.1007/978-3-031-04749-7_11
Caceres MMumey BHusic ERizzi RCairo MSahlin KTomescu A(2021)Safety in multi-assembly via paths appearing in all path covers of a DAGIEEE/ACM Transactions on Computational Biology and Bioinformatics10.1109/TCBB.2021.3131203(1-1)Online publication date: 2021
https://doi.org/10.1109/TCBB.2021.3131203
Georgiadis LItaliano GParotsidis N(2020)Strong Connectivity in Directed Graphs under Failures, with ApplicationsSIAM Journal on Computing10.1137/19M125853049:5(865-926)Online publication date: 1-Sep-2020
https://doi.org/10.1137/19M1258530

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