Approximation Algorithms for Sorting lambda-Permutations by lambda-Operations

Author(s)

Miranda, Guilherme Henrique Santos ^[1] ; Alexandrino, Alexsandro Oliveira ^[1] ; Lintzmayer, Carla Negri ^[2] ; Dias, Zanoni ^[1]

Affiliation

^[1] Univ Estadual Campinas, Inst Comp, BR-13083970 Campinas, SP - Brazil

^[2] Fed Univ ABC, Ctr Math Computat & Cognit, BR-09210580 Santo Andre, SP - Brazil

• Document type: Journal article
• Source: ALGORITHMS; v. 14, n. 6 JUN 2021.
• Web of Science Citations: 0

Abstract

Understanding how different two organisms are is one question addressed by the comparative genomics field. A well-accepted way to estimate the evolutionary distance between genomes of two organisms is finding the rearrangement distance, which is the smallest number of rearrangements needed to transform one genome into another. By representing genomes as permutations, one of them can be represented as the identity permutation, and, so, we reduce the problem of transforming one permutation into another to the problem of sorting a permutation using the minimum number of rearrangements. This work investigates the problems of sorting permutations using reversals and/or transpositions, with some additional restrictions of biological relevance. Given a value lambda, the problem now is how to sort a lambda-permutation, which is a permutation whose elements are less than lambda positions away from their correct places (regarding the identity), by applying the minimum number of rearrangements. Each lambda-rearrangement must have size, at most, lambda, and, when applied to a lambda-permutation, the result should also be a lambda-permutation. We present algorithms with approximation factors of O(lambda(2)), O(lambda), and O(1) for the problems of Sorting lambda-Permutations by lambda-Reversals, by lambda-Transpositions, and by both operations. (AU)

• FAPESP's process: 13/08293-7 - CCES - Center for Computational Engineering and Sciences
• Grantee: Munir Salomao Skaf
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 15/11937-9 - Investigation of hard problems from the algorithmic and structural stand points
• Grantee: Flávio Keidi Miyazawa
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/16871-1 - Problems of sorting permutations by fragmentation-weighted operations
• Grantee: Alexsandro Oliveira Alexandrino
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 17/12646-3 - Déjà vu: feature-space-time coherence from heterogeneous data for media integrity analytics and interpretation of events
• Grantee: Anderson de Rezende Rocha
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/16246-0 - Sensitive media analysis through deep learning architectures
• Grantee: Sandra Eliza Fontes de Avila
• Support Opportunities: Regular Research Grants