scholarly journals Algorithms for Sorting by Reversals or Transpositions, with Application to Genome Rearrangement

2020 ◽  
Author(s):  
Gustavo Rodrigues Galvão ◽  
Zanoni Dias
Keyword(s):  
Comparative Genomics ◽  
Genome Rearrangement ◽  
Heuristic Algorithms ◽  
Combinatorial Problem ◽  
Sorting By Reversals ◽  
Sorting Problem ◽  
Minimum Number ◽  
Phd Thesis

The problem of finding the minimum sequence of rearrangements that transforms one genome into another is a well-studied problem that finds application in comparative genomics. Representing genomes as permutations, in which genes appear as elements, that problem can be reduced to the combinatorial problem of sorting a permutation using a minimum number of rearrangements. Such combinatorial problem varies according to the types of rearrangements considered. The PhD thesis summarized in this paper presents exact, approximation, and heuristic algorithms for solving variants of the permutation sorting problem involving two types of rearrangements: reversals and transpositions.

scholarly journals Minimum Common String Partition Problem: Hardness and Approximations

10.37236/1947 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Avraham Goldstein ◽  
Petr Kolman ◽  
Jie Zheng
Keyword(s):  
Genome Rearrangement ◽  
Linear Time ◽  
Fundamental Problem ◽  
Text Processing ◽  
Partition Problem ◽  
Sorting By Reversals ◽  
String Comparison ◽  
Minimum Number ◽  
Tight Connection ◽  
Minimum Common String Partition

String comparison is a fundamental problem in computer science, with applications in areas such as computational biology, text processing and compression. In this paper we address the minimum common string partition problem, a string comparison problem with tight connection to the problem of sorting by reversals with duplicates, a key problem in genome rearrangement. A partition of a string $A$ is a sequence ${\cal P} = (P_1,P_2,\dots,P_m)$ of strings, called the blocks, whose concatenation is equal to $A$. Given a partition ${\cal P}$ of a string $A$ and a partition ${\cal Q}$ of a string $B$, we say that the pair $\langle{{\cal P},{\cal Q}}\rangle$ is a common partition of $A$ and $B$ if ${\cal Q}$ is a permutation of ${\cal P}$. The minimum common string partition problem (MCSP) is to find a common partition of two strings $A$ and $B$ with the minimum number of blocks. The restricted version of MCSP where each letter occurs at most $k$ times in each input string, is denoted by $k$-MCSP. In this paper, we show that $2$-MCSP (and therefore MCSP) is NP-hard and, moreover, even APX-hard. We describe a $1.1037$-approximation for $2$-MCSP and a linear time $4$-approximation algorithm for $3$-MCSP. We are not aware of any better approximations.

scholarly journals Actor-critic learning-based energy optimization for UAV access and backhaul networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yaxiong Yuan ◽  
Lei Lei ◽  
Thang X. Vu ◽  
Symeon Chatzinotas ◽  
Sumei Sun ◽  
...  
Keyword(s):  
Power Allocation ◽  
Heuristic Algorithms ◽  
Piecewise Linear ◽  
Access Network ◽  
Computation Time ◽  
Combinatorial Problem ◽  
Base Station ◽  
Piecewise Linear Approximation ◽  
Group Scheduling ◽  
User Group

AbstractIn unmanned aerial vehicle (UAV)-assisted networks, UAV acts as an aerial base station which acquires the requested data via backhaul link and then serves ground users (GUs) through an access network. In this paper, we investigate an energy minimization problem with a limited power supply for both backhaul and access links. The difficulties for solving such a non-convex and combinatorial problem lie at the high computational complexity/time. In solution development, we consider the approaches from both actor-critic deep reinforcement learning (AC-DRL) and optimization perspectives. First, two offline non-learning algorithms, i.e., an optimal and a heuristic algorithms, based on piecewise linear approximation and relaxation are developed as benchmarks. Second, toward real-time decision-making, we improve the conventional AC-DRL and propose two learning schemes: AC-based user group scheduling and backhaul power allocation (ACGP), and joint AC-based user group scheduling and optimization-based backhaul power allocation (ACGOP). Numerical results show that the computation time of both ACGP and ACGOP is reduced tenfold to hundredfold compared to the offline approaches, and ACGOP is better than ACGP in energy savings. The results also verify the superiority of proposed learning solutions in terms of guaranteeing the feasibility and minimizing the system energy compared to the conventional AC-DRL.

COMPUTING THE REVERSAL DISTANCE BETWEEN GENOMES IN THE PRESENCE OF MULTI-GENE FAMILIES VIA BINARY INTEGER PROGRAMMING

2007 ◽  
Vol 05 (01) ◽  
pp. 117-133 ◽  
Author(s):  
JAKKARIN SUKSAWATCHON ◽  
CHIDCHANOK LURSINSAP ◽  
MIKAEL BODÉN
Keyword(s):  
Integer Programming ◽  
Combinatorial Problem ◽  
Gene Families ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
High Accuracy ◽  
Biological Data ◽  
Binary Integer Programming ◽  
A Genome ◽  
Minimum Number

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting signed genomic data. Their algorithm determines the minimum number of reversals required for rearranging a genome to another — but only in the absence of gene duplicates. However, duplicates often account for 40% of a genome. In this paper, we show how to extend Hannenhalli and Pevzner's approach to deal with genomes with multi-gene families. We propose a new heuristic algorithm to compute the nearest reversal distance between two genomes with multi-gene families via binary integer programming. The experimental results on both synthetic and real biological data demonstrate that the proposed algorithm is able to find the reversal distance with high accuracy.

scholarly journals A phase transition in the random transposition random walk

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Nathanael Berestycki ◽  
Rick Durrett
Keyword(s):  
Phase Transition ◽  
Genome Rearrangement ◽  
Graph Model ◽  
Random Permutation ◽  
Surprising Result ◽  
Parsimony Method ◽  
Random Graph Model ◽  
Minimum Number ◽  
International Audience ◽  
Random Transposition

International audience Our work is motivated by Bourque-Pevzner's simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising result about the random transposition walk in continuous time on the group of permutations on $n$ elements starting from the identity. Let $D_t$ be the minimum number of transpositions needed to go back to the identity element from the location at time $t$. $D_t$ undergoes a phase transition: for $0 < c ≤ 1$, the distance $D_cn/2 ~ cn/2$, i.e., the distance increases linearly with time; for $c > 1$, $D_cn/2 ~ u(c)n$ where u is an explicit function satisfying $u(x) < x/2$. Moreover we describe the fluctuations of $D_{cn/2}$ about its mean at each of the three stages (subcritical, critical and supercritical). The techniques used involve viewing the cycles in the random permutation as a coagulation-fragmentation process and relating the behavior to the Erdős-Rényi random graph model.

Optimal Distribution of Active Modules in Reconfiguration Planning of Modular Robots

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Meibao Yao ◽  
Xueming Xiao ◽  
Christoph H. Belke ◽  
Hutao Cui ◽  
Jamie Paik
Keyword(s):  
Heuristic Algorithms ◽  
Robotic Systems ◽  
Modular Robots ◽  
Optimal Distribution ◽  
Distribution Problem ◽  
Modular Architecture ◽  
Modular Units ◽  
Minimum Number ◽  
Reconfiguration Planning ◽  
Reduced Time

Reconfigurability in versatile systems of modular robots is achieved by appropriately actuating individual modular units. Optimizing the distribution of active and passive modules in modular architecture can significantly reduce both cost and energy of a reconfiguration task. This paper presents a methodology for planning this distribution in modular robots, resulting in a minimum number of active modules that guarantees the capability to reconfigure. We discuss the optimal distribution problem in layout-based and target-based planning schemes such that modular robots can instantly respond to reconfiguration commands with either an initial planar layout or a target configuration as input. We propose heuristic algorithms as solutions for the different scenarios, which we demonstrate by applying them to Mori, a modular origami robot, in simulation. The results show that our algorithms yield high-quality distribution schemes in reduced time, and are thus viable for real-time applications in modular robotic systems.

HOW CAN PERMUTATIONS BE USED IN THE EVALUATION OF ZONING ALGORITHMS?

1996 ◽  
Vol 10 (03) ◽  
pp. 223-237 ◽  
Author(s):  
SHAHRAM LATIFI
Keyword(s):  
Time Complexity ◽  
Optimal Algorithm ◽  
Correct Order ◽  
Text String ◽  
Sorting Problem ◽  
Minimum Number ◽  
Reading Order ◽  
Random Manner ◽  
The Difference

In processing a page image by a given zoning algorithm (automatic or manual), a certain text string is generated which may not be the same as the correct string. The difference may be due to the incorrect reading order selected by the employed zoning algorithm or poor recognition of characters. A difference algorithm is commonly used to find the best match between the generated string and the correct string. The output of such an algorithm will then be a sequence of matched substrings which are not in the correct order. To determine the performance of a given zoning algorithm, it is of interest to find the minimum number of moves needed to obtain the correct string from the string generated by that algorithm. The problem can be modeled as a sorting problem where a string of n integers ordered in a random manner, must be sorted in ascending (or descending) order. In this paper, we derive bounds on the time complexity of sorting a given string and present a near-optimal algorithm for that.

scholarly journals Approximation Algorithms for Sorting λ-Permutations by λ-Operations

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 175
Author(s):  
Guilherme Henrique Santos Miranda ◽  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Comparative Genomics ◽  
Approximation Algorithms ◽  
Evolutionary Distance ◽  
Biological Relevance ◽  
A Value ◽  
Identity Permutation ◽  
Minimum Number

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 λ, the problem now is how to sort a λ-permutation, which is a permutation whose elements are less than λ positions away from their correct places (regarding the identity), by applying the minimum number of rearrangements. Each λ-rearrangement must have size, at most, λ, and, when applied to a λ-permutation, the result should also be a λ-permutation. We present algorithms with approximation factors of O(λ2), O(λ), and O(1) for the problems of Sorting λ-Permutations by λ-Reversals, by λ-Transpositions, and by both operations.

Sign in / Sign up

Export Citation Format

Share Document