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The Enhanced Double Digest Problem for DNA Physical Mapping [article]

Ming-Yang Kao, Jared Samet, Wing-Kin Sung
2001 arXiv   pre-print
The double digest problem is a common NP-hard approach to constructing physical maps of DNA sequences. This paper presents a new approach called the enhanced double digest problem.  ...  Although this new problem is also NP-hard, it can be solved in linear time in certain theoretically interesting cases.  ...  Then, all the elements in C are different and we can solve the enhanced double digest problem using the algorithm Enhanced-Double-Digest in Section 3.2.  ... 
arXiv:cs/0102010v1 fatcat:niqexd6q3vdbdmu5jqvrayyyiy

DDmap: a MATLAB package for the double digest problem using multiple genetic operators

Licheng Wang, Jingwen Suo, Yun Pan, Lixiang Li
2019 BMC Bioinformatics  
In computational biology, the physical mapping of DNA is a key problem. We know that the double digest problem (DDP) is NP-complete.  ...  Based on our simulations on 1000 random DDP instances by using DDmap, we find that the maximum length of the combining fragments has observable effects towards genetic algorithms for solving the DDP problem  ...  Acknowledgements We thank the anonymous reviewers for giving us valuable suggestions. Availability of data and materials DDmap is open source and available at https://github.com/wanglc2012/DDmap.  ... 
doi:10.1186/s12859-019-2862-x fatcat:3mkfiqjwwbcf3dtcftgsucga5e

Double Digest Revisited: Complexity and Approximability in the Presence of Noisy Data [chapter]

Mark Cieliebak, Stephan Eidenbenz, Gerhard J. Woeginger
2003 Lecture Notes in Computer Science  
We revisit the double digest problem, which occurs in sequencing of large DNA strings and consists of reconstructing the relative positions of cut sites from two different enzymes: we rst show that double  ...  making it impossible to guarantee any approximation ratio at all.  ...  NP-hardness of Finding Feasible Solutions for Optimization Variations of Disjoint Double Digest In this section, we show that all Double Digest optimization variations in which we disallow coincidences  ... 
doi:10.1007/3-540-45071-8_52 fatcat:mwhnq5dpu5aufnl5rszpok5ofm

Genetic Algorithm for Double Digest Problem [chapter]

S. Sur-Kolay, S. Banerjee, S. Mukhopadhyaya, C. A. Murthy
2005 Lecture Notes in Computer Science  
The strongly NP-complete Double Digest Problem (DDP) for physical mapping of DNA, is now used for efficient genotyping. An instance of DDP has multiple distinct solutions.  ...  Existing methods produce a single solution, and are slow for large instances. We employ a type of equivalence among the distinct solutions to obtain almost all of them.  ...  Problem Formulation The combinatorial description of Double Digest Problem (DDP) is as follows [12] : let A = {a i : 1 ≤ i ≤ m}, B = {b i : 1 ≤ i ≤ n} and A + B = {d i : 1 ≤ i ≤ l} m i=1 a i = n i=1  ... 
doi:10.1007/11590316_99 fatcat:trlvwojfwbhxxetdjuu2i26zju

A Randomized, Double-blinded Comparison of Phenylephrine and Ephedrine Infusion Combinations to Maintain Blood Pressure During Spinal Anesthesia for Cesarean Delivery: The Effects on Fetal Acid-Base Status and Hemodynamic Control

W. D. Ngan Kee, A. Lee, K. S. Khaw, F. F. Ng, M. K. Karmakar, T. Gin
2009 Obstetric Anesthesia Digest  
RESULTS: As the proportion of phenylephrine decreased and proportion of ephedrine increased among the groups, the following significant trends were detected: the incidences of hypotension and nausea/vomiting  ...  However, the effect of varying the proportion of vasopressors in such combinations has not been reported.  ...  ACKNOWLEDGMENTS The authors thank the midwives of the Labor Ward, Prince of Wales Hospital, Shatin, Hong Kong, China for their assistance and co-operation.  ... 
doi:10.1097/01.aoa.0000358410.78531.07 fatcat:mmxlmeyqeffini3gsrzb2turay

Multiple solutions of DNA restriction mapping problems

William Schmitt, Michael S Waterman
1991 Advances in Applied Mathematics  
In this paper we define a hierarchy of equivalence relations on the set of all solutions to the mapping problem and study the combinatorics and characterization of the equivalence classes. o 1991 Academic  ...  However, it is also known that under a simple model of randomness the number of solutions to the mapping problem increases exponentially with the length of the DNA molecule.  ...  First of all, the solution to a particular double digest problem is usually far from unique.  ... 
doi:10.1016/0196-8858(91)90028-h fatcat:5hynwbjcbnf6nazo2f5jrys6k4

The restriction mapping problem revisited

Gopal Pandurangan, H. Ramesh
2002 Journal of computer and system sciences (Print)  
We give a fast polynomial time (Oðn 2 log nÞ worst-case) algorithm for finding all the n sites of a DNA molecule using this technique.  ...  Double digest and partial digest are two well-studied techniques for restriction mapping. While double digest is NP-complete, there is no known polynomial-time algorithm for partial digest.  ...  Acknowledgments We are grateful to an anonymous referee for the excellent suggestion of applying our technique to the peptide sequencing problem and for pointing out useful references.  ... 
doi:10.1016/s0022-0000(02)00008-9 fatcat:sbsmbdoa3jcpzk74eit62n4xtm

Genetic algorithm solution for double digest problem

Mohammad Ganjtabesh, H Ahrabian, A Nowzari-Dalini, Z Razaghi Kashani Moghadam
2012 Bioinformation  
The strongly NP-Hard Double Digest Problem, for reconstructing the physical map of DNA sequence, in now using for efficient genotyping.  ...  Most of the existing methods are inefficient in tackling large instances due to the large search space for the problem which grows as a factorial function ISSN 0973-2063 (online) 0973-8894 (print) Bioinformation  ...  Conclusion: A novel genetic algorithm is designed for solving double digest problem.  ... 
doi:10.6026/97320630008453 pmid:22715298 pmcid:PMC3374354 fatcat:tqs3edk6hzbehbfirsjtcngs6i

Quantum Inspired Genetic Algorithm for Double Digest Problem

Jingwen Suo, Lize Gu, Yun Pan, Sijia Yang, Xiaoya Hu
2020 IEEE Access  
The double digest problem (DDP) is a fundamental problem in bioinformatics, and it has been proven to be an NP-hard problem.  ...  The solution of the DDP is a permutation, selected by the QIGA, of all the DNA fragments.  ...  In Fig. 3(b) , only SK05 cannot find the exact solution of the double digest problem.  ... 
doi:10.1109/access.2020.2988117 fatcat:fptmcicewffnfa3g5qvfcvqdhm

PROBLEM DEPARTMENT

G. H. Jamison
1933 School Science and Mathematics  
(a) Asum of X dollars, invested at X per cent, compounded annually, doubles itself in X years. Find X, other than 0.  ...  All readers are invited to propose problems and to solve problems here pro posed.  ... 
doi:10.1111/j.1949-8594.1933.tb14158.x fatcat:p53lhmisqfgbhk3tvojem7f754

PROBLEM DEPARTMENT

G. H. Jamison
1934 School Science and Mathematics  
All readers are invited to propose problems and to solve problems here pro- posed. Drawings to illustrate the problems should be well done in India ink.  ...  Each solution, or proposed problem, sent to the Editor should have the author’s name intro- ducing the problem or solution as on the following pages.  ... 
doi:10.1111/j.1949-8594.1934.tb09781.x fatcat:7wymc4vojjdvtc3rj23dyahuo4

Solving large double digestion problems for DNA restriction mapping by using branch-and-bound integer linear programming

Z. Wu, Y. Zhang
2008 International Journal of Bioinformatics Research and Applications  
The double digestion problem is to find the orders for a and b, given c as the result of the sequence being digested by A and B combined.  ...  The double digestion problem for DNA restriction mapping has been proved to be NPcomplete, and is intractable if the numbers of the DNA fragments generated by the two restriction enzymes are large.  ...  Another issue is the multiple solutions to the mixed-integer programs and hence the double digestion problem.  ... 
doi:10.1504/ijbra.2008.021173 pmid:19008180 fatcat:yavfudk5endq5kppwdyxktw6eu

On the approximability of the Simplified Partial Digest Problem

Jacek Blazewicz, Edmund K. Burke, Marta Kasprzak, Alexandr Kovalev, Mikhail Y. Kovalyov
2009 Discrete Applied Mathematics  
In this paper, we analyse the computational complexity of an optimization version of the Simplified Partial Digest Problem (SPDP), which is a mathematical model for DNA mapping based on the results of  ...  This implies that the problem of maximizing the number of correct elements of the DNA map in the error-free simplified partial digest experiment is pseudopolynomially non-approximable with the approximation  ...  Acknowledgments This work was partially supported by the Polish Ministry of Science grant N519 314635 and the Marie Curie BIOPTRAIN fellowship of Mr. A. Kovalev.  ... 
doi:10.1016/j.dam.2009.04.017 fatcat:xvyuahgqzrecnam2gpygsdjkaa

Advanced Problems and Solutions

1960 The American mathematical monthly  
ADVANCED PROBLEMS AND SOLUTIONS EpITED BY E. P. STaRKE, Rutgers, The State University Send all communications concerning Advanced Problems and Solutions to E. P.  ...  Starke, Rutgers, The State University, New Brunswick, New Jersey. All manuscripts should be type- written with double spacing and margins at least one inch wide.  ... 
doi:10.1080/00029890.1960.11989452 fatcat:i6hml3xthbgbdoqyho3wjy2k2q

DNA-Based Computing of Strategic Assignment Problems

Jian-Jun Shu, Qi-Wen Wang, Kian-Yan Yong
2011 Physical Review Letters  
solving the same problem.  ...  In this Letter, a new approach dealing with strategic assignment problems is proposed based on manipulating DNA strands, which is believed to be better than the conventional silicon-based computing in  ...  -The following DNA-based algorithm is designed to solve the strategic assignment problem: Step 1: Generate all possible solution paths through the graph.  ... 
doi:10.1103/physrevlett.106.188702 pmid:21635133 fatcat:p3swbo3jhzb23f6f5tmiakvjra
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