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Simultaneous Detection and Discrimination of Subsequences Which Are Nonlinearly Extended Elements of the Given Sequences Alphabet in a Quasiperiodic Sequence

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

We consider a posteriori approach to the problem of noise-proof simultaneous detection and discrimination of subsequences-fragments having some given properties in a quasiperiodic sequence. The solution to the problem is stated for the case when the quantity of sought subsequences is unknown. We assume that 1) a finite alphabet of reference sequences is given; 2) a set of permissible deformations is defined for the alphabet, this set gathers all possible extensions of its elements (by duplicating their components); 3) every subsequence-fragment in the quasiperiodic sequence belongs to the set of permissible deformations; 4) subsequences-fragments do not intersect each other, and the difference between the initial positions of two neighboring fragments is limited from above by a given value.

We show that in the framework of a posteriori approach, the problem of simultaneous detection and discrimination reduces to solving an unexplored discrete optimization problem. A polynomial-time algorithm that guarantees the optimal solution to this optimization problem is proposed. The results of the numerical simulation are presented.

The study was supported by the Russian Foundation for Basic Research, projects 19-07-00397 and 19-01-00308, by the Russian Academy of Science (the Program of basic research), project 0314-2019-0015.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090, Novosibirsk, Russia

    Liudmila Mikhailova & Sergey Khamdullin

Authors
  1. Liudmila Mikhailova
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  2. Sergey Khamdullin
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Correspondence to Liudmila Mikhailova .

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Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Mikhailova, L., Khamdullin, S. (2020). Simultaneous Detection and Discrimination of Subsequences Which Are Nonlinearly Extended Elements of the Given Sequences Alphabet in a Quasiperiodic Sequence. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_16

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