TY - GEN

T1 - On a problem of summing elements chosen from the family of finite numerical sequences

AU - Kel’manov, Alexander

AU - Mikhailova, Ludmila

AU - Romanchenko, Semyon

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The tuple of permutations and the tuple of indices are required to be found in the problem considered in order to minimize the sum of elements chosen from the given family of finite numerical sequences subject to some constraints on the elements choice. Namely, given the family of L numerical nonnegative N-element sequences and a positive integer J, it is required to minimize the sum of J intra-sums. Each element corresponds to one element in one of L input sequences, and all possible L-permutations are admissible in this one-to-one correspondence in each intra-sum of L elements. In addition, there are some constraints on the indices of the summed sequence elements. The problem solution is a pair of tuples, namely, (1) a tuple of J permutations on L elements, and (2) a tuple of JL increasing indices. The paper presents an exact polynomial-time algorithm with O(N 5 ) running time for this problem. In particular, the problem is induced by an applied problem of noiseproof searching for repetitions of the given tuple of elements with their possible permutations at each tuple repeat, and finding the positions of these elements in the numerical sequence distorted by noise under some constraints on unknown positions of elements. The applied problem noted is related, for example, to the remote monitoring of several moving objects with possible arbitrary displacements (permutations) of these objects.

AB - The tuple of permutations and the tuple of indices are required to be found in the problem considered in order to minimize the sum of elements chosen from the given family of finite numerical sequences subject to some constraints on the elements choice. Namely, given the family of L numerical nonnegative N-element sequences and a positive integer J, it is required to minimize the sum of J intra-sums. Each element corresponds to one element in one of L input sequences, and all possible L-permutations are admissible in this one-to-one correspondence in each intra-sum of L elements. In addition, there are some constraints on the indices of the summed sequence elements. The problem solution is a pair of tuples, namely, (1) a tuple of J permutations on L elements, and (2) a tuple of JL increasing indices. The paper presents an exact polynomial-time algorithm with O(N 5 ) running time for this problem. In particular, the problem is induced by an applied problem of noiseproof searching for repetitions of the given tuple of elements with their possible permutations at each tuple repeat, and finding the positions of these elements in the numerical sequence distorted by noise under some constraints on unknown positions of elements. The applied problem noted is related, for example, to the remote monitoring of several moving objects with possible arbitrary displacements (permutations) of these objects.

KW - Exact polynomial-time algorithm

KW - Finite numerical sequences

KW - Optimal summing

KW - Permutations

UR - http://www.scopus.com/inward/record.url?scp=85059954814&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11027-7_29

DO - 10.1007/978-3-030-11027-7_29

M3 - Conference contribution

AN - SCOPUS:85059954814

SN - 9783030110260

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 305

EP - 317

BT - Analysis of Images, Social Networks and Texts - 7th International Conference, AIST 2018, Revised Selected Papers

A2 - Panchenko, Alexander

A2 - van der Aalst, Wil M.

A2 - Khachay, Michael

A2 - Pardalos, Panos M.

A2 - Batagelj, Vladimir

A2 - Loukachevitch, Natalia

A2 - Glavaš, Goran

A2 - Ignatov, Dmitry I.

A2 - Kuznetsov, Sergei O.

A2 - Koltsova, Olessia

A2 - Lomazova, Irina A.

A2 - Savchenko, Andrey V.

A2 - Napoli, Amedeo

A2 - Pelillo, Marcello

PB - Springer-Verlag GmbH and Co. KG

T2 - 7th International Conference on Analysis of Images, Social Networks and Texts, AIST 2018

Y2 - 5 July 2018 through 7 July 2018

ER -