This article is cited in 8 scientific papers (total in 8 papers)
Approximation algorithm for one problem of partitioning a sequence
A. V. Kelmanovab, S. A. Khamidullinb
a Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
We consider one NP-hard problem of partitioning of a finite Euclidean vectors sequence into two clusters minimizing the sum of squared distances from the clusters elements to their centers. The cardinalities of the clusters are fixed. The center of the first cluster is defined as the mean value of all vectors in a cluster. The center of the second cluster is given in advance and is equal to 0. Additionally, the partition must satisfy the restriction that for all vectors that are in the first cluster the difference between the indices of two consequent vectors from this cluster is bounded from below and above by some constants. An effective $2$-approximation algorithm for the problem is presented. Bibliogr. 9.
Euclidean vectors sequence, сlusterization, minimum sum-of-squared distances, NP-hardness, effective $2$-approximation algorithm.
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Journal of Applied and Industrial Mathematics, 2014, 8:2, 236–244
A. V. Kelmanov, S. A. Khamidullin, “Approximation algorithm for one problem of partitioning a sequence”, Diskretn. Anal. Issled. Oper., 21:1 (2014), 53–66; J. Appl. Industr. Math., 8:2 (2014), 236–244
Citation in format AMSBIB
\by A.~V.~Kelmanov, S.~A.~Khamidullin
\paper Approximation algorithm for one problem of partitioning a~sequence
\jour Diskretn. Anal. Issled. Oper.
\jour J. Appl. Industr. Math.
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A. V. Kel'manov, L. V. Mikhailova, S. A. Khamidullin, V. I. Khandeev, “An approximation algorithm for the problem of partitioning a sequence into clusters with constraints on their cardinalities”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 88–96
A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “Exact pseudopolynomial algorithm for one sequence partitioning problem”, Autom. Remote Control, 78:1 (2017), 67–74
A. Kel'manov, “Efficient approximation algorithms for some NP-hard problems of partitioning a set and a sequence”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 87–90
A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “A randomized algorithm for a sequence 2-clustering problem”, Comput. Math. Math. Phys., 58:12 (2018), 2078–2085
A. Kel'manov, S. Khamidullin, V. Khandeev, “A randomized algorithm for 2-partition of a sequence”, Analysis of Images, Social Networks and Texts, AIST 2017, Lecture Notes in Computer Science, 10716, eds. W. van der Aalst, D. Ignatov, M. Khachay, S. Kuznetsov, V. Lempitsky, I. Lomazova, N. Loukachevitch, A. Napoli, A. Panchenko, P. Pardalos, A. Savchenko, S. Wasserman, Springer, 2018, 313–322
Kel'manov A., Khamidullin S., Panasenko A., “Exact Algorithm For One Cardinality-Weighted 2-Partitioning Problem of a Sequence”, Learning and Intelligent Optimization, Lion, Lecture Notes in Computer Science, 11968, eds. Matsatsinis N., Marinakis Y., Pardalos P., Springer International Publishing Ag, 2020, 135–145
Kel'manov A. Khamidullin S. Panasenko A., “2-Approximation Polynomial-Time Algorithm For a Cardinality-Weighted 2-Partitioning Problem of a Sequence”, Numerical Computations: Theory and Algorithms, Pt II, Lecture Notes in Computer Science, 11974, ed. Sergeyev Y. Kvasov D., Springer International Publishing Ag, 2020, 386–393
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