A randomized algorithm for 2-partition of a sequence

Alexander Kel’manov, Sergey Khamidullin, Vladimir Khandeev

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

2 Цитирования (Scopus)


In the paper we consider one strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters minimizing the sum over both clusters of intracluster sum of squared distances from clusters elements to their centers. The cardinalities of clusters are assumed to be given. The center of the first cluster is unknown and is defined as the mean value of all points in the cluster. The center of the second one is the origin. Additionally, the difference between the indexes of two consequent points from the first cluster is bounded from below and above by some constants. A randomized algorithm for the problem is proposed. For an established parameter value, given a relative error ε> 0 and fixed γ∈ (0, 1), this algorithm allows to find a (1 + ε) -approximate solution of the problem with a probability of at least 1 - γ in polynomial time. The conditions are established under which the algorithm is polynomial and asymptotically exact.

Язык оригиналаанглийский
Название основной публикацииAnalysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers
РедакторыWMP VanDerAalst, DI Ignatov, M Khachay, SO Kuznetsov, Lempitsky, IA Lomazova, N Loukachevitch, A Napoli, A Panchenko, PM Pardalos, AV Savchenko, S Wasserman
ИздательSpringer-Verlag GmbH and Co. KG
Число страниц10
ISBN (печатное издание)9783319730127
СостояниеОпубликовано - 1 янв. 2018
Событие6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017 - Moscow, Российская Федерация
Продолжительность: 27 июл. 201729 июл. 2017

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том10716 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349


Конференция6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017
Страна/TерриторияРоссийская Федерация


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