@inproceedings{2814262a2b694e3bab793e8f61bf8b4c,

title = "A randomized algorithm for 2-partition of a sequence",

abstract = "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.",

keywords = "Asymptotic accuracy, Euclidean space, Minimum sum-of-squared distances, NP-hardness, Partitioning, Randomized algorithm, Sequence, TIME-SERIES DATA, NP-hardness Randomized algorithm, VECTORS",

author = "Alexander Kel{\textquoteright}manov and Sergey Khamidullin and Vladimir Khandeev",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-73013-4_29",

language = "English",

isbn = "9783319730127",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag GmbH and Co. KG",

pages = "313--322",

editor = "WMP VanDerAalst and DI Ignatov and M Khachay and SO Kuznetsov and Lempitsky and IA Lomazova and N Loukachevitch and A Napoli and A Panchenko and PM Pardalos and AV Savchenko and S Wasserman",

booktitle = "Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers",

address = "Germany",

note = "6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017 ; Conference date: 27-07-2017 Through 29-07-2017",

}