Exact Algorithm for One Cardinality-Weighted 2-Partitioning Problem of a Sequence

Alexander Kel’manov, Sergey Khamidullin, Anna Panasenko

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

1 Citation (Scopus)


We consider a problem of 2-partitioning a finite sequence of points in Euclidean space into two clusters of the given sizes with some additional constraints. The solution criterion is the minimum of the sum (over both clusters) of weighted intracluster sums of squared distances between the elements of each cluster and its center. The weights of the intracluster sums are equal to the cardinalities of the desired clusters. The center of one cluster is given as input, while the center of the other one is unknown and is determined as a geometric center, i.e. as a point of space equal to the mean of the cluster elements. The following constraints hold: the difference between the indices of two subsequent points included in the first cluster is bounded from above and below by given some constants. It is shown that the considered problem is the strongly NP-hard one. An exact algorithm is proposed for the case of integer-valued input of the problem. This algorithm has a pseudopolynomial running time if the space dimension is fixed.

Original languageEnglish
Title of host publicationLearning and Intelligent Optimization - 13th International Conference, LION 13, Revised Selected Papers
EditorsNikolaos F. Matsatsinis, Yannis Marinakis, Panos Pardalos
PublisherSpringer Gabler
Number of pages11
ISBN (Print)9783030386283
Publication statusPublished - 1 Jan 2020
Event13th International Conference on Learning and Intelligent Optimization, LION 13 - Chania, Greece
Duration: 27 May 201931 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11968 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Learning and Intelligent Optimization, LION 13


  • Euclidean space
  • Exact algorithm
  • Fixed space dimension
  • Integer coordinates
  • NP-hard problem
  • Pseudopolynomial time
  • Quadratic variation
  • Sequence of points
  • Weighted 2-partition


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