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The Complexity of Vector Partition.

Shmuel Onn1

  • 1Technion - Israel Institute of Technology, Haifa, Israel.

Vietnam Journal of Mathematics
|September 20, 2021
PubMed
Summary

The vector partition problem divides agents with attribute vectors into groups to minimize costs. Researchers analyzed its complexity based on parameters like agent count and attribute dimensions.

Area of Science:

  • Operations Research
  • Computer Science
  • Discrete Mathematics

Background:

  • The vector partition problem involves partitioning 'n' agents, each with a 'd'-dimensional attribute vector, into 'p' parts.
  • The objective is to minimize a cost function based on the sums of attribute vectors within each part.
  • This problem has significant applications in fields such as clustering, logistics, and healthcare.

Purpose of the Study:

  • To analyze the computational complexity of the vector partition problem.
  • To investigate the parameterized complexity of the problem with respect to parameters 'p', 'd', 'a', and 't'.
  • To identify and highlight open research questions within this domain.

Main Methods:

  • Complexity analysis of the vector partition problem.
Keywords:
ClusteringCombinatorial optimizationInteger programmingParameterized complexityPartition

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  • Parameterized complexity assessment under varying parameter assumptions.
  • Exploration of problem variations based on agent types and attribute values.

    • Main Results:

    • The study examines the computational difficulty of the vector partition problem.
    • Analysis includes how complexity changes with parameters like the number of parts ('p'), attribute dimensions ('d'), and attribute value bounds ('a').
    • The research considers the impact of the number of agent types ('t') on problem complexity.

    Conclusions:

    • The vector partition problem presents significant computational challenges.
    • Understanding its parameterized complexity is crucial for practical applications in optimization and resource allocation.
    • Further research is needed to address the identified open problems and develop efficient algorithms.