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A distributed algorithm for solving large-scale p-median problems using expectation maximization.

Harsha Gwalani1, Joseph Helsing2, Sultanah M Alshammari3

  • 1Department of Computer Science and Engineering, University of North Texas, Denton, Texas, United States.

Peerj. Computer Science
|December 9, 2024
PubMed
Summary
This summary is machine-generated.

We developed EM-FI, a novel distributed algorithm for the p-median problem. It efficiently solves large-scale problems by clustering destinations, offering significant speed improvements without sacrificing solution quality.

Keywords:
Distributed algorithmsHeuristic searchLocation allocationP-median problemParallel computingSpatial data mining

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Area of Science:

  • Operations Research
  • Computer Science
  • Computational Optimization

Background:

  • The p-median problem aims to minimize average distance by selecting p sources for n destinations.
  • It's an NP-hard problem with existing heuristics often lacking scalability for large datasets.
  • Current fast interchange (FI) heuristics are time-inefficient for large-scale applications.

Purpose of the Study:

  • To introduce a scalable and efficient algorithm for solving large-scale p-median problems.
  • To address the limitations of existing methods in terms of computational time.
  • To maintain solution quality while significantly improving processing speed.

Main Methods:

  • A distributed divide and conquer approach named EM-FI.
  • Utilizing Expectation Maximization (EM) to identify spatial clusters of destination locations.
  • Solving clustered subproblems concurrently using integer programming or the FI heuristic.

Main Results:

  • EM-FI demonstrated an order of magnitude improvement in computation time.
  • The algorithm maintained solution quality comparable to optimal or near-optimal results.
  • Effective performance was observed on both synthetic and real-world datasets.

Conclusions:

  • EM-FI offers a highly efficient and scalable solution for large-scale p-median problems.
  • The approach is effective even with limited computational resources.
  • This method advances the practical applicability of solving complex optimization problems.