Optimization Letters

, Volume 10, Issue 1, pp 33–45 | Cite as

Approximating the minimum hub cover problem on planar graphs

  • Belma Yelbay
  • Ş. İlker Birbil
  • Kerem Bülbül
  • Hasan Jamil
Original Paper

Abstract

We study an approximation algorithm with a performance guarantee to solve a new \(\mathcal {NP}\)-hard optimization problem on planar graphs. The problem, which is referred to as the minimum hub cover problem, has recently been introduced to the literature to improve query processing over large graph databases. Planar graphs also arise in various graph query processing applications, such as; biometric identification, image classification, object recognition, and so on. Our algorithm is based on a well-known graph decomposition technique that partitions the graph into a set of outerplanar graphs and provides an approximate solution with a proven performance ratio. We conduct a comprehensive computational experiment to investigate the empirical performance of the algorithm. Computational results demonstrate that the empirical performance of the algorithm surpasses its guaranteed performance. We also apply the same decomposition approach to develop a decomposition-based heuristic, which is much more efficient than the approximation algorithm in terms of computation time. Computational results also indicate that the efficacy of the decomposition-based heuristic in terms of solution quality is comparable to that of the approximation algorithm.

Keywords

Approximation algorithm Query processing Subgraph isomorphism Planar graph decomposition Minimum hub cover problem 

Mathematics Subject Classification

68T20 90C27 05C90 

Notes

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Belma Yelbay
    • 1
  • Ş. İlker Birbil
    • 1
  • Kerem Bülbül
    • 1
  • Hasan Jamil
    • 2
  1. 1.Manufacturing Systems and Industrial EngineeringSabancı UniversityIstanbulTurkey
  2. 2.Department of Computer ScienceUniversity of IdahoMoscowUSA

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