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Approximating Distance Measures for the Skyline

Authors Nirman Kumar, Benjamin Raichel, Stavros Sintos, Gregory Van Buskirk

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Author Details

Nirman Kumar
  • Department of Computer Science, University of Memphis, TN, USA
Benjamin Raichel
  • Department of Computer Science, University of Texas at Dallas, TX, USA
Stavros Sintos
  • Department of Computer Science, Duke University, Durham, NC, USA
Gregory Van Buskirk
  • Department of Computer Science, University of Texas at Dallas, TX, USA

Funding

B. Raichel and G. Van Burskirk are partially supported by NSF CRII Award 1566137 and CAREER Award 1750780. S. Sintos is supported by NSF under grants CCF-15-13816, CCF-15-46392, and IIS-14-08846, by an ARO grant W911NF-15-1-0408, and by BSF Grant 2012/229 from the U.S.-Israel Binational Science Foundation.

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Nirman Kumar, Benjamin Raichel, Stavros Sintos, and Gregory Van Buskirk. Approximating Distance Measures for the Skyline. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICDT.2019.10

Abstract

In multi-parameter decision making, data is usually modeled as a set of points whose dimension is the number of parameters, and the skyline or Pareto points represent the possible optimal solutions for various optimization problems. The structure and computation of such points have been well studied, particularly in the database community. As the skyline can be quite large in high dimensions, one often seeks a compact summary. In particular, for a given integer parameter k, a subset of k points is desired which best approximates the skyline under some measure. Various measures have been proposed, but they mostly treat the skyline as a discrete object. By viewing the skyline as a continuous geometric hull, we propose a new measure that evaluates the quality of a subset by the Hausdorff distance of its hull to the full hull. We argue that in many ways our measure more naturally captures what it means to approximate the skyline. 
For our new geometric skyline approximation measure, we provide a plethora of results. Specifically, we provide (1) a near linear time exact algorithm in two dimensions, (2) APX-hardness results for dimensions three and higher, (3) approximation algorithms for related variants of our problem, and (4) a practical and efficient heuristic which uses our geometric insights into the problem, as well as various experimental results to show the efficacy of our approach.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Skyline
  • Pareto optimal
  • Approximation
  • Hardness
  • Multi-criteria decision making

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