1 Search Results for "Tan, Shuhao"

Document

DOI: 10.4230/LIPIcs.ISAAC.2021.67

Computing Shapley Values for Mean Width in 3-D

Authors: Shuhao Tan

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract

The Shapley value is a classical concept from game theory, which is used to evaluate the importance of a player in a cooperative setting. Assuming that players are inserted in a uniformly random order, the Shapley value of a player p is the expected increase in the value of the characteristic function when p is inserted. Cabello and Chan (SoCG 2019) recently showed how to adapt this to a geometric context on planar point sets. For example, when the characteristic function is the area of the convex hull, the Shapley value of a point is the average amount by which the convex-hull area increases when this point is added to the set. Shapley values can be viewed as an indication of the relative importance/impact of a point on the function of interest. In this paper, we present an efficient algorithm for computing Shapley values in 3-dimensional space, where the function of interest is the mean width of the point set. Our algorithm runs in O(n³log²n) time and O(n) space. This result can be generalized to any point set in d-dimensional space (d ≥ 3) to compute the Shapley values for the mean volume of the convex hull projected onto a uniformly random (d - 2)-subspace in O(n^d log²n) time and O(n) space. These results are based on a new data structure for a dynamic variant of the convolution problem, which is of independent interest. Our data structure supports incremental modifications to n-element vectors (including cyclical rotation by one position). We show that n operations can be executed in O(n log²n) time and O(n) space.

Cite as

Shuhao Tan. Computing Shapley Values for Mean Width in 3-D. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 67:1-67:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{tan:LIPIcs.ISAAC.2021.67,
  author =	{Tan, Shuhao},
  title =	{{Computing Shapley Values for Mean Width in 3-D}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{67:1--67:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.67},
  URN =		{urn:nbn:de:0030-drops-155008},
  doi =		{10.4230/LIPIcs.ISAAC.2021.67},
  annote =	{Keywords: Shapley value, mean width, dynamic convolution}
}

Refine by Author
1 Tan, Shuhao

Refine by Classification
1 Theory of computation → Computational geometry
1 Theory of computation → Data structures design and analysis

Refine by Keyword
1 Shapley value
1 dynamic convolution
1 mean width

Refine by Type
1 document

Refine by Publication Year
1 2021

1 Search Results for "Tan, Shuhao"

Computing Shapley Values for Mean Width in 3-D

Abstract

Cite as

Thanks for your feedback!

Could not send message