On the expected diameter, width, and complexity of a stochastic convex-hull

Jie Xue, Yuan Li, Ravi Janardan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of n points in ℝd each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both n and d. For width, two approximation algorithms are provided: a deterministic O(1)-approximation running in O(nd+1 log n) time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact O(nd)-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
EditorsFaith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
PublisherSpringer Verlag
Pages581-592
Number of pages12
ISBN (Print)9783319621265
DOIs
StatePublished - 2017
Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
Duration: Jul 31 2017Aug 2 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10389 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Symposium on Algorithms and Data Structures, WADS 2017
Country/TerritoryCanada
CitySt. John’s
Period7/31/178/2/17

Keywords

  • Combinatorial complexity
  • Diameter
  • Expectation
  • Uncertain data
  • Width

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