Maintenance of a piercing set for intervals with applications

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Abstract

We show how to efficiently maintain a minimum piercing set for a set S of intervals on the line, under insertions and deletions to/from S. A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c(S) log |S|), where c(S) is the size of the new minimum piercing set. We also show how to maintain a piercing set for S of size at most (1+ε)c(S), for 0 < ε ≤ 1, in (formula presented) amortized time per update. We then apply these results to obtain efficient (sometimes improved) solutions to the following three problems: (i) the shooter location problem, (ii) computing a minimum piercing set for arcs on a circle, and (iii) dynamically maintaining a box cover for a d-dimensional point set.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 11th International Conference, ISAAC 2000, Proceedings
EditorsD.T. Lee, Shang-Hua Teng, Shang-Hua Teng
PublisherSpringer Verlag
Pages552-563
Number of pages12
ISBN (Print)3540412557, 9783540412557
DOIs
StatePublished - 1 Jan 2000
Event11th Annual International Symposium on Algorithms and Computation, ISAAC 2000 - Taipei, Taiwan, Province of China
Duration: 18 Dec 200020 Dec 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1969
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Annual International Symposium on Algorithms and Computation, ISAAC 2000
Country/TerritoryTaiwan, Province of China
CityTaipei
Period18/12/0020/12/00

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