Approximation algorithms for minimum ply covering of points with unit squares and unit disks

被引：0
|
作者：
Durocher, Stephane [1 ]
Keil, J. Mark [2 ]
Mondal, Debajyoti [2 ]
机构：
[1] Univ Manitoba, Dept Comp Sci, Winnipeg, MB, Canada
[2] Univ Saskatchewan, Dept Comp Sci, Saskatoon, SK, Canada
来源：
THEORETICAL COMPUTER SCIENCE | 2025年 / 1024卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Ply; Point covering; Unit disks; Unit squares; Approximation; UNIQUE COVERAGE;
D O I：
10.1016/j.tcs.2024.114906
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Given a set.. of points and a set.. of geometric objects in the Euclidean plane, a minimum ply cover of.. with.. is a subset of.. that covers.. and minimizes the number of objects that share a common intersection, called the minimum ply cover number of.. with... Biedl et al. (2021) [9] showed that for both unit squares and unit disks, determining the minimum ply cover number for a set of points is NP-hard. They gave polynomial-time 2-approximation algorithms for the special case when the minimum ply cover number is constant, and asked whether there exists polynomial-time..(1)- approximation algorithms for these problems. In this paper, we settle the question posed by Biedl et al. by providing polynomial-time..(1)- approximation algorithms for the minimum ply cover problem for both unit squares and unit disks.
引用
收藏
页数：14
相关论文
共 50 条
  • [1] Minimum ply covering of points with disks and squares
    Biedl, Therese
    Biniaz, Ahmad
    Lubiw, Anna
    COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2021, 94
  • [2] Covering Many or Few Points with Unit Disks
    de Berg, Mark
    Cabello, Sergio
    Har-Peled, Sariel
    THEORY OF COMPUTING SYSTEMS, 2009, 45 (03) : 446 - 469
  • [3] Covering points by unit disks of fixed location
    Carmi, Paz
    Katz, Matthew J.
    Lev-Tov, Nissan
    ALGORITHMS AND COMPUTATION, 2007, 4835 : 644 - +
  • [4] Covering Many or Few Points with Unit Disks
    Mark de Berg
    Sergio Cabello
    Sariel Har-Peled
    Theory of Computing Systems, 2009, 45
  • [5] Covering many or few points with unit disks
    de Berg, Mark
    Cabello, Sergio
    Har-Peled, Sariel
    APPROXIMATION AND ONLINE ALGORITHMS, 2006, 4368 : 55 - 68
  • [6] Fast Approximation Algorithms for Multiple Coverage with Unit Disks
    Gao, Xuening
    Guo, Longkun
    Liao, Kewen
    2022 IEEE 23RD INTERNATIONAL SYMPOSIUM ON A WORLD OF WIRELESS, MOBILE AND MULTIMEDIA NETWORKS (WOWMOM 2022), 2022, : 185 - 193
  • [7] TRANSLATIVE COVERING BY UNIT SQUARES
    Januszewski, Janusz
    DEMONSTRATIO MATHEMATICA, 2013, 46 (03) : 605 - 616
  • [8] Covering Segments with Unit Squares
    Acharyya, Ankush
    Nandy, Subhas C.
    Pandit, Supantha
    Roy, Sasanka
    ALGORITHMS AND DATA STRUCTURES: 15TH INTERNATIONAL SYMPOSIUM, WADS 2017, 2017, 10389 : 1 - 12
  • [9] Covering segments with unit squares
    Acharyya, Ankush
    Nandy, Subhas C.
    Pandit, Supantha
    Roy, Sasanka
    COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2019, 79 : 1 - 13
  • [10] APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS
    De, Minati
    Das, Gautam K.
    Carmi, Paz
    Nandy, Subhas C.
    INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS, 2013, 23 (06) : 461 - 477
12345