Generalized Disk Graphs

I.M. Arnporsson, S. Chaplick, J.S. Gylfason, M.M. Halldorsson, J.M. Reynisson, T. Tonoyan*, A. Lubiw, M. Salavatipour

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

A graph G is a Generalized Disk Graph if for some dimension eta >= 1, a non-decreasing sub-linear function f and natural number t, each vertex vi can be assigned a length li and set P-i subset of R-eta of t points such that vivj is an edge of G if and only if l(i) <= l(j) and d(P-i, P-j) <= l(i)f(l(j)/l(i)) + l(i)f(1), where d(center dot, center dot) is the least distance between points in either set. Generalized disk graphs were introduced as a model of wireless network interference and have been shown to be dramatically more accurate than disk graphs or other previously known graph classes. However, their properties have not been studied extensively before.We give a geometric representation of these graphs as intersection graphs of convex shapes, relate them to other geometric intersection graph classes, and solve several important optimization problems on these graphs using the geometric representation; either exactly (in two-dimensions) or approximately (in higher dimensions).
Original languageEnglish
Title of host publicationALGORITHMS AND DATA STRUCTURES, WADS 2021
EditorsA Lubiw, M Salavatipour
PublisherSpringer Nature
Pages115-128
Number of pages14
Volume12808
ISBN (Print)9783030835071
DOIs
Publication statusPublished - 2021
Event17th International Symposium on Algorithms and Data Structures - Online, Dalhousie University, Halifax, Canada
Duration: 9 Aug 202111 Aug 2021
Conference number: 17
https://projects.cs.dal.ca/wads2021/

Publication series

SeriesLecture Notes in Computer Science
Volume12808
ISSN0302-9743

Conference

Conference17th International Symposium on Algorithms and Data Structures
Abbreviated titleWADS 2021
Country/TerritoryCanada
CityHalifax
Period9/08/2111/08/21
Internet address

Keywords

  • Conflict graph
  • SINR model
  • Intersection graph
  • TIME APPROXIMATION SCHEMES
  • INTERSECTION GRAPHS
  • INDEPENDENT SET
  • FAT OBJECTS
  • COMPLEXITY
  • UNION

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