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 language | English |
---|---|
Title of host publication | ALGORITHMS AND DATA STRUCTURES, WADS 2021 |
Editors | A Lubiw, M Salavatipour |
Publisher | Springer Nature |
Pages | 115-128 |
Number of pages | 14 |
Volume | 12808 |
ISBN (Print) | 9783030835071 |
DOIs | |
Publication status | Published - 2021 |
Event | 17th International Symposium on Algorithms and Data Structures - Online, Dalhousie University, Halifax, Canada Duration: 9 Aug 2021 → 11 Aug 2021 Conference number: 17 https://projects.cs.dal.ca/wads2021/ |
Publication series
Series | Lecture Notes in Computer Science |
---|---|
Volume | 12808 |
ISSN | 0302-9743 |
Symposium
Symposium | 17th International Symposium on Algorithms and Data Structures |
---|---|
Abbreviated title | WADS 2021 |
Country/Territory | Canada |
City | Halifax |
Period | 9/08/21 → 11/08/21 |
Internet address |
Keywords
- Conflict graph
- SINR model
- Intersection graph
- TIME APPROXIMATION SCHEMES
- INTERSECTION GRAPHS
- INDEPENDENT SET
- FAT OBJECTS
- COMPLEXITY
- UNION