Generalized Disk Graphs

I.M. Arnporsson; S. Chaplick; J.S. Gylfason; M.M. Halldorsson; J.M. Reynisson; T. Tonoyan

doi:10.1007/978-3-030-83508-8_9

Generalized Disk Graphs

I.M. Arnporsson
, S. Chaplick
, J.S. Gylfason
, M.M. Halldorsson
, J.M. Reynisson
, T. Tonoyan^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

A graph G is a Generalized Disk Graph if for some dimension η≥ 1, a non-decreasing sub-linear function f and natural number t, each vertex v _i can be assigned a length l _i and set P _i⊆ R ^η of t points such that v _iv _j is an edge of G if and only if l _i≤ l _j and d(Pi,Pj)≤lif(lj/li)+lif(1), where d(·, · ) 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	Anna Lubiw, Mohammad Salavatipour
Publisher	Springer Nature
Pages	115-128
Number of pages	14
Volume	12808
ISBN (Print)	9783030835071
DOIs	https://doi.org/10.1007/978-3-030-83508-8_9
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	https://projects.cs.dal.ca/wads2021/

Keywords

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

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10.1007/978-3-030-83508-8_9

Cite this

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title = "Generalized Disk Graphs",

abstract = "A graph G is a Generalized Disk Graph if for some dimension η≥ 1, a non-decreasing sub-linear function f and natural number t, each vertex v i can be assigned a length l i and set P i⊆ R η of t points such that v iv j is an edge of G if and only if l i≤ l j and d(Pi,Pj)≤lif(lj/li)+lif(1), where d(·, · ) 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).",

keywords = "Conflict graph, SINR model, Intersection graph, TIME APPROXIMATION SCHEMES, INTERSECTION GRAPHS, INDEPENDENT SET, FAT OBJECTS, COMPLEXITY, UNION",

author = "I.M. Arnporsson and S. Chaplick and J.S. Gylfason and M.M. Halldorsson and J.M. Reynisson and T. Tonoyan",

note = "Funding Information: Work supported by grant 174484-051 from Icelandic Research Fund and grant 208348-0091 from Icelandic Student Innovation Fund. Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 17th International Symposium on Algorithms and Data Structures, WADS 2021 ; Conference date: 09-08-2021 Through 11-08-2021",

year = "2021",

doi = "10.1007/978-3-030-83508-8\_9",

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isbn = "9783030835071",

volume = "12808",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature",

pages = "115--128",

editor = "Anna Lubiw and Mohammad Salavatipour",

booktitle = "ALGORITHMS AND DATA STRUCTURES, WADS 2021",

address = "Switzerland",

url = "https://projects.cs.dal.ca/wads2021/",

}

Arnporsson, IM, Chaplick, S, Gylfason, JS, Halldorsson, MM, Reynisson, JM & Tonoyan, T 2021, Generalized Disk Graphs. in A Lubiw & M Salavatipour (eds), ALGORITHMS AND DATA STRUCTURES, WADS 2021. vol. 12808, Springer Nature, Lecture Notes in Computer Science, vol. 12808, pp. 115-128, 17th International Symposium on Algorithms and Data Structures, Halifax, Nova Scotia, Canada, 9/08/21. https://doi.org/10.1007/978-3-030-83508-8_9

Generalized Disk Graphs. / Arnporsson, I.M.; Chaplick, S.; Gylfason, J.S. et al.
ALGORITHMS AND DATA STRUCTURES, WADS 2021. ed. / Anna Lubiw; Mohammad Salavatipour. Vol. 12808 Springer Nature, 2021. p. 115-128 (Lecture Notes in Computer Science, Vol. 12808).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Generalized Disk Graphs

AU - Arnporsson, I.M.

AU - Chaplick, S.

AU - Gylfason, J.S.

AU - Halldorsson, M.M.

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AU - Tonoyan, T.

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N2 - A graph G is a Generalized Disk Graph if for some dimension η≥ 1, a non-decreasing sub-linear function f and natural number t, each vertex v i can be assigned a length l i and set P i⊆ R η of t points such that v iv j is an edge of G if and only if l i≤ l j and d(Pi,Pj)≤lif(lj/li)+lif(1), where d(·, · ) 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).

AB - A graph G is a Generalized Disk Graph if for some dimension η≥ 1, a non-decreasing sub-linear function f and natural number t, each vertex v i can be assigned a length l i and set P i⊆ R η of t points such that v iv j is an edge of G if and only if l i≤ l j and d(Pi,Pj)≤lif(lj/li)+lif(1), where d(·, · ) 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).

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KW - SINR model

KW - Intersection graph

KW - TIME APPROXIMATION SCHEMES

KW - INTERSECTION GRAPHS

KW - INDEPENDENT SET

KW - FAT OBJECTS

KW - COMPLEXITY

KW - UNION

U2 - 10.1007/978-3-030-83508-8_9

DO - 10.1007/978-3-030-83508-8_9

M3 - Conference article in proceeding

SN - 9783030835071

VL - 12808

T3 - Lecture Notes in Computer Science

SP - 115

EP - 128

BT - ALGORITHMS AND DATA STRUCTURES, WADS 2021

A2 - Lubiw, Anna

A2 - Salavatipour, Mohammad

PB - Springer Nature

T2 - 17th International Symposium on Algorithms and Data Structures

Y2 - 9 August 2021 through 11 August 2021

ER -

Generalized Disk Graphs

Abstract

Publication series

Symposium

Keywords

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