On Embeddability of Unit Disk Graphs onto Straight Lines
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00114293" target="_blank" >RIV/00216224:14330/20:00114293 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-50026-9_13" target="_blank" >http://dx.doi.org/10.1007/978-3-030-50026-9_13</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-50026-9_13" target="_blank" >10.1007/978-3-030-50026-9_13</a>
Alternative languages
Result language
angličtina
Original language name
On Embeddability of Unit Disk Graphs onto Straight Lines
Original language description
Unit disk graphs are the intersection graphs of unit radius disks in the Euclidean plane. Deciding whether there exists an embedding of a given unit disk graph, i.e., unit disk graph recognition, is an important geometric problem, and has many application areas. In general, this problem is known to be exists{}R-complete. In some applications, the objects that correspond to unit disks have predefined (geometrical) structures to be placed on. Hence, many researchers attacked this problem by restricting the domain of the disk centers. One example to such applications is wireless sensor networks, where each disk corresponds to a wireless sensor node, and a pair of intersecting disks corresponds to a pair of sensors being able to communicate with one another. It is usually assumed that the nodes have identical sensing ranges, and thus a unit disk graph model is used to model problems concerning wireless sensor networks. We consider the unit disk graph realization problem on a restricted domain, by assuming a scenario where the wireless sensor nodes are deployed on the corridors of a building. Based on this scenario, we impose a geometric constraint such that the unit disks must be centered onto given straight lines. In this paper, we first describe a polynomial-time reduction which shows that deciding whether a graph can be realized as unit disks onto given straight lines is NP-hard, when the given lines are parallel to either the x-axis or y-axis. Using the reduction we described, we also show that this problem is NP-complete when the given lines are only parallel to the x-axis (and one another). We obtain these results using the idea of the logic engine introduced by Bhatt and Cosmadakis in 1987
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA20-04567S" target="_blank" >GA20-04567S: Structure of tractable instances of hard algorithmic problems on graphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
International Computer Science Symposium in Russia, CSR 2020
ISBN
9783030500252
ISSN
0302-9743
e-ISSN
0302-9743
Number of pages
14
Pages from-to
184-197
Publisher name
Springer, Cham
Place of publication
Yekaterinburg, Russia
Event location
Yekaterinburg, Russia
Event date
Jan 1, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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