Upward Point Set Embeddings of Paths and Trees
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10439120" target="_blank" >RIV/00216208:11320/21:10439120 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-68211-8_19" target="_blank" >https://doi.org/10.1007/978-3-030-68211-8_19</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-68211-8_19" target="_blank" >10.1007/978-3-030-68211-8_19</a>
Alternative languages
Result language
angličtina
Original language name
Upward Point Set Embeddings of Paths and Trees
Original language description
We study upward planar straight-line embeddings (UPSE) of directed trees on given point sets. The given point set S has size at least the number of vertices in the tree. For the special case where the tree is a path P we show that: (a) If S is one-sided convex, the number of UPSE s equals the number of maximal monotone paths in P. (b) If S is in general position and P is composed by three maximal monotone paths, where the middle path is longer than the other two, then it always admits an UPSE on S. We show that the decision problem of whether there exists an UPSE of a directed tree with n vertices on a fixed point set S of n points is NP-complete, by relaxing the requirements of the previously known result which relied on the presence of cycles in the graph, but instead fixing position of a single vertex. Finally, by allowing extra points, we guarantee that each directed caterpillar on n vertices and with k switches in its backbone admits an UPSE on every set of n2k - 2 points.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
WALCOM: Algorithms and Computation
ISBN
978-3-030-68210-1
ISSN
0302-9743
e-ISSN
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Number of pages
13
Pages from-to
234-246
Publisher name
Springer Science and Business Media Deutschland GmbH
Place of publication
Neuveden
Event location
MM
Event date
Feb 28, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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