---
_id: '19869'
abstract:
- lang: eng
text: Given a connected graph $G$, let a $dT$-spanning tree of $G$ be a spanning
tree of $G$ of maximum degree bounded by $dT$. It is well known that for each
$dT ge 2$ the problem of deciding whether a connected graph has a $dT$-spanning
tree is NP-complete. In this paper we investigate this problem when additionally
connectivity and maximum degree of the graph are given. A complete characterization
of this problem for 2- and 3-connected graphs, for planar graphs, and for $dT=2$
is provided. Our first result is that given a biconnected graph of maximum degree
$2dT-2$, we can find its $dT$-spanning tree in time $O(m+n^3/2)$. For graphs of
higher connectivity we design a polynomial-time algorithm that finds a $dT$-spanning
tree in any $k$-connected graph of maximum degree $k(dT-2)+2$. On the other hand,
we prove that deciding whether a $k$-connected graph of maximum degree $k(dT-2)+3$
has a $dT$-spanning tree is NP-complete, provided $k le 3$. For arbitrary $k ge
3$ we show that verifying whether a $k$-connected graph of maximum degree $k(dT-1)$
has a $dT$-spanning tree is NP-complete. In particular, we prove that the Hamiltonian
path (cycle) problem is NP-complete for $k$-connected $k$-regular graphs, if $k>2$.
This extends the well known result for $k=3$ and fully characterizes the case
$dT=2$. For planar graphs it is NP-complete to decide whether a $k$-connected
planar graph of maximum degree $dG$ has a $dT$-spanning tree for $k=1$ and $dG
> dT ge 2$, for $k=2$ and $dG > 2(dT-1) ge 2$, and for $k=3$ and $dG > dT = 2$.
On the other hand, we show how to find in polynomial (linear or almost linear)
time a $dT$-spanning tree for all other parameters of $k$, $dG$, and $dT$.
author:
- first_name: Artur
full_name: Czumaj, Artur
last_name: Czumaj
- first_name: Willy-Bernhard
full_name: Strothmann, Willy-Bernhard
last_name: Strothmann
citation:
ama: 'Czumaj A, Strothmann W-B. Bounded degree spanning trees. In: Proceedings
of the Fifth Annual European Symposium on Algorithms (ESA’97). ; 1997. doi:10.1007/3-540-63397-9_9'
apa: Czumaj, A., & Strothmann, W.-B. (1997). Bounded degree spanning trees.
Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97).
https://doi.org/10.1007/3-540-63397-9_9
bibtex: '@inproceedings{Czumaj_Strothmann_1997, title={Bounded degree spanning trees},
DOI={10.1007/3-540-63397-9_9},
booktitle={Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)},
author={Czumaj, Artur and Strothmann, Willy-Bernhard}, year={1997} }'
chicago: Czumaj, Artur, and Willy-Bernhard Strothmann. “Bounded Degree Spanning
Trees.” In Proceedings of the Fifth Annual European Symposium on Algorithms
(ESA’97), 1997. https://doi.org/10.1007/3-540-63397-9_9.
ieee: 'A. Czumaj and W.-B. Strothmann, “Bounded degree spanning trees,” 1997, doi:
10.1007/3-540-63397-9_9.'
mla: Czumaj, Artur, and Willy-Bernhard Strothmann. “Bounded Degree Spanning Trees.”
Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97),
1997, doi:10.1007/3-540-63397-9_9.
short: 'A. Czumaj, W.-B. Strothmann, in: Proceedings of the Fifth Annual European
Symposium on Algorithms (ESA’97), 1997.'
date_created: 2020-10-05T07:13:42Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '63'
doi: 10.1007/3-540-63397-9_9
language:
- iso: eng
publication: Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97)
publication_identifier:
isbn:
- '9783540633976'
- '9783540695363'
issn:
- 0302-9743
- 1611-3349
publication_status: published
status: public
title: Bounded degree spanning trees
type: conference
user_id: '15415'
year: '1997'
...
---
_id: '3029'
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
citation:
ama: 'Blömer J. Denesting by bounded degree radicals. In: Algorithms — ESA ’97.
Berlin, Heidelberg: Springer Berlin Heidelberg; 1997:53-63. doi:10.1007/3-540-63397-9_5'
apa: 'Blömer, J. (1997). Denesting by bounded degree radicals. In Algorithms
— ESA ’97 (pp. 53–63). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-63397-9_5'
bibtex: '@inbook{Blömer_1997, place={Berlin, Heidelberg}, title={Denesting by bounded
degree radicals}, DOI={10.1007/3-540-63397-9_5},
booktitle={Algorithms — ESA ’97}, publisher={Springer Berlin Heidelberg}, author={Blömer,
Johannes}, year={1997}, pages={53–63} }'
chicago: 'Blömer, Johannes. “Denesting by Bounded Degree Radicals.” In Algorithms
— ESA ’97, 53–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. https://doi.org/10.1007/3-540-63397-9_5.'
ieee: 'J. Blömer, “Denesting by bounded degree radicals,” in Algorithms — ESA
’97, Berlin, Heidelberg: Springer Berlin Heidelberg, 1997, pp. 53–63.'
mla: Blömer, Johannes. “Denesting by Bounded Degree Radicals.” Algorithms — ESA
’97, Springer Berlin Heidelberg, 1997, pp. 53–63, doi:10.1007/3-540-63397-9_5.
short: 'J. Blömer, in: Algorithms — ESA ’97, Springer Berlin Heidelberg, Berlin,
Heidelberg, 1997, pp. 53–63.'
date_created: 2018-06-05T08:30:40Z
date_updated: 2022-01-06T06:58:52Z
ddc:
- '000'
department:
- _id: '64'
doi: 10.1007/3-540-63397-9_5
file:
- access_level: closed
content_type: application/pdf
creator: feidens
date_created: 2018-06-05T08:31:35Z
date_updated: 2018-06-05T08:31:35Z
file_id: '3030'
file_name: DenestingByBoundedDegreeRevised.pdf
file_size: 1656133
relation: main_file
success: 1
file_date_updated: 2018-06-05T08:31:35Z
has_accepted_license: '1'
page: 53-63
place: Berlin, Heidelberg
publication: Algorithms — ESA '97
publication_identifier:
isbn:
- '9783540633976'
- '9783540695363'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Denesting by bounded degree radicals
type: book_chapter
user_id: '25078'
year: '1997'
...
---
_id: '16568'
abstract:
- lang: eng
text: "We present a data structure problem which describes the requirements of a
simple variant of fully dynamic walk-through animation: We assume the scene to
consist of unit size balls in R2 or higher dimensions. The scene may be arbitrarily
large and has to be stored in secondary memory (discs) with relatively slow access.
We allow a visitor to walk in the scene, and a modeler to update the scene by
insertions and deletions of balls. We focus on the realtime requirement of animation
systems: For some t (specified by the computation power of (the rendering hardware
of) the graphic workstation) the data structure has to guarantee that the balls
within distance t of the current visitor's position are presented to the rendering
hardware, 20 times per second. Insertions and deletions should also be available
to the visitor with small delay, independent of the size of the scene. We present
a data structure that fulfills the above task in realtime. Its runtime is output-sensitive,
i.e. linear in a quantity close to the output size of the query. We further present
(preliminary) experimental results indicating that our structure is efficient
in practice.\r\n"
author:
- first_name: Matthias
full_name: Fischer, Matthias
id: '146'
last_name: Fischer
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Willy-Bernhard
full_name: Strothmann, Willy-Bernhard
last_name: Strothmann
citation:
ama: 'Fischer M, Meyer auf der Heide F, Strothmann W-B. Dynamic data structures
for realtime management of large geometric scenes. In: 5th Annual European
Symposium on Algorithms (ESA ’97). Vol 1284. Lecture Notes in Computer Science.
Springer; 1997:157-170. doi:10.1007/3-540-63397-9_13'
apa: Fischer, M., Meyer auf der Heide, F., & Strothmann, W.-B. (1997). Dynamic
data structures for realtime management of large geometric scenes. 5th Annual
European Symposium on Algorithms (ESA ’97), 1284, 157–170. https://doi.org/10.1007/3-540-63397-9_13
bibtex: '@inproceedings{Fischer_Meyer auf der Heide_Strothmann_1997, place={Berlin,
Heidelberg}, series={Lecture Notes in Computer Science}, title={Dynamic data structures
for realtime management of large geometric scenes}, volume={1284}, DOI={10.1007/3-540-63397-9_13},
booktitle={5th Annual European Symposium on Algorithms (ESA ’97)}, publisher={Springer},
author={Fischer, Matthias and Meyer auf der Heide, Friedhelm and Strothmann, Willy-Bernhard},
year={1997}, pages={157–170}, collection={Lecture Notes in Computer Science} }'
chicago: 'Fischer, Matthias, Friedhelm Meyer auf der Heide, and Willy-Bernhard Strothmann.
“Dynamic Data Structures for Realtime Management of Large Geometric Scenes.” In
5th Annual European Symposium on Algorithms (ESA ’97), 1284:157–70. Lecture
Notes in Computer Science. Berlin, Heidelberg: Springer, 1997. https://doi.org/10.1007/3-540-63397-9_13.'
ieee: 'M. Fischer, F. Meyer auf der Heide, and W.-B. Strothmann, “Dynamic data structures
for realtime management of large geometric scenes,” in 5th Annual European
Symposium on Algorithms (ESA ’97), 1997, vol. 1284, pp. 157–170, doi: 10.1007/3-540-63397-9_13.'
mla: Fischer, Matthias, et al. “Dynamic Data Structures for Realtime Management
of Large Geometric Scenes.” 5th Annual European Symposium on Algorithms (ESA
’97), vol. 1284, Springer, 1997, pp. 157–70, doi:10.1007/3-540-63397-9_13.
short: 'M. Fischer, F. Meyer auf der Heide, W.-B. Strothmann, in: 5th Annual European
Symposium on Algorithms (ESA ’97), Springer, Berlin, Heidelberg, 1997, pp. 157–170.'
date_created: 2020-04-15T11:44:36Z
date_updated: 2026-02-23T16:05:33Z
department:
- _id: '63'
doi: 10.1007/3-540-63397-9_13
intvolume: ' 1284'
language:
- iso: eng
page: 157-170
place: Berlin, Heidelberg
publication: 5th Annual European Symposium on Algorithms (ESA '97)
publication_identifier:
isbn:
- '9783540633976'
- '9783540695363'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer
series_title: Lecture Notes in Computer Science
status: public
title: Dynamic data structures for realtime management of large geometric scenes
type: conference
user_id: '14972'
volume: 1284
year: '1997'
...