[{"language":[{"iso":"eng"}],"_id":"19869","user_id":"15415","department":[{"_id":"63"}],"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 $dT$."}],"status":"public","type":"conference","publication":"Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97)","title":"Bounded degree spanning trees","doi":"10.1007/3-540-63397-9_9","date_updated":"2022-01-06T06:54:14Z","author":[{"first_name":"Artur","full_name":"Czumaj, Artur","last_name":"Czumaj"},{"full_name":"Strothmann, Willy-Bernhard","last_name":"Strothmann","first_name":"Willy-Bernhard"}],"date_created":"2020-10-05T07:13:42Z","year":"1997","citation":{"ama":"Czumaj A, Strothmann W-B. Bounded degree spanning trees. In: <i>Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)</i>. ; 1997. doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_9\">10.1007/3-540-63397-9_9</a>","ieee":"A. Czumaj and W.-B. Strothmann, “Bounded degree spanning trees,” 1997, doi: <a href=\"https://doi.org/10.1007/3-540-63397-9_9\">10.1007/3-540-63397-9_9</a>.","chicago":"Czumaj, Artur, and Willy-Bernhard Strothmann. “Bounded Degree Spanning Trees.” In <i>Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)</i>, 1997. <a href=\"https://doi.org/10.1007/3-540-63397-9_9\">https://doi.org/10.1007/3-540-63397-9_9</a>.","mla":"Czumaj, Artur, and Willy-Bernhard Strothmann. “Bounded Degree Spanning Trees.” <i>Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)</i>, 1997, doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_9\">10.1007/3-540-63397-9_9</a>.","short":"A. Czumaj, W.-B. Strothmann, in: Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97), 1997.","bibtex":"@inproceedings{Czumaj_Strothmann_1997, title={Bounded degree spanning trees}, DOI={<a href=\"https://doi.org/10.1007/3-540-63397-9_9\">10.1007/3-540-63397-9_9</a>}, booktitle={Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)}, author={Czumaj, Artur and Strothmann, Willy-Bernhard}, year={1997} }","apa":"Czumaj, A., &#38; Strothmann, W.-B. (1997). Bounded degree spanning trees. <i>Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97)</i>. <a href=\"https://doi.org/10.1007/3-540-63397-9_9\">https://doi.org/10.1007/3-540-63397-9_9</a>"},"publication_status":"published","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783540633976","9783540695363"]}},{"year":"1997","title":"Denesting by bounded degree radicals","publisher":"Springer Berlin Heidelberg","date_created":"2018-06-05T08:30:40Z","file":[{"access_level":"closed","file_id":"3030","file_name":"DenestingByBoundedDegreeRevised.pdf","file_size":1656133,"date_created":"2018-06-05T08:31:35Z","creator":"feidens","date_updated":"2018-06-05T08:31:35Z","relation":"main_file","success":1,"content_type":"application/pdf"}],"publication":"Algorithms — ESA '97","ddc":["000"],"place":"Berlin, Heidelberg","citation":{"ama":"Blömer J. Denesting by bounded degree radicals. In: <i>Algorithms — ESA ’97</i>. Berlin, Heidelberg: Springer Berlin Heidelberg; 1997:53-63. doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_5\">10.1007/3-540-63397-9_5</a>","chicago":"Blömer, Johannes. “Denesting by Bounded Degree Radicals.” In <i>Algorithms — ESA ’97</i>, 53–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. <a href=\"https://doi.org/10.1007/3-540-63397-9_5\">https://doi.org/10.1007/3-540-63397-9_5</a>.","ieee":"J. Blömer, “Denesting by bounded degree radicals,” in <i>Algorithms — ESA ’97</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 1997, pp. 53–63.","apa":"Blömer, J. (1997). Denesting by bounded degree radicals. In <i>Algorithms — ESA ’97</i> (pp. 53–63). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/3-540-63397-9_5\">https://doi.org/10.1007/3-540-63397-9_5</a>","short":"J. Blömer, in: Algorithms — ESA ’97, Springer Berlin Heidelberg, Berlin, Heidelberg, 1997, pp. 53–63.","bibtex":"@inbook{Blömer_1997, place={Berlin, Heidelberg}, title={Denesting by bounded degree radicals}, DOI={<a href=\"https://doi.org/10.1007/3-540-63397-9_5\">10.1007/3-540-63397-9_5</a>}, booktitle={Algorithms — ESA ’97}, publisher={Springer Berlin Heidelberg}, author={Blömer, Johannes}, year={1997}, pages={53–63} }","mla":"Blömer, Johannes. “Denesting by Bounded Degree Radicals.” <i>Algorithms — ESA ’97</i>, Springer Berlin Heidelberg, 1997, pp. 53–63, doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_5\">10.1007/3-540-63397-9_5</a>."},"page":"53-63","publication_status":"published","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783540633976","9783540695363"]},"has_accepted_license":"1","doi":"10.1007/3-540-63397-9_5","date_updated":"2022-01-06T06:58:52Z","author":[{"first_name":"Johannes","id":"23","full_name":"Blömer, Johannes","last_name":"Blömer"}],"status":"public","type":"book_chapter","file_date_updated":"2018-06-05T08:31:35Z","_id":"3029","user_id":"25078","department":[{"_id":"64"}]},{"publication_status":"published","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783540633976","9783540695363"]},"citation":{"chicago":"Fischer, Matthias, Friedhelm Meyer auf der Heide, and Willy-Bernhard Strothmann. “Dynamic Data Structures for Realtime Management of Large Geometric Scenes.” In <i>5th Annual European Symposium on Algorithms (ESA ’97)</i>, 1284:157–70. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, 1997. <a href=\"https://doi.org/10.1007/3-540-63397-9_13\">https://doi.org/10.1007/3-540-63397-9_13</a>.","ieee":"M. Fischer, F. Meyer auf der Heide, and W.-B. Strothmann, “Dynamic data structures for realtime management of large geometric scenes,” in <i>5th Annual European Symposium on Algorithms (ESA ’97)</i>, 1997, vol. 1284, pp. 157–170, doi: <a href=\"https://doi.org/10.1007/3-540-63397-9_13\">10.1007/3-540-63397-9_13</a>.","ama":"Fischer M, Meyer auf der Heide F, Strothmann W-B. Dynamic data structures for realtime management of large geometric scenes. In: <i>5th Annual European Symposium on Algorithms (ESA ’97)</i>. Vol 1284. Lecture Notes in Computer Science. Springer; 1997:157-170. doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_13\">10.1007/3-540-63397-9_13</a>","apa":"Fischer, M., Meyer auf der Heide, F., &#38; Strothmann, W.-B. (1997). Dynamic data structures for realtime management of large geometric scenes. <i>5th Annual European Symposium on Algorithms (ESA ’97)</i>, <i>1284</i>, 157–170. <a href=\"https://doi.org/10.1007/3-540-63397-9_13\">https://doi.org/10.1007/3-540-63397-9_13</a>","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.","mla":"Fischer, Matthias, et al. “Dynamic Data Structures for Realtime Management of Large Geometric Scenes.” <i>5th Annual European Symposium on Algorithms (ESA ’97)</i>, vol. 1284, Springer, 1997, pp. 157–70, doi:<a href=\"https://doi.org/10.1007/3-540-63397-9_13\">10.1007/3-540-63397-9_13</a>.","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={<a href=\"https://doi.org/10.1007/3-540-63397-9_13\">10.1007/3-540-63397-9_13</a>}, 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} }"},"intvolume":"      1284","page":"157-170","place":"Berlin, Heidelberg","author":[{"id":"146","full_name":"Fischer, Matthias","last_name":"Fischer","first_name":"Matthias"},{"id":"15523","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide","first_name":"Friedhelm"},{"first_name":"Willy-Bernhard","full_name":"Strothmann, Willy-Bernhard","last_name":"Strothmann"}],"volume":1284,"date_updated":"2026-02-23T16:05:33Z","doi":"10.1007/3-540-63397-9_13","type":"conference","status":"public","series_title":"Lecture Notes in Computer Science","user_id":"14972","department":[{"_id":"63"}],"_id":"16568","year":"1997","date_created":"2020-04-15T11:44:36Z","publisher":"Springer","title":"Dynamic data structures for realtime management of large geometric scenes","publication":"5th Annual European Symposium on Algorithms (ESA '97)","abstract":[{"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","lang":"eng"}],"language":[{"iso":"eng"}]}]