[{"language":[{"iso":"eng"}],"_id":"16504","page":"175-203","doi":"10.1016/s0304-3975(98)00020-6","user_id":"15415","publication_identifier":{"issn":["0304-3975"]},"author":[{"last_name":"Bäumker","first_name":"Armin","full_name":"Bäumker, Armin"},{"last_name":"Dittrich","first_name":"Wolfgang","full_name":"Dittrich, Wolfgang"},{"first_name":"Friedhelm","last_name":"Meyer auf der Heide","full_name":"Meyer auf der Heide, Friedhelm","id":"15523"}],"status":"public","year":"1998","title":"Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model","date_updated":"2022-01-06T06:52:52Z","publication_status":"published","date_created":"2020-04-14T12:36:47Z","department":[{"_id":"63"}],"type":"journal_article","citation":{"apa":"Bäumker, A., Dittrich, W., &#38; Meyer auf der Heide, F. (1998). Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model. <i>Theoretical Computer Science</i>, 175–203. <a href=\"https://doi.org/10.1016/s0304-3975(98)00020-6\">https://doi.org/10.1016/s0304-3975(98)00020-6</a>","ieee":"A. Bäumker, W. Dittrich, and F. Meyer auf der Heide, “Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model,” <i>Theoretical Computer Science</i>, pp. 175–203, 1998.","short":"A. Bäumker, W. Dittrich, F. Meyer auf der Heide, Theoretical Computer Science (1998) 175–203.","chicago":"Bäumker, Armin, Wolfgang Dittrich, and Friedhelm Meyer auf der Heide. “Truly Efficient Parallel Algorithms: 1-Optimal Multisearch for an Extension of the BSP Model.” <i>Theoretical Computer Science</i>, 1998, 175–203. <a href=\"https://doi.org/10.1016/s0304-3975(98)00020-6\">https://doi.org/10.1016/s0304-3975(98)00020-6</a>.","mla":"Bäumker, Armin, et al. “Truly Efficient Parallel Algorithms: 1-Optimal Multisearch for an Extension of the BSP Model.” <i>Theoretical Computer Science</i>, 1998, pp. 175–203, doi:<a href=\"https://doi.org/10.1016/s0304-3975(98)00020-6\">10.1016/s0304-3975(98)00020-6</a>.","ama":"Bäumker A, Dittrich W, Meyer auf der Heide F. Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model. <i>Theoretical Computer Science</i>. 1998:175-203. doi:<a href=\"https://doi.org/10.1016/s0304-3975(98)00020-6\">10.1016/s0304-3975(98)00020-6</a>","bibtex":"@article{Bäumker_Dittrich_Meyer auf der Heide_1998, title={Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model}, DOI={<a href=\"https://doi.org/10.1016/s0304-3975(98)00020-6\">10.1016/s0304-3975(98)00020-6</a>}, journal={Theoretical Computer Science}, author={Bäumker, Armin and Dittrich, Wolfgang and Meyer auf der Heide, Friedhelm}, year={1998}, pages={175–203} }"},"publication":"Theoretical Computer Science"},{"department":[{"_id":"63"}],"type":"book_chapter","date_created":"2020-04-15T10:34:15Z","place":"Berlin, Heidelberg","citation":{"short":"F. Meyer auf der Heide, G.T. Martinez, in: LATIN’98: Theoretical Informatics, Berlin, Heidelberg, 1998.","chicago":"Meyer auf der Heide, Friedhelm, and Gabriel Terán Martinez. “Communication-Efficient Parallel Multiway and Approximate Minimum Cut Computation.” In <i>LATIN’98: Theoretical Informatics</i>. Berlin, Heidelberg, 1998. <a href=\"https://doi.org/10.1007/bfb0054332\">https://doi.org/10.1007/bfb0054332</a>.","ieee":"F. Meyer auf der Heide and G. T. Martinez, “Communication-efficient parallel multiway and approximate minimum cut computation,” in <i>LATIN’98: Theoretical Informatics</i>, Berlin, Heidelberg, 1998.","apa":"Meyer auf der Heide, F., &#38; Martinez, G. T. (1998). Communication-efficient parallel multiway and approximate minimum cut computation. In <i>LATIN’98: Theoretical Informatics</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/bfb0054332\">https://doi.org/10.1007/bfb0054332</a>","bibtex":"@inbook{Meyer auf der Heide_Martinez_1998, place={Berlin, Heidelberg}, title={Communication-efficient parallel multiway and approximate minimum cut computation}, DOI={<a href=\"https://doi.org/10.1007/bfb0054332\">10.1007/bfb0054332</a>}, booktitle={LATIN’98: Theoretical Informatics}, author={Meyer auf der Heide, Friedhelm and Martinez, Gabriel Terán}, year={1998} }","ama":"Meyer auf der Heide F, Martinez GT. Communication-efficient parallel multiway and approximate minimum cut computation. In: <i>LATIN’98: Theoretical Informatics</i>. Berlin, Heidelberg; 1998. doi:<a href=\"https://doi.org/10.1007/bfb0054332\">10.1007/bfb0054332</a>","mla":"Meyer auf der Heide, Friedhelm, and Gabriel Terán Martinez. “Communication-Efficient Parallel Multiway and Approximate Minimum Cut Computation.” <i>LATIN’98: Theoretical Informatics</i>, 1998, doi:<a href=\"https://doi.org/10.1007/bfb0054332\">10.1007/bfb0054332</a>."},"publication":"LATIN'98: Theoretical Informatics","user_id":"15415","doi":"10.1007/bfb0054332","language":[{"iso":"eng"}],"_id":"16562","publication_status":"published","date_updated":"2022-01-06T06:52:52Z","publication_identifier":{"isbn":["9783540642756","9783540697152"],"issn":["0302-9743","1611-3349"]},"author":[{"id":"15523","full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","last_name":"Meyer auf der Heide"},{"last_name":"Martinez","first_name":"Gabriel Terán","full_name":"Martinez, Gabriel Terán"}],"year":"1998","title":"Communication-efficient parallel multiway and approximate minimum cut computation","status":"public"},{"doi":"10.1145/276698.276790","user_id":"15415","_id":"16563","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:52:52Z","publication_status":"published","year":"1998","status":"public","title":"Randomized protocols for low-congestion circuit routing in multistage interconnection networks","author":[{"last_name":"Cole","first_name":"Richard","full_name":"Cole, Richard"},{"last_name":"Maggs","first_name":"Bruce M.","full_name":"Maggs, Bruce M."},{"full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide","first_name":"Friedhelm","id":"15523"},{"full_name":"Mitzenmacher, Michael","last_name":"Mitzenmacher","first_name":"Michael"},{"full_name":"Richa, Andréa W.","last_name":"Richa","first_name":"Andréa W."},{"last_name":"Schröder","first_name":"Klaus","full_name":"Schröder, Klaus"},{"first_name":"Ramesh K.","last_name":"Sitaraman","full_name":"Sitaraman, Ramesh K."},{"full_name":"Vöcking, Berthold","last_name":"Vöcking","first_name":"Berthold"}],"publication_identifier":{"isbn":["0897919629"]},"type":"conference","department":[{"_id":"63"}],"date_created":"2020-04-15T10:38:12Z","publication":"Proceedings of the thirtieth annual ACM symposium on Theory of computing  - STOC '98","citation":{"ieee":"R. Cole <i>et al.</i>, “Randomized protocols for low-congestion circuit routing in multistage interconnection networks,” in <i>Proceedings of the thirtieth annual ACM symposium on Theory of computing  - STOC ’98</i>, 1998.","apa":"Cole, R., Maggs, B. M., Meyer auf der Heide, F., Mitzenmacher, M., Richa, A. W., Schröder, K., … Vöcking, B. (1998). Randomized protocols for low-congestion circuit routing in multistage interconnection networks. In <i>Proceedings of the thirtieth annual ACM symposium on Theory of computing  - STOC ’98</i>. <a href=\"https://doi.org/10.1145/276698.276790\">https://doi.org/10.1145/276698.276790</a>","short":"R. Cole, B.M. Maggs, F. Meyer auf der Heide, M. Mitzenmacher, A.W. Richa, K. Schröder, R.K. Sitaraman, B. Vöcking, in: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing  - STOC ’98, 1998.","chicago":"Cole, Richard, Bruce M. Maggs, Friedhelm Meyer auf der Heide, Michael Mitzenmacher, Andréa W. Richa, Klaus Schröder, Ramesh K. Sitaraman, and Berthold Vöcking. “Randomized Protocols for Low-Congestion Circuit Routing in Multistage Interconnection Networks.” In <i>Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing  - STOC ’98</i>, 1998. <a href=\"https://doi.org/10.1145/276698.276790\">https://doi.org/10.1145/276698.276790</a>.","mla":"Cole, Richard, et al. “Randomized Protocols for Low-Congestion Circuit Routing in Multistage Interconnection Networks.” <i>Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing  - STOC ’98</i>, 1998, doi:<a href=\"https://doi.org/10.1145/276698.276790\">10.1145/276698.276790</a>.","bibtex":"@inproceedings{Cole_Maggs_Meyer auf der Heide_Mitzenmacher_Richa_Schröder_Sitaraman_Vöcking_1998, title={Randomized protocols for low-congestion circuit routing in multistage interconnection networks}, DOI={<a href=\"https://doi.org/10.1145/276698.276790\">10.1145/276698.276790</a>}, booktitle={Proceedings of the thirtieth annual ACM symposium on Theory of computing  - STOC ’98}, author={Cole, Richard and Maggs, Bruce M. and Meyer auf der Heide, Friedhelm and Mitzenmacher, Michael and Richa, Andréa W. and Schröder, Klaus and Sitaraman, Ramesh K. and Vöcking, Berthold}, year={1998} }","ama":"Cole R, Maggs BM, Meyer auf der Heide F, et al. Randomized protocols for low-congestion circuit routing in multistage interconnection networks. In: <i>Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing  - STOC ’98</i>. ; 1998. doi:<a href=\"https://doi.org/10.1145/276698.276790\">10.1145/276698.276790</a>"}},{"citation":{"bibtex":"@book{Bäumker_1997, series={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, title={Communication Efficient Parallel Searching}, volume={28}, publisher={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, author={Bäumker, Armin}, year={1997}, collection={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn} }","ama":"Bäumker A. <i>Communication Efficient Parallel Searching</i>. Vol 28. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn; 1997.","mla":"Bäumker, Armin. <i>Communication Efficient Parallel Searching</i>. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","chicago":"Bäumker, Armin. <i>Communication Efficient Parallel Searching</i>. Vol. 28. Verlagsschriftenreihe Des Heinz Nixdorf Instituts, Paderborn. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","short":"A. Bäumker, Communication Efficient Parallel Searching, Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","ieee":"A. Bäumker, <i>Communication Efficient Parallel Searching</i>, vol. 28. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","apa":"Bäumker, A. (1997). <i>Communication Efficient Parallel Searching</i> (Vol. 28). Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn."},"supervisor":[{"id":"15523","first_name":"Friedhelm","last_name":"Meyer auf der Heide","full_name":"Meyer auf der Heide, Friedhelm"}],"date_created":"2020-09-22T12:46:17Z","type":"dissertation","department":[{"_id":"63"},{"_id":"26"}],"status":"public","year":"1997","title":"Communication Efficient Parallel Searching","author":[{"full_name":"Bäumker, Armin","last_name":"Bäumker","first_name":"Armin"}],"publication_identifier":{"isbn":["3-931466-27-2"]},"date_updated":"2022-01-06T06:54:09Z","intvolume":"        28","_id":"19631","series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","language":[{"iso":"eng"}],"user_id":"5786","volume":28},{"volume":27,"user_id":"5786","language":[{"iso":"eng"}],"_id":"19636","series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","intvolume":"        27","date_updated":"2022-01-06T06:54:09Z","author":[{"full_name":"Dittrich, Wolfgang","last_name":"Dittrich","first_name":"Wolfgang"}],"publication_identifier":{"isbn":["3-931466-26-4"]},"title":"Communication and I/O Efficient Parallel Data Structures","status":"public","year":"1997","department":[{"_id":"63"},{"_id":"26"}],"type":"dissertation","date_created":"2020-09-22T12:53:00Z","citation":{"ama":"Dittrich W. <i>Communication and I/O Efficient Parallel Data Structures</i>. Vol 27. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn; 1997.","bibtex":"@book{Dittrich_1997, series={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, title={Communication and I/O Efficient Parallel Data Structures}, volume={27}, publisher={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, author={Dittrich, Wolfgang}, year={1997}, collection={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn} }","mla":"Dittrich, Wolfgang. <i>Communication and I/O Efficient Parallel Data Structures</i>. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","short":"W. Dittrich, Communication and I/O Efficient Parallel Data Structures, Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","chicago":"Dittrich, Wolfgang. <i>Communication and I/O Efficient Parallel Data Structures</i>. Vol. 27. Verlagsschriftenreihe Des Heinz Nixdorf Instituts, Paderborn. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","apa":"Dittrich, W. (1997). <i>Communication and I/O Efficient Parallel Data Structures</i> (Vol. 27). Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn.","ieee":"W. Dittrich, <i>Communication and I/O Efficient Parallel Data Structures</i>, vol. 27. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997."},"supervisor":[{"id":"15523","full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","last_name":"Meyer auf der Heide"}]},{"language":[{"iso":"eng"}],"series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","date_updated":"2022-01-06T06:54:09Z","intvolume":"        35","title":"Bounded Degree Spanning Trees","year":"1997","publication_identifier":{"isbn":["3-931466-34-5"]},"author":[{"last_name":"Strothmann","first_name":"Willy-Bernhard","full_name":"Strothmann, Willy-Bernhard"}],"type":"dissertation","department":[{"_id":"63"},{"_id":"26"}],"file":[{"date_updated":"2020-09-22T12:57:43Z","relation":"main_file","file_size":1172216,"access_level":"closed","file_name":"pub-hni-468.pdf","content_type":"application/pdf","success":1,"file_id":"19638","creator":"koala","date_created":"2020-09-22T12:57:43Z"}],"date_created":"2020-09-22T12:57:53Z","user_id":"5786","ddc":["000"],"volume":35,"publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","_id":"19637","has_accepted_license":"1","status":"public","file_date_updated":"2020-09-22T12:57:43Z","citation":{"ieee":"W.-B. Strothmann, <i>Bounded Degree Spanning Trees</i>, vol. 35. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","apa":"Strothmann, W.-B. (1997). <i>Bounded Degree Spanning Trees</i> (Vol. 35). Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn.","chicago":"Strothmann, Willy-Bernhard. <i>Bounded Degree Spanning Trees</i>. Vol. 35. Verlagsschriftenreihe Des Heinz Nixdorf Instituts, Paderborn. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","short":"W.-B. Strothmann, Bounded Degree Spanning Trees, Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","mla":"Strothmann, Willy-Bernhard. <i>Bounded Degree Spanning Trees</i>. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","bibtex":"@book{Strothmann_1997, series={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, title={Bounded Degree Spanning Trees}, volume={35}, publisher={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}, author={Strothmann, Willy-Bernhard}, year={1997}, collection={Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn} }","ama":"Strothmann W-B. <i>Bounded Degree Spanning Trees</i>. Vol 35. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn; 1997."},"supervisor":[{"id":"15523","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide","first_name":"Friedhelm"}]},{"language":[{"iso":"eng"}],"_id":"19869","user_id":"15415","doi":"10.1007/3-540-63397-9_9","title":"Bounded degree spanning trees","year":"1997","status":"public","author":[{"full_name":"Czumaj, Artur","first_name":"Artur","last_name":"Czumaj"},{"full_name":"Strothmann, Willy-Bernhard","last_name":"Strothmann","first_name":"Willy-Bernhard"}],"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783540633976","9783540695363"]},"publication_status":"published","date_updated":"2022-01-06T06:54:14Z","date_created":"2020-10-05T07:13:42Z","type":"conference","department":[{"_id":"63"}],"publication":"Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97)","citation":{"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>.","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} }","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>.","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>","short":"A. Czumaj, W.-B. Strothmann, in: Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97), 1997.","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>."},"abstract":[{"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 $dT$.","lang":"eng"}]},{"year":"1997","title":"Decremental Biconnectivity on Planar Graphs","status":"public","author":[{"last_name":"Strothmann","first_name":"Willy-Bernhard","full_name":"Strothmann, Willy-Bernhard"},{"full_name":"Lukovszki, Tamás","first_name":"Tamás","last_name":"Lukovszki"}],"date_updated":"2022-01-06T06:53:55Z","has_accepted_license":"1","_id":"18955","language":[{"iso":"eng"}],"user_id":"15415","ddc":["000"],"file_date_updated":"2020-09-03T12:59:44Z","citation":{"mla":"Strothmann, Willy-Bernhard, and Tamás Lukovszki. <i>Decremental Biconnectivity on Planar Graphs</i>. 1997.","bibtex":"@book{Strothmann_Lukovszki_1997, place={Paderborn}, title={Decremental Biconnectivity on Planar Graphs}, author={Strothmann, Willy-Bernhard and Lukovszki, Tamás}, year={1997} }","ama":"Strothmann W-B, Lukovszki T. <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn; 1997.","ieee":"W.-B. Strothmann and T. Lukovszki, <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn, 1997.","apa":"Strothmann, W.-B., &#38; Lukovszki, T. (1997). <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn.","short":"W.-B. Strothmann, T. Lukovszki, Decremental Biconnectivity on Planar Graphs, Paderborn, 1997.","chicago":"Strothmann, Willy-Bernhard, and Tamás Lukovszki. <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn, 1997."},"abstract":[{"lang":"eng","text":"In this paper we present a (randomized) algorithm for maintaining the biconnected components of a dynamic planar graph of $n$ vertices under deletions of edges. The biconnected components can be maintained under any sequence of edge deletions in a total of $O(n log n)$ time, with high probability. This gives $O(log n)$ amortized time per edge deletion, which improves previous (deterministic) results due to Giammarresi and Italiano, where $O(n log^2 n)$ amortized time is needed. Our work describes a simplification of the data structures from [GiIt96] and uses dynamic perfect hashing to reduce the running time. As in the paper by Giammarresi and Italiano, we only need $O(n)$ space. Finally we describe some simply additional operations on the decremental data structure. By aid of them this the data structure is applicable for finding efficiently a $Delta$-spanning tree in a biconnected planar graph with a maximum degree $2Delta-2$ do to Czumaj and Strothmann."}],"file":[{"date_updated":"2020-09-03T12:59:44Z","relation":"main_file","access_level":"closed","file_size":222106,"file_name":"pub-hni-901.pdf","content_type":"application/pdf","success":1,"file_id":"18957","creator":"koala","date_created":"2020-09-03T12:59:44Z"}],"date_created":"2020-09-03T12:59:56Z","place":"Paderborn","type":"report","department":[{"_id":"63"}]},{"page":"39-43","_id":"18575","language":[{"iso":"eng"}],"user_id":"15415","year":"1997","status":"public","title":"Encoding a Triangulation as a Permutation of its Point Set","author":[{"last_name":"Sohler","first_name":"Christian","full_name":"Sohler, Christian"},{"first_name":"Markus","last_name":"Denny","full_name":"Denny, Markus"}],"date_updated":"2022-01-06T06:53:40Z","date_created":"2020-08-28T14:14:57Z","type":"conference","department":[{"_id":"63"}],"publication":"Proceedings of the 9th Canadian Conference on Computational Geometry","citation":{"ama":"Sohler C, Denny M. Encoding a Triangulation as a Permutation of its Point Set. In: <i>Proceedings of the 9th Canadian Conference on Computational Geometry</i>. ; 1997:39-43.","bibtex":"@inproceedings{Sohler_Denny_1997, title={Encoding a Triangulation as a Permutation of its Point Set}, booktitle={Proceedings of the 9th Canadian Conference on Computational Geometry}, author={Sohler, Christian and Denny, Markus}, year={1997}, pages={39–43} }","mla":"Sohler, Christian, and Markus Denny. “Encoding a Triangulation as a Permutation of Its Point Set.” <i>Proceedings of the 9th Canadian Conference on Computational Geometry</i>, 1997, pp. 39–43.","chicago":"Sohler, Christian, and Markus Denny. “Encoding a Triangulation as a Permutation of Its Point Set.” In <i>Proceedings of the 9th Canadian Conference on Computational Geometry</i>, 39–43, 1997.","short":"C. Sohler, M. Denny, in: Proceedings of the 9th Canadian Conference on Computational Geometry, 1997, pp. 39–43.","apa":"Sohler, C., &#38; Denny, M. (1997). Encoding a Triangulation as a Permutation of its Point Set. In <i>Proceedings of the 9th Canadian Conference on Computational Geometry</i> (pp. 39–43).","ieee":"C. Sohler and M. 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