[{"page":"175-203","_id":"16504","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-14T12:36:47Z","publication":"Theoretical Computer Science","language":[{"iso":"eng"}],"year":"1998","publication_identifier":{"issn":["0304-3975"]},"type":"journal_article","status":"public","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>","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>","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>.","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.","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>.","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} }","short":"A. Bäumker, W. Dittrich, F. Meyer auf der Heide, Theoretical Computer Science (1998) 175–203."},"publication_status":"published","user_id":"15415","department":[{"_id":"63"}],"title":"Truly efficient parallel algorithms: 1-optimal multisearch for an extension of the BSP model","author":[{"last_name":"Bäumker","first_name":"Armin","full_name":"Bäumker, Armin"},{"last_name":"Dittrich","full_name":"Dittrich, Wolfgang","first_name":"Wolfgang"},{"id":"15523","last_name":"Meyer auf der Heide","first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm"}],"doi":"10.1016/s0304-3975(98)00020-6"},{"department":[{"_id":"63"}],"publication_status":"published","user_id":"15415","citation":{"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} }","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>.","short":"F. Meyer auf der Heide, G.T. Martinez, in: LATIN’98: Theoretical Informatics, Berlin, Heidelberg, 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>","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>","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.","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>."},"doi":"10.1007/bfb0054332","place":"Berlin, Heidelberg","author":[{"first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide","id":"15523"},{"last_name":"Martinez","first_name":"Gabriel Terán","full_name":"Martinez, Gabriel Terán"}],"title":"Communication-efficient parallel multiway and approximate minimum cut computation","date_updated":"2022-01-06T06:52:52Z","_id":"16562","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783540642756","9783540697152"]},"year":"1998","type":"book_chapter","date_created":"2020-04-15T10:34:15Z","publication":"LATIN'98: Theoretical Informatics"},{"doi":"10.1145/276698.276790","title":"Randomized protocols for low-congestion circuit routing in multistage interconnection networks","author":[{"last_name":"Cole","full_name":"Cole, Richard","first_name":"Richard"},{"first_name":"Bruce M.","full_name":"Maggs, Bruce M.","last_name":"Maggs"},{"id":"15523","last_name":"Meyer auf der Heide","full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm"},{"full_name":"Mitzenmacher, Michael","first_name":"Michael","last_name":"Mitzenmacher"},{"first_name":"Andréa W.","full_name":"Richa, Andréa W.","last_name":"Richa"},{"first_name":"Klaus","full_name":"Schröder, Klaus","last_name":"Schröder"},{"last_name":"Sitaraman","first_name":"Ramesh K.","full_name":"Sitaraman, Ramesh K."},{"full_name":"Vöcking, Berthold","first_name":"Berthold","last_name":"Vöcking"}],"department":[{"_id":"63"}],"citation":{"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>","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>","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.","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>.","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} }","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>.","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."},"user_id":"15415","publication_status":"published","year":"1998","publication_identifier":{"isbn":["0897919629"]},"type":"conference","language":[{"iso":"eng"}],"status":"public","publication":"Proceedings of the thirtieth annual ACM symposium on Theory of computing  - STOC '98","date_created":"2020-04-15T10:38:12Z","date_updated":"2022-01-06T06:52:52Z","_id":"16563"},{"department":[{"_id":"63"},{"_id":"26"}],"series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","citation":{"apa":"Bäumker, A. (1997). <i>Communication Efficient Parallel Searching</i> (Vol. 28). Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn.","ama":"Bäumker A. <i>Communication Efficient Parallel Searching</i>. Vol 28. 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.","ieee":"A. Bäumker, <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.","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} }","short":"A. Bäumker, Communication Efficient Parallel Searching, Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997."},"user_id":"5786","supervisor":[{"id":"15523","last_name":"Meyer auf der Heide","full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm"}],"intvolume":"        28","title":"Communication Efficient Parallel Searching","author":[{"last_name":"Bäumker","first_name":"Armin","full_name":"Bäumker, Armin"}],"date_updated":"2022-01-06T06:54:09Z","_id":"19631","volume":28,"publication_identifier":{"isbn":["3-931466-27-2"]},"type":"dissertation","year":"1997","language":[{"iso":"eng"}],"status":"public","date_created":"2020-09-22T12:46:17Z","publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn"},{"author":[{"last_name":"Dittrich","first_name":"Wolfgang","full_name":"Dittrich, Wolfgang"}],"title":"Communication and I/O Efficient Parallel Data Structures","intvolume":"        27","supervisor":[{"first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide","id":"15523"}],"user_id":"5786","citation":{"short":"W. Dittrich, Communication and I/O Efficient Parallel Data Structures, Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","mla":"Dittrich, Wolfgang. <i>Communication and I/O Efficient Parallel Data Structures</i>. 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} }","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.","ieee":"W. Dittrich, <i>Communication and I/O Efficient Parallel Data Structures</i>, vol. 27. 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.","ama":"Dittrich W. <i>Communication and I/O Efficient Parallel Data Structures</i>. Vol 27. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn; 1997."},"series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","department":[{"_id":"63"},{"_id":"26"}],"publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","date_created":"2020-09-22T12:53:00Z","status":"public","language":[{"iso":"eng"}],"type":"dissertation","publication_identifier":{"isbn":["3-931466-26-4"]},"year":"1997","volume":27,"_id":"19636","date_updated":"2022-01-06T06:54:09Z"},{"series_title":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","citation":{"ieee":"W.-B. Strothmann, <i>Bounded Degree Spanning Trees</i>, vol. 35. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997.","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.","ama":"Strothmann W-B. <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.","short":"W.-B. Strothmann, Bounded Degree Spanning Trees, 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} }","mla":"Strothmann, Willy-Bernhard. <i>Bounded Degree Spanning Trees</i>. Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn, 1997."},"department":[{"_id":"63"},{"_id":"26"}],"author":[{"last_name":"Strothmann","first_name":"Willy-Bernhard","full_name":"Strothmann, Willy-Bernhard"}],"supervisor":[{"full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","id":"15523","last_name":"Meyer auf der Heide"}],"intvolume":"        35","file_date_updated":"2020-09-22T12:57:43Z","_id":"19637","date_updated":"2022-01-06T06:54:09Z","publisher":"Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn","date_created":"2020-09-22T12:57:53Z","status":"public","year":"1997","publication_identifier":{"isbn":["3-931466-34-5"]},"language":[{"iso":"eng"}],"user_id":"5786","file":[{"relation":"main_file","date_updated":"2020-09-22T12:57:43Z","success":1,"creator":"koala","file_size":1172216,"file_name":"pub-hni-468.pdf","access_level":"closed","content_type":"application/pdf","file_id":"19638","date_created":"2020-09-22T12:57:43Z"}],"title":"Bounded Degree Spanning Trees","has_accepted_license":"1","volume":35,"ddc":["000"],"type":"dissertation"},{"date_updated":"2022-01-06T06:54:14Z","_id":"19869","status":"public","type":"conference","publication_identifier":{"isbn":["9783540633976","9783540695363"],"issn":["0302-9743","1611-3349"]},"year":"1997","language":[{"iso":"eng"}],"publication":"Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97)","date_created":"2020-10-05T07:13:42Z","department":[{"_id":"63"}],"user_id":"15415","publication_status":"published","citation":{"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>","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>","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>.","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>.","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} }","short":"A. Czumaj, W.-B. Strothmann, in: Proceedings of the Fifth Annual European Symposium on Algorithms (ESA’97), 1997."},"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"}],"doi":"10.1007/3-540-63397-9_9","author":[{"last_name":"Czumaj","first_name":"Artur","full_name":"Czumaj, Artur"},{"first_name":"Willy-Bernhard","full_name":"Strothmann, Willy-Bernhard","last_name":"Strothmann"}],"title":"Bounded degree spanning trees"},{"citation":{"ieee":"W.-B. Strothmann and T. Lukovszki, <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn, 1997.","chicago":"Strothmann, Willy-Bernhard, and Tamás 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.","ama":"Strothmann W-B, Lukovszki T. <i>Decremental Biconnectivity on Planar Graphs</i>. Paderborn; 1997.","short":"W.-B. Strothmann, T. Lukovszki, Decremental Biconnectivity on Planar Graphs, Paderborn, 1997.","bibtex":"@book{Strothmann_Lukovszki_1997, place={Paderborn}, title={Decremental Biconnectivity on Planar Graphs}, author={Strothmann, Willy-Bernhard and Lukovszki, Tamás}, year={1997} }","mla":"Strothmann, Willy-Bernhard, and Tamás Lukovszki. <i>Decremental Biconnectivity on Planar Graphs</i>. 1997."},"user_id":"15415","department":[{"_id":"63"}],"title":"Decremental Biconnectivity on Planar Graphs","author":[{"last_name":"Strothmann","full_name":"Strothmann, Willy-Bernhard","first_name":"Willy-Bernhard"},{"first_name":"Tamás","full_name":"Lukovszki, Tamás","last_name":"Lukovszki"}],"file":[{"file_name":"pub-hni-901.pdf","file_size":222106,"creator":"koala","date_created":"2020-09-03T12:59:44Z","access_level":"closed","file_id":"18957","content_type":"application/pdf","date_updated":"2020-09-03T12:59:44Z","relation":"main_file","success":1}],"place":"Paderborn","abstract":[{"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.","lang":"eng"}],"has_accepted_license":"1","_id":"18955","file_date_updated":"2020-09-03T12:59:44Z","date_updated":"2022-01-06T06:53:55Z","date_created":"2020-09-03T12:59:56Z","ddc":["000"],"language":[{"iso":"eng"}],"type":"report","year":"1997","status":"public"},{"year":"1997","type":"conference","language":[{"iso":"eng"}],"status":"public","publication":"Proceedings of the 9th Canadian Conference on Computational Geometry","date_created":"2020-08-28T14:14:57Z","date_updated":"2022-01-06T06:53:40Z","_id":"18575","page":"39-43","title":"Encoding a Triangulation as a Permutation of its Point Set","author":[{"last_name":"Sohler","first_name":"Christian","full_name":"Sohler, Christian"},{"full_name":"Denny, Markus","first_name":"Markus","last_name":"Denny"}],"department":[{"_id":"63"}],"citation":{"ama":"Sohler C, Denny M. 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Denny, “Encoding a Triangulation as a Permutation of its Point Set,” in <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.","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.","short":"C. Sohler, M. 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Exploiting locality for data management in systems of limited bandwidth. In: <i>Proceedings 38th Annual Symposium on Foundations of Computer Science</i>. ; 1997. doi:<a href=\"https://doi.org/10.1109/sfcs.1997.646117\">10.1109/sfcs.1997.646117</a>","apa":"Maggs, B. M., Meyer auf der Heide, F., Vöcking, B., &#38; Westermann, M. (1997). Exploiting locality for data management in systems of limited bandwidth. <i>Proceedings 38th Annual Symposium on Foundations of Computer Science</i>. <a href=\"https://doi.org/10.1109/sfcs.1997.646117\">https://doi.org/10.1109/sfcs.1997.646117</a>","ieee":"B. M. Maggs, F. Meyer auf der Heide, B. Vöcking, and M. 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Parallel Computing in Paderborn: The SFB 376 “Massive Parallelism — Algorithms, Design Methods, Applications.” In: <i>Informatik ’97 Informatik Als Innovationsmotor</i>. Berlin, Heidelberg; 1997. doi:<a href=\"https://doi.org/10.1007/978-3-642-60831-5_22\">10.1007/978-3-642-60831-5_22</a>","apa":"Meyer auf der Heide, F., &#38; Decker, T. (1997). Parallel Computing in Paderborn: The SFB 376 “Massive Parallelism — Algorithms, Design Methods, Applications.” In <i>Informatik ’97 Informatik als Innovationsmotor</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-60831-5_22\">https://doi.org/10.1007/978-3-642-60831-5_22</a>","ieee":"F. Meyer auf der Heide and T. Decker, “Parallel Computing in Paderborn: The SFB 376 ‘Massive Parallelism — Algorithms, Design Methods, Applications,’” in <i>Informatik ’97 Informatik als Innovationsmotor</i>, Berlin, Heidelberg, 1997.","chicago":"Meyer auf der Heide, Friedhelm, and Thomas Decker. “Parallel Computing in Paderborn: The SFB 376 ‘Massive Parallelism — Algorithms, Design Methods, Applications.’” In <i>Informatik ’97 Informatik Als Innovationsmotor</i>. 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Decker, in: Informatik ’97 Informatik Als Innovationsmotor, Berlin, Heidelberg, 1997."},"user_id":"15415","publication_status":"published","department":[{"_id":"63"}],"publication":"Informatik ’97 Informatik als Innovationsmotor","date_created":"2020-04-16T10:48:16Z","year":"1997","publication_identifier":{"issn":["1431-472X"],"isbn":["9783540630661","9783642608315"]},"type":"book_chapter","language":[{"iso":"eng"}],"status":"public","_id":"16693","date_updated":"2022-01-06T06:52:54Z"}]