[{"title":"Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots","abstract":[{"text":"Approximate computing has shown to provide new ways to improve performance\r\nand power consumption of error-resilient applications. While many of these\r\napplications can be found in image processing, data classification or machine\r\nlearning, we demonstrate its suitability to a problem from scientific\r\ncomputing. Utilizing the self-correcting behavior of iterative algorithms, we\r\nshow that approximate computing can be applied to the calculation of inverse\r\nmatrix p-th roots which are required in many applications in scientific\r\ncomputing. Results show great opportunities to reduce the computational effort\r\nand bandwidth required for the execution of the discussed algorithm, especially\r\nwhen targeting special accelerator hardware.","lang":"eng"}],"doi":"10.1109/LES.2017.2760923","project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1"},{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"user_id":"16153","external_id":{"arxiv":["1703.02283"]},"publication":"Embedded Systems Letters","type":"journal_article","volume":10,"page":" 33-36","issue":"2","author":[{"orcid":"0000-0002-5708-7632","id":"24135","last_name":"Lass","first_name":"Michael","full_name":"Lass, Michael"},{"last_name":"Kühne","id":"49079","full_name":"Kühne, Thomas","first_name":"Thomas"},{"id":"16153","last_name":"Plessl","first_name":"Christian","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982"}],"intvolume":"        10","publication_status":"published","citation":{"chicago":"Lass, Michael, Thomas Kühne, and Christian Plessl. “Using Approximate Computing for the Calculation of Inverse Matrix P-Th Roots.” <i>Embedded Systems Letters</i> 10, no. 2 (2018): 33–36. <a href=\"https://doi.org/10.1109/LES.2017.2760923\">https://doi.org/10.1109/LES.2017.2760923</a>.","ieee":"M. Lass, T. Kühne, and C. Plessl, “Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots,” <i>Embedded Systems Letters</i>, vol. 10, no. 2, pp. 33–36, 2018.","apa":"Lass, M., Kühne, T., &#38; Plessl, C. (2018). Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots. <i>Embedded Systems Letters</i>, <i>10</i>(2), 33–36. <a href=\"https://doi.org/10.1109/LES.2017.2760923\">https://doi.org/10.1109/LES.2017.2760923</a>","ama":"Lass M, Kühne T, Plessl C. Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots. <i>Embedded Systems Letters</i>. 2018;10(2):33-36. doi:<a href=\"https://doi.org/10.1109/LES.2017.2760923\">10.1109/LES.2017.2760923</a>","short":"M. Lass, T. Kühne, C. Plessl, Embedded Systems Letters 10 (2018) 33–36.","mla":"Lass, Michael, et al. “Using Approximate Computing for the Calculation of Inverse Matrix P-Th Roots.” <i>Embedded Systems Letters</i>, vol. 10, no. 2, IEEE, 2018, pp. 33–36, doi:<a href=\"https://doi.org/10.1109/LES.2017.2760923\">10.1109/LES.2017.2760923</a>.","bibtex":"@article{Lass_Kühne_Plessl_2018, title={Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots}, volume={10}, DOI={<a href=\"https://doi.org/10.1109/LES.2017.2760923\">10.1109/LES.2017.2760923</a>}, number={2}, journal={Embedded Systems Letters}, publisher={IEEE}, author={Lass, Michael and Kühne, Thomas and Plessl, Christian}, year={2018}, pages={33–36} }"},"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"}],"publisher":"IEEE","date_created":"2017-07-25T14:41:08Z","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1943-0663"],"eissn":["1943-0671"]},"year":"2018","_id":"20","date_updated":"2022-01-06T06:54:18Z"},{"type":"conference","year":"2018","language":[{"iso":"eng"}],"status":"public","publication":"Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies","date_created":"2020-10-23T16:46:30Z","date_updated":"2022-01-06T06:54:21Z","page":"1930–1940","_id":"20188","title":"The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants","author":[{"last_name":"Habernal","full_name":"Habernal, Ivan","first_name":"Ivan"},{"first_name":"Henning","full_name":"Wachsmuth, Henning","id":"3900","last_name":"Wachsmuth"},{"last_name":"Gurevych","first_name":"Iryna","full_name":"Gurevych, Iryna"},{"first_name":"Benno","full_name":"Stein, Benno","last_name":"Stein"}],"department":[{"_id":"600"}],"citation":{"mla":"Habernal, Ivan, et al. “The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants.” <i>Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies</i>, 2018, pp. 1930–1940.","bibtex":"@inproceedings{Habernal_Wachsmuth_Gurevych_Stein_2018, title={The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants}, booktitle={Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies}, author={Habernal, Ivan and Wachsmuth, Henning and Gurevych, Iryna and Stein, Benno}, year={2018}, pages={1930–1940} }","short":"I. Habernal, H. Wachsmuth, I. Gurevych, B. Stein, in: Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, 2018, pp. 1930–1940.","apa":"Habernal, I., Wachsmuth, H., Gurevych, I., &#38; Stein, B. (2018). The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants. In <i>Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies</i> (pp. 1930–1940).","ama":"Habernal I, Wachsmuth H, Gurevych I, Stein B. The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants. In: <i>Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies</i>. ; 2018:1930–1940.","chicago":"Habernal, Ivan, Henning Wachsmuth, Iryna Gurevych, and Benno Stein. “The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants.” In <i>Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies</i>, 1930–1940, 2018.","ieee":"I. Habernal, H. Wachsmuth, I. Gurevych, and B. Stein, “The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants,” in <i>Proceedings of the 16th Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies</i>, 2018, pp. 1930–1940."},"user_id":"82920"},{"conference":{"end_date":"2018-06-18","name":"The 13th Workshop on the Economics of Networks, Systems and Computation (NetEcon 2018)","start_date":"2018-06-18","location":"Irvine, California, USA"},"author":[{"orcid":"0000-0003-1348-6516","id":"14052","last_name":"Feldotto","first_name":"Matthias","full_name":"Feldotto, Matthias"},{"full_name":"Haake, Claus-Jochen","first_name":"Claus-Jochen","last_name":"Haake","id":"20801"},{"id":"40384","last_name":"Skopalik","first_name":"Alexander","full_name":"Skopalik, Alexander"},{"full_name":"Stroh-Maraun, Nadja","first_name":"Nadja","id":"13264","last_name":"Stroh-Maraun"}],"citation":{"apa":"Feldotto, M., Haake, C.-J., Skopalik, A., &#38; Stroh-Maraun, N. (2018). Disaggregating User Evaluations Using the Shapley Value. In <i>Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)</i> (pp. 5:1-5:6). Irvine, California, USA. <a href=\"https://doi.org/10.1145/3230654.3230659\">https://doi.org/10.1145/3230654.3230659</a>","ama":"Feldotto M, Haake C-J, Skopalik A, Stroh-Maraun N. Disaggregating User Evaluations Using the Shapley Value. In: <i>Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)</i>. ; 2018:5:1-5:6. doi:<a href=\"https://doi.org/10.1145/3230654.3230659\">10.1145/3230654.3230659</a>","chicago":"Feldotto, Matthias, Claus-Jochen Haake, Alexander Skopalik, and Nadja Stroh-Maraun. “Disaggregating User Evaluations Using the Shapley Value.” In <i>Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)</i>, 5:1-5:6, 2018. <a href=\"https://doi.org/10.1145/3230654.3230659\">https://doi.org/10.1145/3230654.3230659</a>.","ieee":"M. Feldotto, C.-J. Haake, A. Skopalik, and N. Stroh-Maraun, “Disaggregating User Evaluations Using the Shapley Value,” in <i>Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)</i>, Irvine, California, USA, 2018, pp. 5:1-5:6.","mla":"Feldotto, Matthias, et al. “Disaggregating User Evaluations Using the Shapley Value.” <i>Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)</i>, 2018, pp. 5:1-5:6, doi:<a href=\"https://doi.org/10.1145/3230654.3230659\">10.1145/3230654.3230659</a>.","bibtex":"@inproceedings{Feldotto_Haake_Skopalik_Stroh-Maraun_2018, title={Disaggregating User Evaluations Using the Shapley Value}, DOI={<a href=\"https://doi.org/10.1145/3230654.3230659\">10.1145/3230654.3230659</a>}, booktitle={Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)}, author={Feldotto, Matthias and Haake, Claus-Jochen and Skopalik, Alexander and Stroh-Maraun, Nadja}, year={2018}, pages={5:1-5:6} }","short":"M. Feldotto, C.-J. Haake, A. Skopalik, N. Stroh-Maraun, in: Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018), 2018, pp. 5:1-5:6."},"publication_status":"published","department":[{"_id":"541"},{"_id":"63"},{"_id":"205"},{"_id":"475"}],"date_created":"2018-05-22T10:28:51Z","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-1-4503-5916-0"]},"year":"2018","status":"public","_id":"2831","file_date_updated":"2018-08-15T07:30:50Z","date_updated":"2022-01-06T06:58:01Z","title":"Disaggregating User Evaluations Using the Shapley Value","file":[{"creator":"nmaraun","file_name":"Disaggregating User Evaluations Using the Shapley Value.pdf","file_size":1450171,"content_type":"application/pdf","access_level":"closed","file_id":"3910","date_created":"2018-08-15T07:30:50Z","relation":"main_file","date_updated":"2018-08-15T07:30:50Z","success":1}],"project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Project Area A","_id":"2"},{"name":"SFB 901 - Subproject A3","_id":"7"}],"abstract":[{"text":"We consider a market where final products or services are compositions of a number of basic services. Users are asked to evaluate the quality of the composed product after purchase. The quality of the basic service influences the performance of the composed services but cannot be observed directly. The question we pose is whether it is possible to use user evaluations on composed services to assess the quality of basic services. We discuss how to combine aggregation of evaluations across users and disaggregation of information on composed services to derive valuations for the single components. As a solution we propose to use the (weighted) average as aggregation device in connection with the Shapley value as disaggregation method, since this combination fulfills natural requirements in our context. In addition, we address some occurring computational issues: We give an approximate solution concept using only a limited number of evaluations which guarantees nearly optimal results with reduced running time. Lastly, we show that a slightly modified Shapley value and the weighted average are still applicable if the evaluation profiles are incomplete.","lang":"eng"}],"has_accepted_license":"1","doi":"10.1145/3230654.3230659","user_id":"14052","publication":"Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)","ddc":["040"],"type":"conference","page":"5:1-5:6"},{"publication":"Algorithmica","ddc":["000"],"type":"journal_article","page":"1556–1574","volume":80,"issue":"5","title":"Towards Flexible Demands in Online Leasing Problems. ","file":[{"date_created":"2018-11-02T15:18:16Z","access_level":"closed","content_type":"application/pdf","file_id":"5298","file_name":"TowardsFlexibleDemandsInOnline.pdf","file_size":600583,"creator":"ups","success":1,"relation":"main_file","date_updated":"2018-11-02T15:18:16Z"}],"project":[{"_id":"1","name":"SFB 901"},{"name":"SFB 901 - Project Area C","_id":"4"},{"_id":"16","name":"SFB 901 - Subproject C4"}],"has_accepted_license":"1","doi":"10.1007/s00453-018-0420-y","user_id":"477","date_created":"2018-05-24T08:32:38Z","publisher":"Springer","language":[{"iso":"eng"}],"year":"2018","status":"public","file_date_updated":"2018-11-02T15:18:16Z","_id":"2848","date_updated":"2022-01-06T06:58:06Z","author":[{"first_name":"Shouwei","full_name":"Li, Shouwei","last_name":"Li"},{"id":"37612","last_name":"Markarian","full_name":"Markarian, Christine","first_name":"Christine"},{"full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","id":"15523","last_name":"Meyer auf der Heide"}],"intvolume":"        80","citation":{"short":"S. Li, C. Markarian, F. Meyer auf der Heide, Algorithmica 80 (2018) 1556–1574.","mla":"Li, Shouwei, et al. “Towards Flexible Demands in Online Leasing Problems. .” <i>Algorithmica</i>, vol. 80, no. 5, Springer, 2018, pp. 1556–1574, doi:<a href=\"https://doi.org/10.1007/s00453-018-0420-y\">10.1007/s00453-018-0420-y</a>.","bibtex":"@article{Li_Markarian_Meyer auf der Heide_2018, title={Towards Flexible Demands in Online Leasing Problems. }, volume={80}, DOI={<a href=\"https://doi.org/10.1007/s00453-018-0420-y\">10.1007/s00453-018-0420-y</a>}, number={5}, journal={Algorithmica}, publisher={Springer}, author={Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm}, year={2018}, pages={1556–1574} }","chicago":"Li, Shouwei, Christine Markarian, and Friedhelm Meyer auf der Heide. “Towards Flexible Demands in Online Leasing Problems. .” <i>Algorithmica</i> 80, no. 5 (2018): 1556–1574. <a href=\"https://doi.org/10.1007/s00453-018-0420-y\">https://doi.org/10.1007/s00453-018-0420-y</a>.","ieee":"S. Li, C. Markarian, and F. Meyer auf der Heide, “Towards Flexible Demands in Online Leasing Problems. ,” <i>Algorithmica</i>, vol. 80, no. 5, pp. 1556–1574, 2018.","ama":"Li S, Markarian C, Meyer auf der Heide F. Towards Flexible Demands in Online Leasing Problems. . <i>Algorithmica</i>. 2018;80(5):1556–1574. doi:<a href=\"https://doi.org/10.1007/s00453-018-0420-y\">10.1007/s00453-018-0420-y</a>","apa":"Li, S., Markarian, C., &#38; Meyer auf der Heide, F. (2018). Towards Flexible Demands in Online Leasing Problems. . <i>Algorithmica</i>, <i>80</i>(5), 1556–1574. <a href=\"https://doi.org/10.1007/s00453-018-0420-y\">https://doi.org/10.1007/s00453-018-0420-y</a>"},"department":[{"_id":"63"}]},{"publication_identifier":{"unknown":["1432-4350"]},"year":"2018","language":[{"iso":"eng"}],"status":"public","date_created":"2018-05-24T08:39:15Z","publisher":"Springer","date_updated":"2022-01-06T06:58:06Z","file_date_updated":"2018-11-02T15:24:32Z","_id":"2849","author":[{"last_name":"Abu-Khzam","full_name":"Abu-Khzam, Faisal N. ","first_name":"Faisal N. "},{"id":"37612","last_name":"Markarian","first_name":"Christine","full_name":"Markarian, Christine"},{"full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","last_name":"Meyer auf der Heide","id":"15523"},{"last_name":"Schubert","full_name":"Schubert, Michael","first_name":"Michael"}],"department":[{"_id":"63"}],"citation":{"ama":"Abu-Khzam FN, Markarian C, Meyer auf der Heide F, Schubert M. Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks. <i>Theory of Computing Systems</i>. 2018. doi:<a href=\"https://doi.org/10.1007/s00224-017-9836-z\">10.1007/s00224-017-9836-z</a>","apa":"Abu-Khzam, F. N., Markarian, C., Meyer auf der Heide, F., &#38; Schubert, M. (2018). Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks. <i>Theory of Computing Systems</i>. <a href=\"https://doi.org/10.1007/s00224-017-9836-z\">https://doi.org/10.1007/s00224-017-9836-z</a>","chicago":"Abu-Khzam, Faisal N. , Christine Markarian, Friedhelm Meyer auf der Heide, and Michael Schubert. “Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-Hoc Networks.” <i>Theory of Computing Systems</i>, 2018. <a href=\"https://doi.org/10.1007/s00224-017-9836-z\">https://doi.org/10.1007/s00224-017-9836-z</a>.","ieee":"F. N. Abu-Khzam, C. Markarian, F. Meyer auf der Heide, and M. Schubert, “Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks,” <i>Theory of Computing Systems</i>, 2018.","mla":"Abu-Khzam, Faisal N., et al. “Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-Hoc Networks.” <i>Theory of Computing Systems</i>, Springer, 2018, doi:<a href=\"https://doi.org/10.1007/s00224-017-9836-z\">10.1007/s00224-017-9836-z</a>.","bibtex":"@article{Abu-Khzam_Markarian_Meyer auf der Heide_Schubert_2018, title={Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks}, DOI={<a href=\"https://doi.org/10.1007/s00224-017-9836-z\">10.1007/s00224-017-9836-z</a>}, journal={Theory of Computing Systems}, publisher={Springer}, author={Abu-Khzam, Faisal N.  and Markarian, Christine and Meyer auf der Heide, Friedhelm and Schubert, Michael}, year={2018} }","short":"F.N. Abu-Khzam, C. Markarian, F. Meyer auf der Heide, M. Schubert, Theory of Computing Systems (2018)."},"type":"journal_article","ddc":["000"],"publication":"Theory of Computing Systems","project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Project Area A","_id":"2"},{"name":"SFB 901 - Subproject A1","_id":"5"}],"doi":"10.1007/s00224-017-9836-z","has_accepted_license":"1","title":"Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks","file":[{"date_updated":"2018-11-02T15:24:32Z","relation":"main_file","success":1,"file_name":"ApproximationAndHeuristicAlgor.pdf","file_size":1371624,"creator":"ups","date_created":"2018-11-02T15:24:32Z","file_id":"5301","content_type":"application/pdf","access_level":"closed"}],"user_id":"477"},{"date_updated":"2022-01-06T06:58:07Z","file_date_updated":"2018-11-13T13:15:19Z","_id":"2850","status":"public","language":[{"iso":"eng"}],"type":"conference","year":"2018","date_created":"2018-05-24T08:41:48Z","publication":"Ninth International Conference on Fun with Algorithms (FUN)","ddc":["000"],"department":[{"_id":"63"},{"_id":"238"}],"user_id":"15415","citation":{"ama":"Hamann H, Markarian C, Meyer auf der Heide F, Wahby M. Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets. In: <i>Ninth International Conference on Fun with Algorithms (FUN)</i>. ; 2018. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FUN.2018.22\">10.4230/LIPIcs.FUN.2018.22</a>","apa":"Hamann, H., Markarian, C., Meyer auf der Heide, F., &#38; Wahby, M. (2018). Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets. In <i>Ninth International Conference on Fun with Algorithms (FUN)</i>. <a href=\"https://doi.org/10.4230/LIPIcs.FUN.2018.22\">https://doi.org/10.4230/LIPIcs.FUN.2018.22</a>","chicago":"Hamann, Heiko, Christine Markarian, Friedhelm Meyer auf der Heide, and Mostafa Wahby. “Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse Based on Online Connected Dominating Sets.” In <i>Ninth International Conference on Fun with Algorithms (FUN)</i>, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.FUN.2018.22\">https://doi.org/10.4230/LIPIcs.FUN.2018.22</a>.","ieee":"H. Hamann, C. Markarian, F. Meyer auf der Heide, and M. Wahby, “Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets,” in <i>Ninth International Conference on Fun with Algorithms (FUN)</i>, 2018.","mla":"Hamann, Heiko, et al. “Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse Based on Online Connected Dominating Sets.” <i>Ninth International Conference on Fun with Algorithms (FUN)</i>, 2018, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FUN.2018.22\">10.4230/LIPIcs.FUN.2018.22</a>.","bibtex":"@inproceedings{Hamann_Markarian_Meyer auf der Heide_Wahby_2018, title={Pick, Pack, &#38; Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.FUN.2018.22\">10.4230/LIPIcs.FUN.2018.22</a>}, booktitle={Ninth International Conference on Fun with Algorithms (FUN)}, author={Hamann, Heiko and Markarian, Christine and Meyer auf der Heide, Friedhelm and Wahby, Mostafa}, year={2018} }","short":"H. Hamann, C. Markarian, F. Meyer auf der Heide, M. 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Markarian, in: International Workshop on Combinatorial Algorithms (IWOCA), Cham, 2018.","apa":"Markarian, C. (2018). An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest. <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">https://doi.org/10.1007/978-3-319-94667-2_18</a>","ama":"Markarian C. An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest. In: <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. ; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>","ieee":"C. Markarian, “An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest,” 2018, doi: <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">10.1007/978-3-319-94667-2_18</a>.","chicago":"Markarian, Christine. “An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest.” In <i>International Workshop on Combinatorial Algorithms (IWOCA)</i>. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-94667-2_18\">https://doi.org/10.1007/978-3-319-94667-2_18</a>."},"doi":"10.1007/978-3-319-94667-2_18","abstract":[{"lang":"eng","text":"We study the Online Prize-collecting Node-weighted Steiner Forest problem (OPC-NWSF) in which we are given an undirected graph \\(G=(V, E)\\) with \\(|V| = n\\) and node-weight function \\(w: V \\rightarrow \\mathcal {R}^+\\). A sequence of k pairs of nodes of G, each associated with a penalty, arrives online. OPC-NWSF asks to construct a subgraph H such that each pair \\(\\{s, t\\}\\) is either connected (there is a path between s and t in H) or its associated penalty is paid. The goal is to minimize the weight of H and the total penalties paid. The current best result for OPC-NWSF is a randomized \\(\\mathcal {O}(\\log ^4 n)\\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014). We improve this by proposing a randomized \\(\\mathcal {O}(\\log n \\log k)\\)-competitive algorithm for OPC-NWSF, which is optimal up to constant factor since OPC-NWSF has a randomized lower bound of \\(\\varOmega (\\log ^2 n)\\) due to Korman [11]. Moreover, our result also implies an improvement for two special cases of OPC-NWSF, the Online Prize-collecting Node-weighted Steiner Tree problem (OPC-NWST) and the Online Node-weighted Steiner Forest problem (ONWSF). In OPC-NWST, there is a distinguished node which is one of the nodes in each pair. In ONWSF, all penalties are set to infinity. The currently best known results for OPC-NWST and ONWSF are a randomized \\(\\mathcal {O}(\\log ^3 n)\\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014) and a randomized \\(\\mathcal {O}(\\log n \\log ^2 k)\\)-competitive algorithm due to Hajiaghayi et al. (FOCS 2013), respectively."}],"place":"Cham","author":[{"last_name":"Markarian","first_name":"Christine","full_name":"Markarian, Christine"}],"title":"An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest"},{"_id":"2471","file_date_updated":"2018-11-06T15:15:38Z","date_updated":"2022-01-06T06:56:32Z","publisher":"IEEE Computer Society","date_created":"2018-04-23T11:40:20Z","status":"public","year":"2018","language":[{"iso":"eng"}],"citation":{"short":"F. Mohr, M.D. Wever, E. 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