--- _id: '20817' author: - first_name: Marcin full_name: Bienkowski, Marcin last_name: Bienkowski - first_name: Björn full_name: Feldkord, Björn id: '22704' last_name: Feldkord - first_name: Pawel full_name: Schmidt, Pawel last_name: Schmidt citation: ama: 'Bienkowski M, Feldkord B, Schmidt P. A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location. In: Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS). ; 2021:14:1-14:17. doi:10.4230/LIPIcs.STACS.2021.14' apa: Bienkowski, M., Feldkord, B., & Schmidt, P. (2021). A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location. In Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS) (pp. 14:1-14:17). https://doi.org/10.4230/LIPIcs.STACS.2021.14 bibtex: '@inproceedings{Bienkowski_Feldkord_Schmidt_2021, title={A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location}, DOI={10.4230/LIPIcs.STACS.2021.14}, booktitle={Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS)}, author={Bienkowski, Marcin and Feldkord, Björn and Schmidt, Pawel}, year={2021}, pages={14:1-14:17} }' chicago: Bienkowski, Marcin, Björn Feldkord, and Pawel Schmidt. “A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location.” In Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS), 14:1-14:17, 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.14. ieee: M. Bienkowski, B. Feldkord, and P. Schmidt, “A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location,” in Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17. mla: Bienkowski, Marcin, et al. “A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location.” Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17, doi:10.4230/LIPIcs.STACS.2021.14. short: 'M. Bienkowski, B. Feldkord, P. Schmidt, in: Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17.' date_created: 2020-12-21T13:46:16Z date_updated: 2022-01-06T06:54:40Z department: - _id: '63' doi: 10.4230/LIPIcs.STACS.2021.14 language: - iso: eng page: 14:1 - 14:17 project: - _id: '1' name: SFB 901 - _id: '2' name: SFB 901 - Project Area A - _id: '5' name: SFB 901 - Subproject A1 publication: Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS) publication_status: published status: public title: A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location type: conference user_id: '22704' year: '2021' ... --- _id: '22510' abstract: - lang: eng text: 'Over the past decades, the Gathering problem, which asks to gather a group of robots in finite time given some restrictions, has been intensively studied. In this paper, we are given a group of n autonomous, dimensionless, deterministic, and anonymous robots, with bounded viewing range. Assuming a continuous time model, the goal is to gather these robots into one point in finite time. We introduce a simple convergence criterion that defines a new class of algorithms which perform gathering in O(nd) time, where d is the diameter of the initial robot configuration. We show that some gathering algorithms in the literature belong to this class and propose two new algorithms that belong to this class and have quadratic running time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center algorithm (S-GTRC). We prove that the latter can perform gathering without collision by using a slightly more complex robot model: non oblivious, chiral, and luminous (i.e. robots have observable external memory, as in [8]). We also consider a variant of the Gathering problem, the Near-Gathering problem, in which robots must get close to each other without colliding. We show that S-GTRC solves the Near-Gathering problem in quadratic time and assumes a weaker robot model than the one assumed in the current state-of-the-art.' author: - first_name: Shouwei full_name: Li, Shouwei last_name: Li - first_name: Christine full_name: Markarian, Christine last_name: Markarian - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide - first_name: Pavel full_name: Podlipyan, Pavel last_name: Podlipyan citation: ama: Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. A continuous strategy for collisionless gathering. Theoretical Computer Science. 2021;852:41-60. doi:10.1016/j.tcs.2020.10.037 apa: Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan, P. (2021). A continuous strategy for collisionless gathering. Theoretical Computer Science, 852, 41–60. https://doi.org/10.1016/j.tcs.2020.10.037 bibtex: '@article{Li_Markarian_Meyer auf der Heide_Podlipyan_2021, title={A continuous strategy for collisionless gathering}, volume={852}, DOI={10.1016/j.tcs.2020.10.037}, journal={Theoretical Computer Science}, author={Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={41–60} }' chicago: 'Li, Shouwei, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “A Continuous Strategy for Collisionless Gathering.” Theoretical Computer Science 852 (2021): 41–60. https://doi.org/10.1016/j.tcs.2020.10.037.' ieee: S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “A continuous strategy for collisionless gathering,” Theoretical Computer Science, vol. 852, pp. 41–60, 2021. mla: Li, Shouwei, et al. “A Continuous Strategy for Collisionless Gathering.” Theoretical Computer Science, vol. 852, 2021, pp. 41–60, doi:10.1016/j.tcs.2020.10.037. short: S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science 852 (2021) 41–60. date_created: 2021-06-28T09:24:15Z date_updated: 2022-01-06T06:55:35Z department: - _id: '63' doi: 10.1016/j.tcs.2020.10.037 intvolume: ' 852' keyword: - Local algorithms - Distributed algorithms - Collisionless gathering - Mobile robots - Multiagent system language: - iso: eng page: 41-60 publication: Theoretical Computer Science publication_identifier: issn: - 0304-3975 publication_status: published status: public title: A continuous strategy for collisionless gathering type: journal_article user_id: '15415' volume: 852 year: '2021' ... --- _id: '22511' abstract: - lang: eng text: "In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile robots with limited viewing range in the plane. Remarquably, this algorithm exploits the fact that during its execution, many collisions of robots occur. Such collisions are interpreted as a success because it is assumed that such collided robots behave the same from now on. This is acceptable under the assumption that each robot is represented by a single point. Otherwise, collisions should be avoided. In this paper, we consider a continuous Go-To-The-Center algorithm in which the robots continuously observe the positions of their neighbors and adapt their speed (assuming a speed limit) and direction. Our first results are time bounds of O(n2) for gathering in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center considering only the neighbors of a robot with respect to the Gabriel subgraph of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that this modification still correctly executes gathering in one and two dimensions, with the same time bounds as above. Simulations exhibit a severe difference of the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms: Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm, typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center algorithm for one dimension. In two-dimensional Euclidean space, we conjecture that the “collisionless property” holds for almost every initial configuration. We support our conjecture with measurements obtained from the simulation where robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms.\r\n" author: - first_name: Shouwei full_name: Li, Shouwei last_name: Li - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide - first_name: Pavel full_name: Podlipyan, Pavel last_name: Podlipyan citation: ama: Li S, Meyer auf der Heide F, Podlipyan P. The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. Theoretical Computer Science. 2021;852:29-40. doi:10.1016/j.tcs.2020.11.009 apa: Li, S., Meyer auf der Heide, F., & Podlipyan, P. (2021). The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. Theoretical Computer Science, 852, 29–40. https://doi.org/10.1016/j.tcs.2020.11.009 bibtex: '@article{Li_Meyer auf der Heide_Podlipyan_2021, title={The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots}, volume={852}, DOI={10.1016/j.tcs.2020.11.009}, journal={Theoretical Computer Science}, author={Li, Shouwei and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={29–40} }' chicago: 'Li, Shouwei, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile Autonomous Robots.” Theoretical Computer Science 852 (2021): 29–40. https://doi.org/10.1016/j.tcs.2020.11.009.' ieee: S. Li, F. Meyer auf der Heide, and P. Podlipyan, “The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots,” Theoretical Computer Science, vol. 852, pp. 29–40, 2021. mla: Li, Shouwei, et al. “The Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile Autonomous Robots.” Theoretical Computer Science, vol. 852, 2021, pp. 29–40, doi:10.1016/j.tcs.2020.11.009. short: S. Li, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science 852 (2021) 29–40. date_created: 2021-06-28T09:34:45Z date_updated: 2022-01-06T06:55:35Z department: - _id: '63' doi: 10.1016/j.tcs.2020.11.009 intvolume: ' 852' keyword: - Local algorithms - Distributed algorithms - Collisionless gathering - Mobile robots - Multiagent system language: - iso: eng page: 29-40 publication: Theoretical Computer Science publication_identifier: issn: - 0304-3975 publication_status: published status: public title: The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots type: journal_article user_id: '15415' volume: 852 year: '2021' ... --- _id: '26986' author: - first_name: Jannik full_name: Castenow, Jannik id: '38705' last_name: Castenow - first_name: Thorsten full_name: Götte, Thorsten id: '34727' last_name: Götte - first_name: Till full_name: Knollmann, Till id: '39241' last_name: Knollmann orcid: 0000-0003-2014-4696 - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide citation: ama: 'Castenow J, Götte T, Knollmann T, Meyer auf der Heide F. The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation. In: Johnen C, Schiller EM, Schmid S, eds. Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021. Vol 13046. LNCS. Springer; 2021:289-304. doi:10.1007/978-3-030-91081-5_19' apa: Castenow, J., Götte, T., Knollmann, T., & Meyer auf der Heide, F. (2021). The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation. In C. Johnen, E. M. Schiller, & S. Schmid (Eds.), Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021 (Vol. 13046, pp. 289–304). Springer. https://doi.org/10.1007/978-3-030-91081-5_19 bibtex: '@inproceedings{Castenow_Götte_Knollmann_Meyer auf der Heide_2021, series={LNCS}, title={The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation}, volume={13046}, DOI={10.1007/978-3-030-91081-5_19}, booktitle={Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021}, publisher={Springer}, author={Castenow, Jannik and Götte, Thorsten and Knollmann, Till and Meyer auf der Heide, Friedhelm}, editor={Johnen, C. and Schiller, E.M. and Schmid, S.}, year={2021}, pages={289–304}, collection={LNCS} }' chicago: Castenow, Jannik, Thorsten Götte, Till Knollmann, and Friedhelm Meyer auf der Heide. “The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation.” In Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, edited by C. Johnen, E.M. Schiller, and S. Schmid, 13046:289–304. LNCS. Springer, 2021. https://doi.org/10.1007/978-3-030-91081-5_19. ieee: 'J. Castenow, T. Götte, T. Knollmann, and F. Meyer auf der Heide, “The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation,” in Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, Online, 2021, vol. 13046, pp. 289–304, doi: 10.1007/978-3-030-91081-5_19.' mla: Castenow, Jannik, et al. “The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation.” Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, edited by C. Johnen et al., vol. 13046, Springer, 2021, pp. 289–304, doi:10.1007/978-3-030-91081-5_19. short: 'J. Castenow, T. Götte, T. Knollmann, F. Meyer auf der Heide, in: C. Johnen, E.M. Schiller, S. Schmid (Eds.), Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, Springer, 2021, pp. 289–304.' conference: end_date: 2021-11-20 location: Online name: 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems start_date: 2021-11-17 date_created: 2021-10-28T07:01:30Z date_updated: 2022-01-07T15:24:10Z department: - _id: '63' doi: 10.1007/978-3-030-91081-5_19 editor: - first_name: C. full_name: Johnen, C. last_name: Johnen - first_name: E.M. full_name: Schiller, E.M. last_name: Schiller - first_name: S. full_name: Schmid, S. last_name: Schmid external_id: arxiv: - '2109.11856' intvolume: ' 13046' language: - iso: eng page: '289-304 ' project: - _id: '106' name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme' publication: Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021 publication_status: published publisher: Springer series_title: LNCS status: public title: The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation type: conference user_id: '38705' volume: 13046 year: '2021' ... --- _id: '27778' abstract: - lang: eng text: "Consider a set of jobs connected to a directed acyclic task graph with a\r\nfixed source and sink. The edges of this graph model precedence constraints and\r\nthe jobs have to be scheduled with respect to those. We introduce the Server\r\nCloud Scheduling problem, in which the jobs have to be processed either on a\r\nsingle local machine or on one of many cloud machines. Both the source and the\r\nsink have to be scheduled on the local machine. For each job, processing times\r\nboth on the server and in the cloud are given. Furthermore, for each edge in\r\nthe task graph, a communication delay is included in the input and has to be\r\ntaken into account if one of the two jobs is scheduled on the server, the other\r\nin the cloud. The server can process jobs sequentially, whereas the cloud can\r\nserve as many as needed in parallel, but induces costs. We consider both\r\nmakespan and cost minimization. The main results are an FPTAS with respect for\r\nthe makespan objective for a fairly general case and strong hardness for the\r\ncase with unit processing times and delays." author: - first_name: Marten full_name: Maack, Marten id: '88252' last_name: Maack - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide - first_name: Simon full_name: Pukrop, Simon id: '44428' last_name: Pukrop citation: ama: Maack M, Meyer auf der Heide F, Pukrop S. Full Version -- Server Cloud Scheduling. arXiv:210802109. Published online 2021. apa: Maack, M., Meyer auf der Heide, F., & Pukrop, S. (2021). Full Version -- Server Cloud Scheduling. In arXiv:2108.02109. bibtex: '@article{Maack_Meyer auf der Heide_Pukrop_2021, title={Full Version -- Server Cloud Scheduling}, journal={arXiv:2108.02109}, author={Maack, Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}, year={2021} }' chicago: Maack, Marten, Friedhelm Meyer auf der Heide, and Simon Pukrop. “Full Version -- Server Cloud Scheduling.” ArXiv:2108.02109, 2021. ieee: M. Maack, F. Meyer auf der Heide, and S. Pukrop, “Full Version -- Server Cloud Scheduling,” arXiv:2108.02109. 2021. mla: Maack, Marten, et al. “Full Version -- Server Cloud Scheduling.” ArXiv:2108.02109, 2021. short: M. Maack, F. Meyer auf der Heide, S. Pukrop, ArXiv:2108.02109 (2021). date_created: 2021-11-24T13:23:58Z date_updated: 2022-09-27T15:03:19Z department: - _id: '63' - _id: '26' language: - iso: eng publication: arXiv:2108.02109 status: public title: Full Version -- Server Cloud Scheduling type: preprint user_id: '44428' year: '2021' ... --- _id: '44234' author: - first_name: Thilo Frederik full_name: Berger, Thilo Frederik last_name: Berger citation: ama: Berger TF. Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation.; 2021. apa: Berger, T. F. (2021). Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation. bibtex: '@book{Berger_2021, title={Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation}, author={Berger, Thilo Frederik}, year={2021} }' chicago: Berger, Thilo Frederik. Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation, 2021. ieee: T. F. Berger, Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation. 2021. mla: Berger, Thilo Frederik. Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation. 2021. short: T.F. Berger, Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation, 2021. date_created: 2023-04-27T15:34:07Z date_updated: 2023-04-27T15:34:17Z department: - _id: '63' language: - iso: eng project: - _id: '1' name: 'SFB 901: SFB 901' - _id: '2' name: 'SFB 901 - A: SFB 901 - Project Area A' - _id: '5' name: 'SFB 901 - A1: SFB 901 - Subproject A1' status: public supervisor: - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide title: Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource Allocation type: bachelorsthesis user_id: '39241' year: '2021' ... --- _id: '44233' author: - first_name: Sebastian full_name: Pranger, Sebastian last_name: Pranger citation: ama: Pranger S. Online K-Facility Reallocation Using k-Server Algorithms.; 2021. apa: Pranger, S. (2021). Online k-Facility Reallocation using k-Server Algorithms. bibtex: '@book{Pranger_2021, title={Online k-Facility Reallocation using k-Server Algorithms}, author={Pranger, Sebastian}, year={2021} }' chicago: Pranger, Sebastian. Online K-Facility Reallocation Using k-Server Algorithms, 2021. ieee: S. Pranger, Online k-Facility Reallocation using k-Server Algorithms. 2021. mla: Pranger, Sebastian. Online K-Facility Reallocation Using k-Server Algorithms. 2021. short: S. Pranger, Online K-Facility Reallocation Using k-Server Algorithms, 2021. date_created: 2023-04-27T15:31:26Z date_updated: 2023-04-27T15:31:57Z department: - _id: '63' language: - iso: eng project: - _id: '1' name: 'SFB 901: SFB 901' - _id: '2' name: 'SFB 901 - A: SFB 901 - Project Area A' - _id: '5' name: 'SFB 901 - A1: SFB 901 - Subproject A1' status: public supervisor: - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide title: Online k-Facility Reallocation using k-Server Algorithms type: bachelorsthesis user_id: '39241' year: '2021' ... --- _id: '19899' abstract: - lang: eng text: "Most existing robot formation problems seek a target formation of a certain\r\nminimal and, thus, efficient structure. Examples include the Gathering\r\nand the Chain-Formation problem. In this work, we study formation problems that\r\ntry to reach a maximal structure, supporting for example an efficient\r\ncoverage in exploration scenarios. A recent example is the NASA Shapeshifter\r\nproject, which describes how the robots form a relay chain along which gathered\r\ndata from extraterrestrial cave explorations may be sent to a home base.\r\n As a first step towards understanding such maximization tasks, we introduce\r\nand study the Max-Chain-Formation problem, where $n$ robots are ordered along a\r\nwinding, potentially self-intersecting chain and must form a connected,\r\nstraight line of maximal length connecting its two endpoints. We propose and\r\nanalyze strategies in a discrete and in a continuous time model. In the\r\ndiscrete case, we give a complete analysis if all robots are initially\r\ncollinear, showing that the worst-case time to reach an\r\n$\\varepsilon$-approximation is upper bounded by $\\mathcal{O}(n^2 \\cdot \\log\r\n(n/\\varepsilon))$ and lower bounded by $\\Omega(n^2 \\cdot~\\log\r\n(1/\\varepsilon))$. If one endpoint of the chain remains stationary, this result\r\ncan be extended to the non-collinear case. If both endpoints move, we identify\r\na family of instances whose runtime is unbounded. For the continuous model, we\r\ngive a strategy with an optimal runtime bound of $\\Theta(n)$. Avoiding an\r\nunbounded runtime similar to the discrete case relies crucially on a\r\ncounter-intuitive aspect of the strategy: slowing down the endpoints while all\r\nother robots move at full speed. Surprisingly, we can show that a similar trick\r\ndoes not work in the discrete model." author: - first_name: Jannik full_name: Castenow, Jannik id: '38705' last_name: Castenow - first_name: Peter full_name: Kling, Peter last_name: Kling - first_name: Till full_name: Knollmann, Till id: '39241' last_name: Knollmann orcid: 0000-0003-2014-4696 - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide citation: ama: 'Castenow J, Kling P, Knollmann T, Meyer auf der Heide F. A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up. In: Devismes S, Mittal N, eds. Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings. Vol 12514. Lecture Notes in Computer Science (LNCS). Springer; 2020:65-80. doi:10.1007/978-3-030-64348-5_6' apa: Castenow, J., Kling, P., Knollmann, T., & Meyer auf der Heide, F. (2020). A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up. In S. Devismes & N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings (Vol. 12514, pp. 65–80). Springer. https://doi.org/10.1007/978-3-030-64348-5_6 bibtex: '@inproceedings{Castenow_Kling_Knollmann_Meyer auf der Heide_2020, series={Lecture Notes in Computer Science (LNCS)}, title={A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up}, volume={12514}, DOI={10.1007/978-3-030-64348-5_6}, booktitle={Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings}, publisher={Springer}, author={Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}, editor={Devismes , Stéphane and Mittal, Neeraj Editors}, year={2020}, pages={65–80}, collection={Lecture Notes in Computer Science (LNCS)} }' chicago: Castenow, Jannik, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide. “A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up.” In Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings, edited by Stéphane Devismes and Neeraj Mittal, 12514:65–80. Lecture Notes in Computer Science (LNCS). Springer, 2020. https://doi.org/10.1007/978-3-030-64348-5_6. ieee: J. Castenow, P. Kling, T. Knollmann, and F. Meyer auf der Heide, “A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up,” in Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings, 2020, vol. 12514, pp. 65–80. mla: Castenow, Jannik, et al. “A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up.” Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings, edited by Stéphane Devismes and Neeraj Mittal, vol. 12514, Springer, 2020, pp. 65–80, doi:10.1007/978-3-030-64348-5_6. short: 'J. Castenow, P. Kling, T. Knollmann, F. Meyer auf der Heide, in: S. Devismes , N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings, Springer, 2020, pp. 65–80.' date_created: 2020-10-06T07:27:10Z date_updated: 2022-01-06T06:54:14Z department: - _id: '63' doi: 10.1007/978-3-030-64348-5_6 editor: - first_name: 'Stéphane ' full_name: 'Devismes , Stéphane ' last_name: 'Devismes ' - first_name: 'Neeraj ' full_name: 'Mittal, Neeraj ' last_name: Mittal external_id: arxiv: - '2010.02043 ' intvolume: ' 12514' language: - iso: eng page: 65-80 publication: Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings publication_identifier: isbn: - 978-3-030-64347-8 publication_status: published publisher: Springer series_title: Lecture Notes in Computer Science (LNCS) status: public title: A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up type: conference user_id: '38705' volume: 12514 year: '2020' ... --- _id: '20159' abstract: - lang: eng text: "Let G = (V,E) be an undirected graph on n vertices with non-negative capacities on its edges. The mincut sensitivity problem for the insertion of an edge is defined as follows. Build a compact data structure for G and a given set S ⊆ V of vertices that, on receiving any edge (x,y) ∈ S×S of positive capacity as query input, can efficiently report the set of all pairs from S× S whose mincut value increases upon insertion of the edge (x,y) to G. The only result that exists for this problem is for a single pair of vertices (Picard and Queyranne, Mathematical Programming Study, 13 (1980), 8-16). We present the following results for the single source and the all-pairs versions of this problem. \r\n1) Single source: Given any designated source vertex s, there exists a data structure of size \U0001D4AA(|S|) that can output all those vertices from S whose mincut value to s increases upon insertion of any given edge. The time taken by the data structure to answer any query is \U0001D4AA(|S|). \r\n2) All-pairs: There exists an \U0001D4AA(|S|²) size data structure that can output all those pairs of vertices from S× S whose mincut value gets increased upon insertion of any given edge. The time taken by the data structure to answer any query is \U0001D4AA(k), where k is the number of pairs of vertices whose mincut increases. \r\nFor both these versions, we also address the problem of reporting the values of the mincuts upon insertion of any given edge. To derive our results, we use interesting insights into the nearest and the farthest mincuts for a pair of vertices. In addition, a crucial result, that we establish and use in our data structures, is that there exists a directed acyclic graph of \U0001D4AA(n) size that compactly stores the farthest mincuts from all vertices of V to a designated vertex s in the graph. We believe that this result is of independent interest, especially, because it also complements a previously existing result by Hariharan et al. (STOC 2007) that the nearest mincuts from all vertices of V to s is a laminar family, and hence, can be stored compactly in a tree of \U0001D4AA(n) size." author: - first_name: Surender full_name: Baswana, Surender last_name: Baswana - first_name: Shiv full_name: Gupta, Shiv last_name: Gupta - first_name: Till full_name: Knollmann, Till id: '39241' last_name: Knollmann orcid: 0000-0003-2014-4696 citation: ama: 'Baswana S, Gupta S, Knollmann T. Mincut Sensitivity Data Structures for the Insertion of an Edge. In: Grandoni F, Herman G, Sanders P, eds. 28th Annual European Symposium on Algorithms (ESA 2020). Vol 173. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik; 2020:12:1-12:14. doi:10.4230/LIPIcs.ESA.2020.12' apa: 'Baswana, S., Gupta, S., & Knollmann, T. (2020). Mincut Sensitivity Data Structures for the Insertion of an Edge. In F. Grandoni, G. Herman, & P. Sanders (Eds.), 28th Annual European Symposium on Algorithms (ESA 2020) (Vol. 173, pp. 12:1-12:14). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.12' bibtex: '@inproceedings{Baswana_Gupta_Knollmann_2020, place={Dagstuhl, Germany}, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Mincut Sensitivity Data Structures for the Insertion of an Edge}, volume={173}, DOI={10.4230/LIPIcs.ESA.2020.12}, booktitle={28th Annual European Symposium on Algorithms (ESA 2020)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}, author={Baswana, Surender and Gupta, Shiv and Knollmann, Till}, editor={Grandoni, Fabrizio and Herman, Grzegorz and Sanders, PeterEditors}, year={2020}, pages={12:1-12:14}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }' chicago: 'Baswana, Surender, Shiv Gupta, and Till Knollmann. “Mincut Sensitivity Data Structures for the Insertion of an Edge.” In 28th Annual European Symposium on Algorithms (ESA 2020), edited by Fabrizio Grandoni, Grzegorz Herman, and Peter Sanders, 173:12:1-12:14. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.12.' ieee: S. Baswana, S. Gupta, and T. Knollmann, “Mincut Sensitivity Data Structures for the Insertion of an Edge,” in 28th Annual European Symposium on Algorithms (ESA 2020), 2020, vol. 173, pp. 12:1-12:14. mla: Baswana, Surender, et al. “Mincut Sensitivity Data Structures for the Insertion of an Edge.” 28th Annual European Symposium on Algorithms (ESA 2020), edited by Fabrizio Grandoni et al., vol. 173, Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2020, pp. 12:1-12:14, doi:10.4230/LIPIcs.ESA.2020.12. short: 'S. Baswana, S. Gupta, T. Knollmann, in: F. Grandoni, G. Herman, P. Sanders (Eds.), 28th Annual European Symposium on Algorithms (ESA 2020), Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2020, pp. 12:1-12:14.' date_created: 2020-10-21T12:00:20Z date_updated: 2022-01-06T06:54:20Z department: - _id: '63' doi: 10.4230/LIPIcs.ESA.2020.12 editor: - first_name: Fabrizio full_name: Grandoni, Fabrizio last_name: Grandoni - first_name: Grzegorz full_name: Herman, Grzegorz last_name: Herman - first_name: Peter full_name: Sanders, Peter last_name: Sanders intvolume: ' 173' keyword: - Mincut - Sensitivity - Data Structure language: - iso: eng page: 12:1-12:14 place: Dagstuhl, Germany publication: 28th Annual European Symposium on Algorithms (ESA 2020) publication_identifier: isbn: - 978-3-95977-162-7 issn: - 1868-8969 publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik series_title: Leibniz International Proceedings in Informatics (LIPIcs) status: public title: Mincut Sensitivity Data Structures for the Insertion of an Edge type: conference user_id: '39241' volume: 173 year: '2020' ... --- _id: '20185' author: - first_name: Jannik full_name: Castenow, Jannik id: '38705' last_name: Castenow - first_name: Jonas full_name: Harbig, Jonas id: '47213' last_name: Harbig - first_name: Daniel full_name: Jung, Daniel id: '37827' last_name: Jung - first_name: Till full_name: Knollmann, Till id: '39241' last_name: Knollmann orcid: 0000-0003-2014-4696 - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide citation: ama: 'Castenow J, Harbig J, Jung D, Knollmann T, Meyer auf der Heide F. Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility . In: Devismes S, Mittal N, eds. Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings . Vol 12514. Lecture Notes in Computer Science (LNCS). Springer; 2020:60-64. doi:10.1007/978-3-030-64348-5_5' apa: 'Castenow, J., Harbig, J., Jung, D., Knollmann, T., & Meyer auf der Heide, F. (2020). Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility . In S. Devismes & N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings (Vol. 12514, pp. 60–64). Springer. https://doi.org/10.1007/978-3-030-64348-5_5' bibtex: '@inproceedings{Castenow_Harbig_Jung_Knollmann_Meyer auf der Heide_2020, series={Lecture Notes in Computer Science (LNCS)}, title={Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility }, volume={12514}, DOI={10.1007/978-3-030-64348-5_5}, booktitle={Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings }, publisher={Springer}, author={Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}, editor={Devismes, Stéphane and Mittal, NeerajEditors}, year={2020}, pages={60–64}, collection={Lecture Notes in Computer Science (LNCS)} }' chicago: 'Castenow, Jannik, Jonas Harbig, Daniel Jung, Till Knollmann, and Friedhelm Meyer auf der Heide. “Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility .” In Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , edited by Stéphane Devismes and Neeraj Mittal, 12514:60–64. Lecture Notes in Computer Science (LNCS). Springer, 2020. https://doi.org/10.1007/978-3-030-64348-5_5.' ieee: 'J. Castenow, J. Harbig, D. Jung, T. Knollmann, and F. Meyer auf der Heide, “Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility ,” in Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , 2020, vol. 12514, pp. 60–64.' mla: 'Castenow, Jannik, et al. “Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility .” Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , edited by Stéphane Devismes and Neeraj Mittal, vol. 12514, Springer, 2020, pp. 60–64, doi:10.1007/978-3-030-64348-5_5.' short: 'J. Castenow, J. Harbig, D. Jung, T. Knollmann, F. Meyer auf der Heide, in: S. Devismes, N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , Springer, 2020, pp. 60–64.' date_created: 2020-10-23T08:50:28Z date_updated: 2022-01-06T06:54:21Z department: - _id: '63' doi: 10.1007/978-3-030-64348-5_5 editor: - first_name: 'Stéphane ' full_name: 'Devismes, Stéphane ' last_name: Devismes - first_name: Neeraj full_name: ' Mittal, Neeraj' last_name: ' Mittal' external_id: arxiv: - '2010.04424 ' intvolume: ' 12514' language: - iso: eng page: 60-64 publication: 'Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings ' publication_identifier: isbn: - 978-3-030-64347-8 publication_status: published publisher: Springer series_title: Lecture Notes in Computer Science (LNCS) status: public title: 'Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility ' type: conference user_id: '38705' volume: 12514 year: '2020' ...