--- _id: '8793' abstract: - lang: eng text: We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff. acknowledgement: "We are grateful to Matthias Függer and Thomas Nowak for having raised our interest in the problem studied in this paper.\r\nThis work has been supported the Austrian Science Fund (FWF) projects S11405, S11407 (RiSE), and P28182 (ADynNet)." article_processing_charge: No article_type: original author: - first_name: Martin full_name: Zeiner, Martin last_name: Zeiner - first_name: Ulrich full_name: Schmid, Ulrich last_name: Schmid - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X citation: ama: Zeiner M, Schmid U, Chatterjee K. Optimal strategies for selecting coordinators. Discrete Applied Mathematics. 2021;289(1):392-415. doi:10.1016/j.dam.2020.10.022 apa: Zeiner, M., Schmid, U., & Chatterjee, K. (2021). Optimal strategies for selecting coordinators. Discrete Applied Mathematics. Elsevier. https://doi.org/10.1016/j.dam.2020.10.022 chicago: Zeiner, Martin, Ulrich Schmid, and Krishnendu Chatterjee. “Optimal Strategies for Selecting Coordinators.” Discrete Applied Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.dam.2020.10.022. ieee: M. Zeiner, U. Schmid, and K. Chatterjee, “Optimal strategies for selecting coordinators,” Discrete Applied Mathematics, vol. 289, no. 1. Elsevier, pp. 392–415, 2021. ista: Zeiner M, Schmid U, Chatterjee K. 2021. Optimal strategies for selecting coordinators. Discrete Applied Mathematics. 289(1), 392–415. mla: Zeiner, Martin, et al. “Optimal Strategies for Selecting Coordinators.” Discrete Applied Mathematics, vol. 289, no. 1, Elsevier, 2021, pp. 392–415, doi:10.1016/j.dam.2020.10.022. short: M. Zeiner, U. Schmid, K. Chatterjee, Discrete Applied Mathematics 289 (2021) 392–415. date_created: 2020-11-22T23:01:26Z date_published: 2021-01-31T00:00:00Z date_updated: 2023-08-04T11:12:41Z day: '31' ddc: - '510' department: - _id: KrCh doi: 10.1016/j.dam.2020.10.022 external_id: isi: - '000596823800035' file: - access_level: open_access checksum: f1039ff5a2d6ca116720efdb84ee9d5e content_type: application/pdf creator: dernst date_created: 2021-02-04T11:28:42Z date_updated: 2021-02-04T11:28:42Z file_id: '9089' file_name: 2021_DiscreteApplMath_Zeiner.pdf file_size: 652739 relation: main_file success: 1 file_date_updated: 2021-02-04T11:28:42Z has_accepted_license: '1' intvolume: ' 289' isi: 1 issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '01' oa: 1 oa_version: Published Version page: 392-415 project: - _id: 25F2ACDE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11402-N23 name: Rigorous Systems Engineering - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: Discrete Applied Mathematics publication_identifier: issn: - 0166218X publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Optimal strategies for selecting coordinators tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 289 year: '2021' ... --- _id: '5857' abstract: - lang: eng text: 'A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is [Formula presented](n−1), and that this bound is best possible for infinitely many values of n.' article_processing_charge: No article_type: original author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: János full_name: Pach, János last_name: Pach citation: ama: 'Fulek R, Pach J. Thrackles: An improved upper bound. Discrete Applied Mathematics. 2019;259(4):266-231. doi:10.1016/j.dam.2018.12.025' apa: 'Fulek, R., & Pach, J. (2019). Thrackles: An improved upper bound. Discrete Applied Mathematics. Elsevier. https://doi.org/10.1016/j.dam.2018.12.025' chicago: 'Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.dam.2018.12.025.' ieee: 'R. Fulek and J. Pach, “Thrackles: An improved upper bound,” Discrete Applied Mathematics, vol. 259, no. 4. Elsevier, pp. 266–231, 2019.' ista: 'Fulek R, Pach J. 2019. Thrackles: An improved upper bound. Discrete Applied Mathematics. 259(4), 266–231.' mla: 'Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics, vol. 259, no. 4, Elsevier, 2019, pp. 266–231, doi:10.1016/j.dam.2018.12.025.' short: R. Fulek, J. Pach, Discrete Applied Mathematics 259 (2019) 266–231. date_created: 2019-01-20T22:59:17Z date_published: 2019-04-30T00:00:00Z date_updated: 2023-08-24T14:39:33Z day: '30' department: - _id: UlWa doi: 10.1016/j.dam.2018.12.025 external_id: arxiv: - '1708.08037' isi: - '000466061100020' intvolume: ' 259' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.08037 month: '04' oa: 1 oa_version: Preprint page: 266-231 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Discrete Applied Mathematics publication_identifier: issn: - 0166218X publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '433' relation: earlier_version status: public scopus_import: '1' status: public title: 'Thrackles: An improved upper bound' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 259 year: '2019' ...