--- _id: '2156' abstract: - lang: eng text: We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s). acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258. author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Xiaoyin full_name: Ge, Xiaoyin last_name: Ge - first_name: Yusu full_name: Wang, Yusu last_name: Wang citation: ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169' apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In Proceedings of the Annual Symposium on Computational Geometry (pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169' chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In Proceedings of the Annual Symposium on Computational Geometry, 464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169. ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 464–473. ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.' mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73, doi:10.1145/2582112.2582169. short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473. conference: end_date: 2014-06-11 location: Kyoto, Japan name: 'SoCG: Symposium on Computational Geometry' start_date: 2014-06-08 date_created: 2018-12-11T11:56:02Z date_published: 2014-06-01T00:00:00Z date_updated: 2021-01-12T06:55:39Z day: '01' department: - _id: HeEd doi: 10.1145/2582112.2582169 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1307.2839 month: '06' oa: 1 oa_version: Submitted Version page: 464 - 473 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the Annual Symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4850' quality_controlled: '1' scopus_import: 1 status: public title: Measuring distance between Reeb graphs type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ...