{"page":"2242 - 2257","external_id":{"arxiv":["1604.00960"],"isi":["000450810500036"]},"language":[{"iso":"eng"}],"scopus_import":"1","date_created":"2018-12-11T11:44:24Z","status":"public","day":"06","_id":"58","publication":"SIAM Journal on Discrete Mathematics","publication_status":"published","date_published":"2018-09-06T00:00:00Z","article_processing_charge":"No","month":"09","oa_version":"Preprint","publisher":"Society for Industrial and Applied Mathematics ","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"first_name":"Erel","full_name":"Segal Halevi, Erel","last_name":"Segal Halevi"}],"citation":{"ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X."},"doi":"10.1137/16M110407X","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"intvolume":" 32","type":"journal_article","title":"Counting blanks in polygonal arrangements","publist_id":"7996","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"date_updated":"2023-09-11T12:48:39Z","ec_funded":1,"oa":1,"volume":32,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","isi":1,"department":[{"_id":"HeEd"}],"year":"2018","issue":"3","abstract":[{"text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.","lang":"eng"}],"quality_controlled":"1"}