# Bipartite diameter and other measures under translation

Boris Aronov, Omrit Filtser, Matthew J. Katz, Khadijeh Sheikhan

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

## ملخص

Let A and B be two sets of points in Rd, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).

اللغة الأصلية الإنجليزيّة 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 Rolf Niedermeier, Christophe Paul Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 9783959771009 https://doi.org/10.4230/LIPIcs.STACS.2019.8 نُشِر - 1 مارس 2019 نعم 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 - Berlin, ألمانياالمدة: ١٣ مارس ٢٠١٩ → ١٦ مارس ٢٠١٩

### سلسلة المنشورات

الاسم Leibniz International Proceedings in Informatics, LIPIcs 126 1868-8969

### !!Conference

!!Conference 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 ألمانيا Berlin ١٣/٠٣/١٩ → ١٦/٠٣/١٩