TY - GEN
T1 - Bipartite diameter and other measures under translation
AU - Aronov, Boris
AU - Filtser, Omrit
AU - Katz, Matthew J.
AU - Sheikhan, Khadijeh
N1 - Publisher Copyright:
© Boris Aronov, Omrit Filtser, Matthew J. Katz, and Khadijeh Sheikhan.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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).
AB - 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).
KW - Geometric optimization
KW - Minimum-width annulus
KW - Translation-invariant similarity measures
UR - http://www.scopus.com/inward/record.url?scp=85074924983&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.STACS.2019.8
DO - 10.4230/LIPIcs.STACS.2019.8
M3 - Conference contribution
AN - SCOPUS:85074924983
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
A2 - Niedermeier, Rolf
A2 - Paul, Christophe
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
Y2 - 13 March 2019 through 16 March 2019
ER -