TY - GEN
T1 - Bottleneck non-crossing matching in the plane
AU - Abu-Affash, A. Karim
AU - Carmi, Paz
AU - Katz, Matthew J.
AU - Trabelsi, Yohai
PY - 2012/10/1
Y1 - 2012/10/1
N2 - Let P be a set of 2n points in the plane, and let M C (resp., M NC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing M NC. We present an O(n 1.5log 0.5 n)-time algorithm that computes a non-crossing matching M of P, such that bn(M) ≤ 2√10·bnM NC, where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(M NC)/bn(M NC) ≤ 22√10. We also show that when the points of P are in convex position, one can compute M NC in O(n 3) time. (In the full version of this paper, we also prove that the problem is NP-hard and does not admit a PTAS.)
AB - Let P be a set of 2n points in the plane, and let M C (resp., M NC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing M NC. We present an O(n 1.5log 0.5 n)-time algorithm that computes a non-crossing matching M of P, such that bn(M) ≤ 2√10·bnM NC, where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(M NC)/bn(M NC) ≤ 22√10. We also show that when the points of P are in convex position, one can compute M NC in O(n 3) time. (In the full version of this paper, we also prove that the problem is NP-hard and does not admit a PTAS.)
UR - https://www.scopus.com/pages/publications/84866696901
U2 - 10.1007/978-3-642-33090-2_5
DO - 10.1007/978-3-642-33090-2_5
M3 - Conference contribution
AN - SCOPUS:84866696901
SN - 9783642330896
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 36
EP - 47
BT - Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings
T2 - 20th Annual European Symposium on Algorithms, ESA 2012
Y2 - 10 September 2012 through 12 September 2012
ER -