TY - JOUR
T1 - Bottleneck non-crossing matching in the plane
AU - Karim Abu-Affash, A.
AU - Carmi, Paz
AU - Katz, Matthew J.
AU - Trabelsi, Yohai
PY - 2014
Y1 - 2014
N2 - Let P be a set of 2n points in the plane, and let MC (resp., MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing MNC. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].
AB - Let P be a set of 2n points in the plane, and let MC (resp., MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing MNC. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].
KW - Approximation algorithms
KW - Bottleneck matching
KW - NP-hardness
KW - Non-crossing configuration
UR - http://www.scopus.com/inward/record.url?scp=84888435552&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2013.10.005
DO - 10.1016/j.comgeo.2013.10.005
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84888435552
SN - 0925-7721
VL - 47
SP - 447
EP - 457
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3 PART A
ER -