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

Y1 - 2012

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 - http://www.scopus.com/inward/record.url?scp=84866696901&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33090-2_5

DO - 10.1007/978-3-642-33090-2_5

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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 -