We study online matching in the Euclidean 2-dimensional plane with non-crossing constraint. The offline version was introduced by Atallah 1985 and studied more recently Bose et al. input to monochromatic (MNM) problem consists of a sequence points. Upon arrival point, an algorithm can decide match it previously unmatched point or leave unmatched. line segments corresponding edges should not cro...

Given a set of $n$ red and blue points in the plane, we are interested matching with by straight line segments so that do not cross. We develop range tools for dealing non-crossing matchings convex position. It turns out naturally partition into groups refer to as orbits, number properties prove useful studying efficiently processing matchings. Bottleneck is such minimizes length longest segmen...

A major obstacle to understanding classical genetic crossing over in higher organisms has been the lack of sufficient knowledge concerning the structure of chromosomes. Without accurate information, in particular, as to how the hereditary substance (DNA) is built into the chromosome, it may be premature to devise models depicting how that material may be recombined in crossing over. In recent y...

This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Ω(12.52 ) noncrossing spanning trees and Ω(13.61 ) non-crossing forests. This improves the previous lower bounds on the maximum number of non...

A non-crossing pairing on a binary string pairs ones and zeroes such that the arcs representing the pairings are non-crossing. A binary string is well-balanced if it is of the form 11011202 . . . 1r0r . In this paper we establish connections between non-crossing pairings of well-balanced binary strings and various lattice paths in plane. We show that for well-balanced binary strings with a1 ≤ a...

The complexity of pairwise RNA structure alignment depends on the structural restrictions assumed for both the input structures and the computed consensus structure. For arbitrarily crossing input and consensus structures, the problem is NP-hard. For non-crossing consensus structures, Jiang et al’s algorithm [1] computes the alignment in O(nm) time where n and m denote the lengths of the two in...

Let K′ be a knot that admits no cosmetic crossing changes and let C be a prime, non-cable knot. Then any knot that is a satellite of C with winding number zero and pattern K′ admits no cosmetic crossing changes. As a consequence we prove the nugatory crossing conjecture for Whitehead doubles of prime, non-cable knots.

Abstract. In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is used to obtain the explicit formulas for some special cases. Bijection is also established between generalized non-crossing trees with special patter...

Non –crossing set partitions are counted by the Catalan numbers and have been extensively studied in mathematics. We introduce the concept of a non-crossing tree partition and then use generating functions to count the number non-crossing tree partitions in Ordered and Binary Phylogenetic trees. In addition, we explore the connection between convexity, tree partitions and independent sets. Last...