Optimal Circular Arc Representations: Properties, Recognition, and Construction

AbstractWe investigate some properties of minimal interval and circular arc representations and give several optimal sequential and parallel recognition and construction algorithms. We show that, among other things, given ans×tinterval or circular arc representation matrix, •deciding if the representation is minimal can be done inO(logs) time withO(st/logs) EREW PRAM processors, or inO(1) time withO(st) common CRCW PRAM processors; •constructing an equivalent minimum interval representation can be done inO(log(st)) time withO(st/log(st)) EREW PRAM processors, or inO(logt/loglogt) time withO(stloglogt/logt) common CRCW PRAM processors, or inO(1) time withO(st) BSR processors; •constructing an equivalent minimal circular arc representation can be done inO(st) time

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

Convex-Arc Drawings of Pseudolines

A weak pseudoline arrangement is a topological generalization of a line arrangement, consisting of curves topologically equivalent to lines that cross each other at most once. We consider arrangements that are outerplanar---each crossing is incident to an unbounded face---and simple---each crossing point is the crossing of only two curves. We show that these arrangements can be represented by chords of a circle, by convex polygonal chains with only two bends, or by hyperbolic lines. Simple but non-outerplanar arrangements (non-weak) can be represented by convex polygonal chains or convex smooth curves of linear complexity.Comment: 11 pages, 8 figures. A preliminary announcement of these results was made as a poster at the 21st International Symposium on Graph Drawing, Bordeaux, France, September 2013, and published in Lecture Notes in Computer Science 8242, Springer, 2013, pp. 522--52

Comparative study on the application of evolutionary optimization techniques to orbit transfer maneuvers

Orbit transfer maneuvers are here considered as benchmark cases for comparing performance of different optimization techniques in the framework of direct methods. Two different classes of evolutionary algorithms, a conventional genetic algorithm and an estimation of distribution method, are compared in terms of performance indices statistically evaluated over a prescribed number of runs. At the same time, two different types of problem representations are considered, a first one based on orbit propagation and a second one based on the solution of Lambert’s problem for direct transfers. In this way it is possible to highlight how problem representation affects the capabilities of the considered numerical approaches