A greedy algorithm for interval greedoids

Oriented Interval Greedoids

We propose a definition of an oriented interval greedoid that simultaneously generalizes the notion of an oriented matroid and the construction on antimatroids introduced by L. J. Billera, S. K. Hsiao, and J. S. Provan in Enumeration in convex geometries and associated polytopal subdivisions of spheres [Discrete Comput. Geom. 39 (2008), no. 1-3, 123–137]. As for of oriented matroids, associated...

A Class of Greedy Algorithms and Its Relation to Greedoids

Non-interval greedoids and the transposition property

In previous papers we have mainly studied greedoids with the interval property. This paper exhibits 11 classes of greedoids whose members do not necessarily have the interval property. These non-interval greedoids are related to some fundamental algorithms and procedural principles like Gaussian elimination, blossom trees, series-parallel decomposition, ear decomposition, retracting and dismant...

Performance of a greedy algorithm for edge covering by cliques in interval graphs

In this paper a greedy algorithm to detect conflict cliques in interval graphs and circular-arc graphs is analysed. In a graph, a stable set requires that at most one vertex is chosen for each edge. It is equivalent to requiring that at most one vertex for each maximal clique is chosen. We show that this algorithm finds all maximal cliques for interval graphs, i.e. it can compute the convex hul...

Gauss elimination algorithm for interval matrix