Geometric Lower Bounds for Parametric Matroid Optimization (1998) [13 citations — 1 self]
Popular Tags
No tags have been applied to this document.
BibTeX | Add To MetaCart
author = {David Eppstein},
title = {Geometric Lower Bounds for Parametric Matroid Optimization},
year = {1998}
}
Bookmarks
OpenURL
Abstract:
We relate the sequence of minimum bases of a matroid with linearly varying weights to three problems from combinatorial geometry: k-sets, lower envelopes of line segments, and convex polygons in line arrangements. Using these relations we show new lower bounds on the number of base changes in such sequences: #(nr 1/3 ) for a general n-element matroid with rank r , and #(m#(n)) for the special case of parametric graph minimum spanning trees. The only previous lower bound was #(n log r) for uniform matroids; upper bounds of O(mn 1/2 ) for arbitrary matroids and O(mn 1/2 / log # n) for uniform matroids were also known. 1 Introduction In this paper we study connections between combinatorial geometry and matroid optimization theory, as represented by the following problem. Parametric matroid optimization. Given a matroid for which the elements have weights that vary as a linear function of a parameter t , what is the sequence of minimum weight bases over the range of values o...
