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1995
ACM

Geometric lower bounds for parametric matroid optimization

8 years 10 months ago
Geometric lower bounds for parametric matroid optimization
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: (nr1/3 ) for a general n-element matroid with rank r, and (mα(n)) for the special case of parametric graph minimum spanning trees. The only previous lower bound was (n logr) for uniform matroids; upper bounds of O(mn1/2 ) for arbitrary matroids and O(mn1/2 / log∗ n) for uniform matroids were also known.
David Eppstein
Added 26 Aug 2010
Updated 26 Aug 2010
Type Conference
Year 1995
Where STOC
Authors David Eppstein
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