We give an optimal bound on the number of transitions of the minimum weight base of an integer valued parametric polymatroid. This generalizes and unifies Tamal Dey's O(k1/3n) upper bound on the number of k-sets (and the complexity of the k-level of a straight-line arrangement), David Eppstein's lower bound on the number of transitions of the minimum weight base of a parametric matroid, and also the Θ (kn) bound on the complexity of the at-most-k level (the union of i-levels for i = 1, 2, ..., k) of a straight-line arrangement. As applications, we improve Welzl's upper bound on the sum of the complexities of multiple levels, and apply this bound to the number of different equal-sized-bucketings of a planar point set with parallel partition lines. We also consider an application to a special parametric transportation problem.
|Number of pages||10|
|Publication status||Published - 1 Jan 1999|
|Event||Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA|
Duration: 17 Jan 1999 → 19 Jan 1999
|Conference||Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms|
|City||Baltimore, MD, USA|
|Period||17/01/99 → 19/01/99|