Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Random knapsack in expected polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Minimum spanning trees made easier via multi-objective optimization
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Multicriteria Optimization
On the approximation ability of evolutionary optimization with application to minimum set cover
Artificial Intelligence
Hi-index | 0.00 |
We give faster approximation algorithms for the generalization of two NP-hard spanning tree problems. First, we investigate the problem of minimizing the degree of minimum spanning forests. Fischer [3] has shown how to compute a minimum spanning tree of degree at most b Δ* + ⌈logbn⌉ in time O(n$^{\rm 4 + 1/ ln {\it b}}$) for any b1, where Δ* is the value of an optimal solution. We model our generalization as a multi-objective optimization problem and give a deterministic algorithm that computes for each number of connected components a solution with the same approximation quality as the algorithm of Fischer and runs in time O(n$^{\rm 3 + 1/ ln {\it b}}$). After that, we take a multi-objective view on the problem of computing minimum spanning trees with nonuniform degree bounds, which has been examined by Könemann and Ravi [7]. Given degree bounds Bv for each vertex v ∈ V, we construct an algorithm that computes for each number of connected components a spanning forest in which each vertex v has degree O(Bv + log n) and whose weight is at most a constant times the weight of a minimum spanning forest obeying the degree bounds. The total runtime of our algorithm is O(n$^{\rm 3 + 2 / ln {\it b}}$) for an arbitrary constant b1. Setting b=ek, k 2/3 an arbitrary constant, the runtime is by a factor n$^{\rm 3-2/{\it k}}$ log n less than the given bound by Könemann and Ravi.