Offline algorithms for dynamic minimum spanning tree problems
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Notes on computing peaks in k-levels and parametric spanning trees
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Using sparsification for parametric minimum spanning tree problems
Nordic Journal of Computing
Parametric and Kinetic Minimum Spanning Trees
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Possibilistic bottleneck combinatorial optimization problems with ill-known weights
International Journal of Approximate Reasoning
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The result. Parametric optimization problems that concern graphs with continuously changing edge weights have been explored by numerous researchers, with motivation ranging from sensitivity analysis to mobile-data applications. For instance, Dey [5] has shown that for an undirected graph with n vertices and m edges where the edge weights are linear functions in one parameter ("time"), the minimum spanning tree (MST) can undergo at most O(mn1/3) changes (edge swaps). Agarwal et al. [1] have given data structures to maintain the MST over time, with a cost of O(n2/3 polylog n) per change. Fernandez-Baca et al. [7] have given an algorithm to compute all changes to the MST in O(mn log n) total time.