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arXiv · 2401.07341

Binary weights spanning trees and the $k$-red spanning tree problem in linear time

Dorit S. Hochbaum
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Abstract

We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem, of finding a spanning tree with a pre-specified sum of weights, is NP-hard. In contrast, for a graph with binary weights associated with the edges, it is shown that the minimum spanning tree and finding a spanning tree with a given total sum, are solvable in linear time with simple algorithms.

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Dorit S. Hochbaum. 2024-01-14. Binary weights spanning trees and the $k$-red spanning tree problem in linear time. https://arxiv.org/abs/2401.07341

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