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

2024/01/14 by Dorit S. Hochbaum, Hochbaum, Dorit S.
Computer Science · Engineering · #Advanced Optical Network Technologies #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Network Traffic and Congestion Control #VLSI and FPGA Design Techniques

paper · pdf · doi:10.48550/arxiv.2401.07341

openalex publication_date 2024/01/14 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

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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