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arXiv · 2510.01392

The Steiner Path Aggregation Problem

Da Qi Chen·Daniel Hathcock·D Ellis Hershkowitz·R. Ravi
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Abstract

In the Steiner Path Aggregation Problem, our goal is to aggregate paths in a directed network into a single arborescence without significantly disrupting the paths. In particular, we are given a directed multigraph with colored arcs, a root, and $k$ terminals, each of which has a monochromatic path to the root. Our goal is to find an arborescence in which every terminal has a path to the root, and its path does not switch colors too many times. We give an efficient algorithm that finds such a solution with at most $2\log_{4/3}k$ color switches. Up to constant factors this is the best possible universal bound, as there are graphs requiring at least $\log_2 k$ color switches.

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Da Qi Chen, Daniel Hathcock, D Ellis Hershkowitz, R. Ravi. 2025-10-01. The Steiner Path Aggregation Problem. https://doi.org/10.1016/j.ipl.2025.106608

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