Paths and Intersections: Recognizing Outerplanar Metrics

Yu Chen; Zihan Tan

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arXiv · 2606.25827

Paths and Intersections: Recognizing Outerplanar Metrics

Yu Chen·Zihan Tan

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Abstract

We study the following distance realization problem: given a metric $D$ on a set $T$ of terminals, does there exist an (edge-weighted) outerplanar graph $G$, such that $T\subseteq V(G)$, and for every pair $t,t'\in T$, $\textsf{dist}_G(t,t')=D(t,t')$? We first prove that there is no ``local characterization'', forming a contrast with trees and Okamura-Seymour instances. Our main result is an efficient algorithm for this problem whose running time is polynomial in $|T|$. Both our proof and our algorithm utilize a recent new approach of analyzing graph structures, by viewing graphs as paths and their intersections, which we believe is of independent interest.

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BibTeX RIS

Yu Chen, Zihan Tan. 2026-06-24. Paths and Intersections: Recognizing Outerplanar Metrics. https://arxiv.org/abs/2606.25827

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