Nearly Optimal Sparse Navigable Graphs in General Metrics

We study approximation algorithms for constructing sparse navigable graphs in general metrics. Given an $n$-point metric $(P,d)$ and a parameter $α\ge1$, a directed graph on $P$ is $α$-navigable if, for every pair of distinct points $s,t\in P$, the source $s$ has an outgoing neighbor $p$ with $d(p,t)

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40146
Primary Topic
Complexity and Algorithms in Graphs
Type
preprint
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preprint

Nearly Optimal Sparse Navigable Graphs in General Metrics

Hongyi Chen, Tianyi Zhang
arXiv (Cornell University)
Complexity and Algorithms in Graphs
preprint

Nearly Optimal Sparse Navigable Graphs in General Metrics

Hongyi Chen, Tianyi Zhang
preprint en

Abstract

We study approximation algorithms for constructing sparse navigable graphs in general metrics. Given an $n$-point metric $(P,d)$ and a parameter $α\ge1$, a directed graph on $P$ is $α$-navigable if, for every pair of distinct points $s,t\in P$, the source $s$ has an outgoing neighbor $p$ with $d(p,t)

arXiv (Cornell University)
Complexity and Algorithms in Graphs
DOIOpen Access PDFOpenAlex
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Nearly Optimal Sparse Navigable Graphs in General Metrics — Hongyi Chen, Tianyi Zhang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS