Approximating Approximate Distance Oracles
Michael Dinitz, Zeyu Zhang

TL;DR
This paper investigates how to optimize approximate distance oracles for specific metric spaces, providing approximation algorithms and bounds for well-known classes like Thorup-Zwick and Ptrau-Roditty.
Contribution
It introduces approximation algorithms for finding minimal size oracles within certain classes, with proven bounds and integrality gaps, and extends to outlier scenarios using SDP relaxations.
Findings
O(( log n))-approximation for Thorup-Zwick and Ptrau-Roditty oracles
Matching ( log n)) lower bounds for these problems
Approximation of oracles with outliers using SDP relaxations
Abstract
Given a finite metric space , an approximate distance oracle is a data structure which, when queried on two points , returns an approximation to the the actual distance between and which is within some bounded stretch factor of the true distance. There has been significant work on the tradeoff between the important parameters of approximate distance oracles (and in particular between the size, stretch, and query time), but in this paper we take a different point of view, that of per-instance optimization. If we are given an particular input metric space and stretch bound, can we find the smallest possible approximate distance oracle for that particular input? Since this question is not even well-defined, we restrict our attention to well-known classes of approximate distance oracles, and study whether we can optimize over those classes. In particular, we give…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Cryptography and Data Security
