$\boldsymbol{Steiner}$-Hardness: A Query Hardness Measure for Graph-Based ANN Indexes
Zeyu Wang, Qitong Wang, Xiaoxing Cheng, Peng Wang, Themis Palpanas,, Wei Wang

TL;DR
This paper introduces Steiner-hardness, a new graph-native measure for assessing query difficulty in graph-based approximate nearest neighbor indexes, showing better correlation with actual effort than existing measures.
Contribution
It proposes a theoretical framework and an efficient algorithm to compute Steiner-hardness, improving the understanding and evaluation of query hardness in graph indexes.
Findings
Steiner-hardness correlates better with query effort than LID.
The proposed method efficiently computes Steiner-hardness using DST problem solvers.
Evaluation reveals new ranking insights for index robustness.
Abstract
Graph-based indexes have been widely employed to accelerate approximate similarity search of high-dimensional vectors. However, the performance of graph indexes to answer different queries varies vastly, leading to an unstable quality of service for downstream applications. This necessitates an effective measure to test query hardness on graph indexes. Nonetheless, popular distance-based hardness measures like LID lose their effects due to the ignorance of the graph structure. In this paper, we propose -hardness, a novel connection-based graph-native query hardness measure. Specifically, we first propose a theoretical framework to analyze the minimum query effort on graph indexes and then define -hardness as the minimum effort on a representative graph. Moreover, we prove that our -hardness is highly relevant to the classical Directed Tree (DST)…
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Taxonomy
TopicsAdvanced Graph Neural Networks · Graph Theory and Algorithms · Machine Learning and Algorithms
