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Embeddings and Labeling Schemes for A*

Authors Talya Eden, Piotr Indyk, Haike Xu

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Author Details

Talya Eden
  • Massachusetts Institute of Technology, Cambridge, MA, USA
  • Boston University, MA, USA
Piotr Indyk
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Haike Xu
  • Tsinghua University, Beijing, China

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Talya Eden, Piotr Indyk, and Haike Xu. Embeddings and Labeling Schemes for A*. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 62:1-62:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function h(u,t) that estimates the shortest distance from any input node u to the destination t. Traditionally, heuristics have been handcrafted by domain experts. However, over the last few years, there has been a growing interest in learning heuristic functions. Such learned heuristics estimate the distance between given nodes based on "features" of those nodes. In this paper we formalize and initiate the study of such feature-based heuristics. In particular, we consider heuristics induced by norm embeddings and distance labeling schemes, and provide lower bounds for the tradeoffs between the number of dimensions or bits used to represent each graph node, and the running time of the A* algorithm. We also show that, under natural assumptions, our lower bounds are almost optimal.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • A* algorithm
  • path finding
  • graph search


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