On the Properties of All-Pair Heuristics

Shahaf S. Shperberg, Ariel Felner, Lior Siag, Nathan R. Sturtevant

Research output: Contribution to journalConference articlepeer-review


While most work in heuristic search concentrates on goalspecific heuristics, which estimate the shortest path cost from any state to the goal, we explore all-pair heuristics that estimate distances between all pairs of states. We examine the relationship between these heuristic functions and the shortest distance function they estimate, revealing that all-pair consistent heuristics may violate the triangle inequality. Thus, we introduce a new property for heuristics called ∆-consistency, requiring adherence to the triangle inequality. Additionally, we present a method for transforming standard consistent heuristics to be ∆-consistent, showcasing its benefits through a synthetic example. We then show that common heuristic families inherently exhibit ∆-consistency. This positive finding encourages the use of all-pair consistent heuristics, and prompts further investigation into the optimality of A, when given an all-pair heuristic instead of a goal-specific heuristic.

Original languageEnglish
Pages (from-to)127-133
Number of pages7
JournalThe International Symposium on Combinatorial Search
Issue number1
StatePublished - 2024
Externally publishedYes
Event17th International Symposium on Combinatorial Search, SoCS 2024 - Kananaskis, Canada
Duration: 6 Jun 20248 Jun 2024

Bibliographical note

Publisher Copyright:
© 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.


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