MM: A bidirectional search algorithm that is guaranteed to meet in the middle

Robert C. Holte, Ariel Felner, Guni Sharon, Nathan R. Sturtevant, Jingwei Chen

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Bidirectional search algorithms interleave two separate searches, a normal search forward from the start state, and a search backward from the goal. It is well known that adding a heuristic to unidirectional search dramatically reduces the search effort. By contrast, despite decades of research, bidirectional heuristic search has not yet had a major impact. Additionally, no comprehensive theory was ever devised to understand the nature of bidirectional heuristic search. In this paper we aim to close this gap. We first present MM, a novel bidirectional heuristic search algorithm. Unlike previous bidirectional heuristic search algorithms, MM's forward and backward searches are guaranteed to “meet in the middle”, i.e. never expand a node beyond the solution midpoint. Based on this unique attribute we present a novel framework for comparing MM, A*, and their brute-force variants. We do this by dividing the entire state space into disjoint regions based on their distance from the start and goal. This allows us to perform a comparison of these algorithms on a per region basis and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Original languageEnglish
Pages (from-to)232-266
Number of pages35
JournalArtificial Intelligence
StatePublished - Nov 2017
Externally publishedYes

Bibliographical note

Funding Information:
Thanks to Joseph Barker for answering questions and providing extra data related to [4] and to Sandra Zilles and André Grahl Pereira for suggesting improvements in the theoretical analysis of MM . Financial support for this research was in part provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by Israel Science Foundation (ISF) grants # 417/3 and # 212/17 . Computational facilities for some of our experiments were provided by Compute Canada. This material is based upon work supported by the National Science Foundation under Grant No. 1551406 .

Publisher Copyright:
© 2017 Elsevier B.V.


  • Bidirectional search
  • Heuristic search


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