Bidirectional Search That Is Guaranteed to Meet in the Middle

@inproceedings{Holte2016BidirectionalST,
  title={Bidirectional Search That Is Guaranteed to Meet in the Middle},
  author={Robert C. Holte and Ariel Felner and Guni Sharon and Nathan R Sturtevant},
  booktitle={AAAI},
  year={2016}
}
We present MM, the first bidirectional heuristic search algorithm whose forward and backward searches are guaranteed to "meet in the middle", i.e. never expand a node beyond the solution midpoint. [] Key Method We also present a novel framework for comparing MM, A*, and brute-force search, and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Figures and Tables from this paper

MM: A bidirectional search algorithm that is guaranteed to meet in the middle
The Minimal Set of States that Must Be Expanded in a Front-to-End Bidirectional Search
TLDR
The nature of the number of nodes that must be expanded in any front-to-end bidirectional search is studied and it is shown that a theoretical parameterized generalization of MM, with the correct parameter, is the optimal front- to-end Bidirectional Search.
Optimally Efficient Bidirectional Search
TLDR
This paper presents the Fractional MM algorithm and its sibling, the MT algorithm, which is simpler to analyze and develops variants of these algorithms that are optimally efficient, each under different assumptions on the information available to the algorithm.
Extended Abstract: An Improved Priority Function for Bidirectional Heuristic Search
TLDR
MMe is presented, which enhances MM’s priority function and is expected to expand fewer nodes than MM under most circumstances and is compared with MM on the 10-Pancake problem.
Sufficient Conditions for Node Expansion in Bidirectional Heuristic Search
TLDR
The sufficient conditions are used to prove that the front-to-front biddirectional search algorithm BDS1 is optimally efficient, in terms of node expansion, among a broad class of bidirectional search algorithms, for a specific class of problem instances.
Minimizing Node Expansions in Bidirectional Search with Consistent Heuristics
TLDR
This paper generalizes the bidirectional result to more complex settings where more information on the problem domain can be exploited and uses a novel algorithm called MT, which is similar to Fractional MM and is also optimally effective, but simpler to analyze.
An Improved Meet in the Middle Algorithm for Graphs with Unit Costs
TLDR
This paper proves several new properties of the Meet in the Middle bidirectional heuristic search algorithm when applied to graphs with unit edge costs, including that the length of the first path discovered by MM never exceeds the optimal length by more than one and that if the longest path found is odd, then it must be optimal.
Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions
TLDR
This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs of states for bidirectional search with consistent heuristics, and presents a new admissible front-to-end biddirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions.
Multi-Directional Heuristic Search
In the Multi-Agent Meeting problem (MAM), the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a
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References

SHOWING 1-10 OF 35 REFERENCES
D-Node Retargeting in Bidirectional Heuristic Search
TLDR
This paper presents an efficient algorithm for bidirectional heuristic search and compares this algorithm with de Champeaux's BHFFA on the basis of search efficiency, solution quality, and computational cost.
Bidirectional Heuristic Search Again
TLDR
Extensive modifications of a previously published bidirectional heuristic search algorithm are presented and theoretical results encompass the generalisation of the unidirectional optimality theorem.
Switching from Bidirectional to Unidirectional Search
TLDR
This work developed a new approach to improving traditional bidirectional search with "front-to-end" evaluations, switching to unidirectionalSearch after the search frontiers meet for the first time (with the first solution found).
An Improved Bidirectional Heuristic Search Algorithm
A modification of Pohl's bidirectional heuristic search algorithm is described together with a simplified implementation. Theorems are proved about conditions yielding shortest paths. The results are
A two-phase bidirectional heuristic search algorithm
TLDR
This work describes a new best-first bidirectional heuristic search algorithm with two phases based on a critical review of the basic search reduction operations in previous algorithms like BS* or Switch-A*.
Memory-Bounded Bidirectional Search
TLDR
Bidirectional search appears to be the best approach to solving difficult problems, and this indicates the extreme usefulness of a paradigm that was neglected for long.
BIDA: An Improved Perimeter Search Algorithm
An Optimal Bidirectional Search Algorithm
Several optimality theorems hold for the A* algorithm, one important says: A* dominates every other admissible heuristic search algorithm assumed that the underlying heuristic function is monotone.
Limitations of Front-To-End Bidirectional Heuristic Search
TLDR
It is shown that on the four-peg Towers Of Hanoi with arbitrary start and goal states, bidirectional brute-force search outperforms unidirectional heuristic search using pattern-database heuristics.
BS*: An Admissible Bidirectional Staged Heuristic Search Algorithm
...
1
2
3
4
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