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Breadth-first branch-and-bound search

Algorithms AIMech:BreadthFirstBranchAndBound DRAFT

Aliases: BFBnB

A heuristic graph-search procedure that expands states in breadth-first layers and prunes candidate paths whose accumulated cost plus an admissible remaining-cost estimate exceeds a supplied solution-cost bound; the formulation curated here assumes uniform positive edge costs, scaled to one.

Identity Notes & Concept Scope The BFBnB search strategy is distinguished from BFIDA*, which obtains bounds by repeated searches, and from width-pruned beam search. Breadth-first heuristic search names the broader family in Zhou and Hansen; that umbrella phrase is not asserted as an exact alias. Frontier, sparse-memory and layered duplicate-detection implementations are alternatives, not mandatory simultaneous components. No normalized identity match was found across the 442 AIO and 135 prior native records; ignored-inclusive text hits in the main checkout were prior discovery leads, source citations, scope contrasts and DCBSS substring matches, plus seven public certificate-data substring matches, not existing concept records.

Claims & Grounded Evidence

2 Claims

Mechanism #search-procedure

For a unit-cost graph, process nodes by increasing depth g and evaluate f=g+h with admissible h. Under a hypothetical bound U, retain f≤U. If U is the cost of an actual retained incumbent and only improvement is needed, f≥U can instead be pruned; failure to improve then preserves the incumbent. Memory-saving implementations retain enough information for duplicate detection and use relay nodes to reconstruct a found path by recursively solving subproblems.

supports Source: Breadth-first heuristic search · Locator: Sections 3–3.5, printed pp. 389–395 / PDF pp. 5–11; Figure 2 and the actual-incumbent versus hypothetical-bound distinction on printed pp. 393–394

Limitation #resource-scope

The authors consider frontier, sparse-memory and layered duplicate handling, and relay-based path recovery. The potential reduction in stored search nodes is problem dependent; neither a fixed total-memory bound nor a universal advantage over A* follows. Nonuniform-cost extensions are outlined as future work.

supports Source: Breadth-first heuristic search · Locator: Sections 2.2–3.4, 6.1–6.2; printed pp. 387–392 and 405–406 / PDF pp. 3–8 and 21–22

⚠️ Curated Limitations & Negative Results

The scope is uniform positive costs and an admissible heuristic. A valid upper bound must cover a real solution for a single-pass optimal-solution guarantee; an unsuccessful hypothetical contour does not establish that the original problem is unsolvable.
The layered implementation needs enough previous-layer information for the graph structure; retaining one previous layer is not a universal duplicate-elimination rule for directed graphs.
Memory-saving implementations can still run out of memory in a large frontier. The paper explicitly does not prove universally lower peak memory than best-first search.
The f≥U option is valid for improving an actual incumbent, not for an inclusive hypothetical contour with no stored solution. Preserving the incumbent when no improvement exists is an explicit operational consequence of that distinction.
The record does not certify the printed pseudocode for all base cases, graph-locality claims under every pruning policy, or nonuniform-cost extensions.

Artificial Intelligence Ontology (AIO) Grounding

Explicit AIO Snapshot Assessment: No Match

Rationale: No suitable AIO counterpart for this graph/state-space search procedure was identified in the inspected snapshot. Using graphs, evaluation functions or a search subroutine in an AI system does not equate the algorithm with a learned model, a learning task or a mathematical function.

Search Scope: All 442 pinned AIO labels and scoped synonyms and 135 preceding native identities were compared. Both updated checkouts were searched including hidden and ignored files. Exact CLASS nodes and edges for GraphLanguageModel, ReasoningLLM, NeuroSymbolicLLM, MachineLearningTask, MathematicalFunction and ReinforcementLearning were inspected, alongside semantic search for search, planning, heuristic, path, traversal, symbolic, reasoning and graph terminology.

Examined AIO Candidate	Rejection Reason
`AIO:GraphLanguageModel`	A language model operating on structured graph representations is not a graph traversal or shortest-path algorithm.
`AIO:ReasoningLLM`	Language-task deductive inference does not denote general state-space search.
`AIO:NeuroSymbolicLLM`	A language-model architecture combining neural and symbolic components is not the search procedure itself.
`AIO:MachineLearningTask`	Building methods that learn from data is not the identity of an algorithm traversing a specified graph.
`AIO:MathematicalFunction`	The search procedure is distinct from the mathematical functions it may evaluate.
`AIO:ReinforcementLearning`	A learning task balancing exploration and exploitation is distinct from deterministic graph/state-space traversal.

Evidence Sources & Primary Literature

2 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`method-source`	Breadth-first heuristic search Rong Zhou, Eric A. Hansen	primary paper full_text	ID: doi:10.1016/j.artint.2005.12.002 sha256:9f094b2d1e98…
`resource-scope`	Breadth-first heuristic search Rong Zhou, Eric A. Hansen	primary paper full_text	ID: doi:10.1016/j.artint.2005.12.002 sha256:9f094b2d1e98…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-11T06:16:04Z

Updated: 2026-10-11T06:16:04Z

Source File: data/curated/BreadthFirstBranchAndBound.yaml