Is speedy search the same as breadth-first search?

No. Breadth-first search orders by depth already reached; speedy search orders by estimated distance remaining.

Does it use the cost already paid along a path?

Not in its basic priority rule, which focuses on estimated remaining action count.

Is it always faster than cost-based greedy search?

No. Results depend on the problem, heuristic quality, and implementation; research includes domains favoring either signal.

AI Glossary / Graphs and symbolic AI / Intermediate

Speedy search

Definition

Speedy search is a greedy best-first search strategy that prioritizes states by an estimate of the number of actions remaining to a goal. Its aim is to find a solution quickly, without using those actions' costs as the priority criterion. It is a satisficing search method: finding an acceptable solution can matter more than proving that the solution has minimum cost.

What it means

Distance-to-go and cost-to-go answer different questions. A two-action route may cost much more than a five-action route. Speedy search uses an estimate commonly written d(n), representing remaining action count, rather than a cost estimate h(n).
The name describes the intended search behavior, not a guarantee that it is always the fastest algorithm. A misleading distance estimate can still direct the search into unhelpful regions. Also distinguish time spent computing a plan from time spent executing it: a plan with few symbolic actions may contain an action that is slow or expensive in the real world.

How it works

Maintain a frontier of generated states and select a state with a small estimated distance-to-go. Expand it to generate successor states, assign their distance estimates, and continue until a goal is selected under the chosen stopping rule.
The core priority does not add the cost already spent reaching a state. Practical implementations still need goal tests, tie-breaking rules, state records, and duplicate handling. Those details can affect performance. If an application requires a solution-cost bound, pure distance-prioritized greedy search does not supply that guarantee merely because its distance heuristic is accurate.

Three practical examples

A planning benchmark can compare time to the first feasible plan when actions have very different modeled costs.
A puzzle-solving experiment can use estimated remaining moves to direct exploration toward a goal.
A workflow prototype can explore a quick-feasibility search, then separately inspect the resource cost of the resulting action sequence before treating it as usable.

Think of it this way

Think of looking for an exit by choosing the corridor that seems to require the fewest remaining turns. That can help reach an exit quickly, but the corridor may include a long staircase or an expensive access point. The analogy is limited because the algorithm compares frontier states across a search structure; it is not simply a person committing physically to one corridor.

Worked example

Consider an original directed search graph with start S and goal G. One route is S - A - G, with costs 1 and 100. The other route is S - B - C - D - G, with cost 1 on each of its four edges. There are no other edges.
Suppose the distance estimates are exact: d(A) = 1, d(B) = 3, d(C) = 2, d(D) = 1, and d(G) = 0. After expanding S, the frontier contains A and B. Speedy search selects A because 1 is smaller than 3.
Expanding A generates G, whose distance estimate is zero. With goal testing when a state is selected, the next selected state is G, and the search returns S - A - G. That plan uses two actions but costs 101. The alternative uses four actions and costs 4.
A greedy search using exact remaining cost would instead rank B, whose remaining cost is 3, ahead of A, whose remaining cost is 100. This comparison isolates the difference between the two priority signals. It does not imply that cost-based greedy search is generally optimal, because it also ignores the cost already incurred.
The absence of a cost guarantee is especially clear if the A - G cost is replaced by a large number M. The distance priorities and selected route remain unchanged, while the returned cost becomes 1 + M. Relative to the four-cost alternative, the ratio can grow arbitrarily large. Even perfect remaining-action estimates do not bound the monetary or resource cost.

Illustrative case study

In a fictional operations-planning exercise, a team wants a feasible arrangement quickly enough to inspect several alternatives. It experiments with speedy search using remaining task count as a heuristic. The first returned plan includes a single expensive outsourcing action.
The team records both planning runtime and the modeled execution cost, rather than calling the first result best. It decides whether the workflow's acceptance criteria require a cost-aware method or a later improvement stage. The case illustrates an objective mismatch; it does not assert that the search strategy produced a commercial saving or a universal speed advantage.

Common misconceptions and mistakes

Speedy search does not mean any search implementation that runs quickly. It names a particular use of a distance-to-go heuristic. A distance estimate is not automatically a time estimate, and neither is necessarily a cost estimate.
Do not assume admissibility of a heuristic turns greedy search into A*. Do not ignore duplicate-state behavior when comparing implementations. A small heuristic value may be wrong or may belong to a large plateau, so the number of expansions and actual runtime must be measured rather than inferred from the algorithm's name.

Business use

The concept helps teams separate two priorities: obtaining a feasible answer soon and obtaining a low-cost answer. It can serve as a useful baseline when the first priority dominates, provided the returned plan is still assessed against the application's acceptance conditions.
Evaluation should report time to solution, memory use, success rate under the test limits, and solution quality. Comparing only runtime can hide a large cost increase; comparing only plan cost can hide that one method failed to produce an answer within the available time.

Check your understanding

State X is estimated to be two actions from a goal, while Y is one action away but very expensive. Which does pure speedy search prefer?

Answer: Y, assuming no tie or other overriding rule, because its remaining-action estimate is smaller. The expensive action does not enter the basic priority.

Related terms

Greedy best-first search
Distance-to-go heuristic
Cost-to-go heuristic
Satisficing search
A*
Weighted A*
Search frontier

Learn next

Next, redraw the worked graph with every edge costing one. Action count and path cost then agree for those routes, though heuristic errors can still matter. Compare distance-to-go with depth-from-start and explain why adding the two would define a different priority from pure speedy search.

Sources

AIMA original glossary sentences, speedy search: https://raw.githubusercontent.com/aimacode/aima-glossary/master/sentences.txt Wilt and Ruml, Speedy versus Greedy Search: https://www.ijcai.org/Proceedings/15/Papers/616.pdf Thayer and Ruml, Using Distance Estimates in Heuristic Search: https://www.cs.unh.edu/~ruml/papers/d-tutorial.pdf

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