# <u>Correction</u> to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths"

@article{Hart1972uCorrectionuT, title={<u>Correction</u> to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths"}, author={P. Hart and N. Nilsson and B. Raphael}, journal={SIGART Newsl.}, year={1972}, volume={37}, pages={28-29} }

Our paper on the use of heuristic information in graph searching defined a path-finding algorithm, A*, and proved that it had two important properties. In the notation of the paper, we proved that if the heuristic function ñ (n) is a lower bound on the true minimal cost from node n to a goal node, then A* is <u>admissible;</u> i.e., it would find a minimal cost path if any path to a goal node existed. Further, we proved that if the heuristic function also satisfied something called the <u… Expand

#### 159 Citations

On the Complexity of Admissible Search Algorithms

- Mathematics, Computer Science
- Artif. Intell.
- 1977

This paper analyzes the complexity of heuristic search algorithms, i.e. algorithms which find the shortest path in a graph by using an estimate to guide the search and presents a new search algorithm which runs in O(N2) steps in the worst case and which never requires more steps than A*. Expand

Completeness and Admissibility for General Heuristic Search Algorithms—A Theoretical Study: Basic Concepts and Proofs

- Computer Science
- J. Heuristics
- 1999

General theorems about the completeness and the sub-admissibility that widely extend the previous results are proved and provide a theoretical support for using diverse kinds of Heuristic Search algorithms in enlarged contexts, specially when the state graphs and the evaluation functions are less constrained than ordinarily. Expand

Generalized best-first search strategies and the optimality of A*

- Mathematics, Computer Science
- JACM
- 1985

It is shown that several known properties of A* retain their form and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A* is indeed optimal. Expand

A heuristic search approach for solving a minimum path problem requiring arc cost determination

- Computer Science
- IEEE Trans. Syst. Man Cybern. Part A
- 1996

Two generalizations of A*, BA* and DA, which consider the problem of finding a minimum cost path from the start node to a finite goal node set in a directed OR-graph, are presented and analyzed. Expand

A Metric Space Approach to the Specification of the Heuristic Function for the A* Algorithm

- Computer Science, Mathematics
- IEEE Trans. Syst. Man Cybern. Syst.
- 1994

It is shown how to specify an admissible and monotone heuristic function for a wide class of problem domains and applications to an optimal parts distribution problem in flexible manufacturing systems and artificial intelligence planning problems are provided. Expand

Reconsideration of a theorem on admissible ordered search algorithms

- Mathematics, Computer Science
- ACM '76
- 1976

An improved proof is presented for a theorem on search algorithms which find minimal cost paths in a graph. The theorem essentially states that when searching for a minimal cost path in a graph, a… Expand

A heuristic search algorithm for path determination with learning

- Computer Science
- IEEE Trans. Syst. Man Cybern. Part A
- 1998

An algorithm for finding a least-cost-path from start node to goal node set in a directed graph, adaptive A*(AA*), which can be used to automate knowledge acquisition, so that A* exhibits a form of machine learning. Expand

A best-first search algorithm guided by a set-valued heuristic

- Mathematics, Computer Science
- IEEE Trans. Syst. Man Cybern.
- 1995

Presents an algorithm, called A/sup G/, for finding the least-cost path from start node to goal node set in an OR-graph, where arc costs are scalar-valued and the cost of each path is the sum of the… Expand

Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties

- Computer Science
- Algorithms
- 2020

This paper focuses on a variant of this problem in which additional penalties are incurred at the vertices, and proposes two variants of Dijkstra’s algorithm that operate on the original, unexpanded graph. Expand

Multiobjective A*

- Computer Science
- JACM
- 1991

A multiobjective generalization of the heuristic search algorithm A* is presented and it is shown that &fOA * is complete and, when used with a suitably defined set of admissible heuristic functions, admissible. Expand

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Write to: Miss Liz Klein ACM 1133 Avenue of the Americas New York

- Write to: Miss Liz Klein ACM 1133 Avenue of the Americas New York