<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={Peter E. Hart and Nils J. Nilsson and Bertram 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… 

Figures from this paper

On the Complexity of Admissible Search Algorithms

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

TLDR
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.

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

TLDR
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.

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

TLDR
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.

Reconsideration of a theorem on admissible ordered search algorithms

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

A heuristic search algorithm for path determination with learning

TLDR
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.

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

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

Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties

TLDR
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.

Multiobjective A*

TLDR
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.

A methodology for solving facility layout problem considering barriers: genetic algorithm coupled with A* search

TLDR
This work proposes a new methodology and mathematical formulation to address the facility layout problem to minimise the total material handling cost subjected to production-derived constraints and combines a genetic algorithm and a homogenous methodology to improve the quality of the facility layouts.
...

References

SHOWING 1-9 OF 9 REFERENCES

Review of "Problem-Solving Methods in Artificial Intelligence by Nils J. Nilsson", McGraw-Hill Pub.

TLDR
This book is not a survey on theorem proving programs, but the description of a program developed from 1960 to 1965, and includes three chapters that deal with resolution-based theorem-proving in the predicate calculus and its applications to problem solving.

Realization of a geometry theorem proving machine

TLDR
The technique of heuristic programming is under detailed investigation as a means to the end of applying large-scale digital computers to the solution of a difficult class of problems currently considered to be beyond their capabilities; namely those problems that seem to require the agent of human intelligence and ingenuity for their solution.

Some Studies in Machine Learning Using the Game of Checkers

  • A. Samuel
  • Computer Science
    IBM J. Res. Dev.
  • 1959
TLDR
A new signature-table technique is described together with an improved book-learning procedure which is thought to be much superior to the linear polynomial method and to permit the program to look ahead to a much greater depth than it otherwise could do.

Applied Dynamic Programming

Computers and Thought

Computers and Thought showcases the work of the scientists who not only defined the field of Artificial Intelligence, but who are responsible for having developed it into what it is today. Originally

Solutions of the shortestroute problem-a review

  • Operations Res
  • 1960

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

The shortest path through a maze

  • Proc. Internat'l Symp. on Theory of Switching pt. 2. Also
  • 1957