<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
On the Complexity of Admissible Search Algorithms
  • A. Martelli
  • Mathematics, Computer Science
  • Artif. Intell.
  • 1977
TLDR
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
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. Expand
Generalized best-first search strategies and the optimality of A*
TLDR
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
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. Expand
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. Expand
Reconsideration of a theorem on admissible ordered search algorithms
  • M. Newborn
  • 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, aExpand
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. Expand
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 theExpand
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. Expand
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. 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