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

@article{Dechter1985GeneralizedBS, title={Generalized best-first search strategies and the optimality of A*}, author={R. Dechter and J. Pearl}, journal={J. ACM}, year={1985}, volume={32}, pages={505-536} }

This paper reports several properties of heuristic best-first search strategies whose scoring functions ƒ depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A* retain their form (with the minmax of f playing the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis… Expand

#### Figures and Topics from this paper

#### 980 Citations

The optimality of A

- Computer Science
- 1988

This paper examines the computational optimality of A*, in the sense of never expanding a node that could be skipped by some other algorithm having access to the same heuristic information that A*… Expand

Space-efficient search algorithms

- Computer Science
- CSUR
- 1995

The main problem with best-first search, however, is that it must store in memory all the frontier nodes in order to determine the best node to expand next, which has been the focus of a significant body of research over the past decade, which is briefly surveyed in this article. Expand

Understanding the Search Behaviour of Greedy Best-First Search

- Computer Science
- SOCS
- 2017

The concept of high-water mark benches is introduced, which separate the search space into areas that are searched by a GBFS algorithm in sequence and show that some states are expanded by all GBFS searches, while others are expanded only if certain conditions are met. Expand

Search behavior of greedy best-first search

- Computer Science
- 2019

The search behavior of Greedy best-first search is examined and algorithms for extracting the set of states that GBFS potentially expands and for computing the best-case and worst-case behavior are presented. Expand

Best-First Search with Maximum Edge Cost Functions

- Mathematics, Computer Science
- ISAIM
- 2008

This paper presents an algorithm, MaxBF, that is analogous to A* but meant to solve these maximum edge cost problems, and shows that, although MaxBF never needs to reopen closed nodes, it may find an alternate path to a closed node that appears better than the original path. Expand

COMPARISON OF VARIOUS HEURISTIC SEARCH TECHNIQUES FOR FINDING SHORTEST PATH

- Computer Science
- 2014

This paper presents an alternative data structure multi-level link list and applies the heuristic technique to solve shortest path problem and indicates that use of this type of data structure helps in improving the performance of algorithms drastically. Expand

Heuristic Search for m Best Solutions with Applications to Graphical Models

- 2011

The paper focuses on finding the m best solutions to a combinatorial optimization problems using Best-First or Branch-and-Bound search. We are interested in graphical model optimization tasks (e.g.,… Expand

A heuristic search strategy for optimization of trade-off cost measures

- Computer Science
- [Proceedings] Third International Conference on Tools for Artificial Intelligence - TAI 91
- 1991

It is shown that MULT* is an admissible algorithm and it has many of the important properties of A*. Expand

Weighted Best-First Search for W-Optimal Solutions over Graphical Models

- 2014

The paper explores the potential of weighted best-first search schemes as anytime optimization algorithms for solving graphical models tasks such as MPE (Most Probable Explanation) or MAP (Maximum a… Expand

New Search Heuristics for Max-CSP

- Mathematics, Computer Science
- CP
- 2000

These algorithms are compared with a state of the art complete algorithm as well as with the stochastic local search anytime approach, demonstrating superiority in some problem cases. Expand

#### References

SHOWING 1-10 OF 29 REFERENCES

Studies in Semi-Admissible Heuristics

- Mathematics, Computer Science
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- 1982

Three extensions of the A* search algorithm are introduced which improve the search efficiency by relaxing the admissibility condition and are shown to be significant in difficult problems, i.e., problems requiring a large number of expansions due to the presence of many subtours of roughly equal costs. Expand

Searching for an Optimal Path in a Tree with Random Costs

- Mathematics, Computer Science
- Artif. Intell.
- 1983

It is shown that for p 1/2, every algorithm which guarantees finding an exact cheapest path, or even a path within a fixed cost ratio of the cheapest, must run in exponential average time. Expand

The Heuristic Search under Conditions of Error

- Mathematics, Computer Science
- Artif. Intell.
- 1974

This paper introduces a new restriction upon the heuristic, called the “bandwidth” condition, that enables the ordered search to better cope with time and space difficulties, and provides some additional insight to the general problem of searching game trees. Expand

Search Algorithms Under Different Kinds of Heuristics—A Comparative Study

- Computer Science, Mathematics
- JACM
- 1983

Three heuristic search algorithms, called algorithms a, b and c, are presented and it is shown that on the whole a and b are inferior to c, which is a slightly modified version of b. Expand

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

- Computer Science
- SGAR
- 1972

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… Expand

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

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

- Computer Science
- IEEE Trans. Syst. Sci. Cybern.
- 1968

How heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching is described and an optimality property of a class of search strategies is demonstrated. Expand

A Heuristic Search Algorithm with Modifiable Estimate

- Mathematics, Computer Science
- Artif. Intell.
- 1984

It is proved to never expand more nodes than B or A∗ and to expand a much smaller number of them in some cases and a proof that no overall optimal algorithm exists if the cost of an algorithm is measured by the total number of node expansions. Expand

On the Discovery and Generation of Certain Heuristics

- Computer Science, Mathematics
- AI Mag.
- 1983

It is demonstrated that these heuristics can be obtained by the process of deleting constraints from the original problem and solving the relaxed problem which ensues, and a scheme for generating such heuristic mechanically is outlined. Expand

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

- Computer Science
- SGAR
- 1971

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. Expand