## Depth-first Iterative-Deepening: An Optimal Admissible Tree Search (1985)

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Venue: | Artificial Intelligence |

Citations: | 423 - 17 self |

### BibTeX

@ARTICLE{Korf85depth-firstiterative-deepening:,

author = {Richard E. Korf},

title = {Depth-first Iterative-Deepening: An Optimal Admissible Tree Search},

journal = {Artificial Intelligence},

year = {1985},

volume = {27},

pages = {97--109}

}

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### Abstract

The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iteratiw-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential pee searches. The algorithm has been used successfully in chess programs, has been eflectiuely combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth-first iteratiw-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifeen Puzzle within practical resource limits. 1.

### Citations

1032 |
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
- Hart, Nilsson, et al.
- 1968
(Show Context)
Citation Context ... algorithm was used to find solutions up to 11 moves long on a DEC VAX 111780. 1 6. Heuristic Search Depth-first iterative-deepening can also be combined with a best-first heuristic search such as A* =-=[6]-=-. The idea is that successive iterations correspond not to increasing depth of search, but rather to increasing values of the total cost of a path. For A*, this total cost is composed of the cost so f... |

56 |
Learning to Solve Problems by Searching for Macro-Operators
- Korf
- 1985
(Show Context)
Citation Context ...hing scheme is used to I perform the matching in constant time per node, this algorithm will find an optimal solution of length d in time O(ba) and space O(bdR). In experiments involving Rubik's Cube =-=[8]-=-, which has an effective branching factor of 13.5, this algorithm was used to find solutions up to 11 moves long on a DEC VAX 111780. 1 6. Heuristic Search Depth-first iterative-deepening can also be ... |

19 |
Human Problem Solving (Prentice-Hall
- Newell, Simon
- 1972
(Show Context)
Citation Context ...ensions for exponential tree searches. Since almost all heuristic tree searches have exponential complexity, this is a fairly general result. We begin with the problem-space model of Newell and Simon =-=[9]-=-. A problem space consists of a set of states and a set of operators that are partial functions that map states into states. A problem is a problem space together with a particular initial state and a... |

13 | The do-calculus revisited
- Pearl
- 2012
(Show Context)
Citation Context ...ons of IDA* do not affect the asymptotic order of the total number of nodes [18]. Thus, IDA* expands the same number of nodes, asymptotically, as A*. Furthermore, a recent result of Dechter and Pearl =-=[5]-=- shows that A* is optimal, in terms of number of nodes expanded, over the class of admissible best-first searches with monotone heuristics. Therefore, IDA* is asymptotically optimal in terms of time f... |

7 | Heuristics (Addison-Wesley - Pearl - 1984 |

3 |
A quantitative study of search methods and the effect of constraint satisfaction technical report
- Berliner, Goetsch
- 1984
(Show Context)
Citation Context ...tions are counted in the cost, the extra computation required by iterative-deepening is insignificant. Pearl [12] initially suggested the iterative-deepening extension of A*, and Berliner and Goetsch =-=[3]-=- have implemented such an algorithm concurrently with this work. We will analyze several search algorithms along three dimensions: the amount of time they take, the amount of space they use, and the c... |

2 | Artificial intelligence (McGraw-Hill - Rich - 1983 |

2 |
Artificial intelligence (Addison-Wesley
- Winston
- 1984
(Show Context)
Citation Context ...ithm that is documented in the literature is in Slate and Atkin's Chess 4.5 program [15]. Berliner [2] has observed that breadth-first search is inferior to the iterative-deepening algorithm. Winston =-=[16]-=- shows that for two-person game searches where only terminal-node static evaluations are counted in the cost, the extra computation required by iterative-deepening is insignificant. Pearl [12] initial... |

1 | Handbook of ArtificialIntcIligence (Kaufmann - Barr, Feigenbaum - 1981 |

1 |
Artificial Intelligence Syllabus
- Berliner, Search
- 1983
(Show Context)
Citation Context ...sevier Science Publishers B.V. (North-Holland)s98 R.E. KORF independently. The first use of the algorithm that is documented in the literature is in Slate and Atkin's Chess 4.5 program [15]. Berliner =-=[2]-=- has observed that breadth-first search is inferior to the iterative-deepening algorithm. Winston [16] shows that for two-person game searches where only terminal-node static evaluations are counted i... |

1 |
Infroduction to Automata 77teory
- Hopcroft, Ullman
- 1979
(Show Context)
Citation Context .... constant coefficient as search depth goes to infinity. R.E. KORF To show that this is optimal, we note that any algorithm which uses f(n) time must use at least k log f(n) space for some constant k =-=[7]-=-. The reason is that the algorithm must proceed through f(n) distinct states before looping or terminating, and hence must be able to store that many distinct states. Since storing f(n) states require... |

1 |
A heuristic search algorithm with modifiable estimate
- Mirb
- 1984
(Show Context)
Citation Context ...l.ex proofs will establish the same results without it. As a practical matter, however, almost alls104 R.E. KORF ! reasonable cost functions are monotone [ll]. In fact, using an idea proposed by MCrd =-=[17]-=-, we can formally make this assumption without loss of generality, as shown in the following lemma. Lemma 6.2. For any admissible cost function f, we can construct a monotone admissible function f whi... |