Proceedings Article•
Finding optimal solutions to Rubik's cube using pattern databases
27 Jul 1997-pp 700-705
TL;DR: The first optimal solutions to random instances of Rubik's Cube are found, and it is hypothesized that the overall performance of the program obeys a relation in which the product of the time and space used equals the size of the state space.
Abstract: We have found the first optimal solutions to random instances of Rubik's Cube. The median optimal solution length appears to be 18 moves. The algorithm used is iterative-deepening-A* (IDA*), with a lower-bound heuristic function based on large memory-based lookup tables, or "pattern databases" (Culberson and Schaeffer 1996). These tables store the exact number of moves required to solve various subgoals of the problem, in this case subsets of the individual movable cubies. We characterize the effectiveness of an admissible heuristic function by its expected value, and hypothesize that the overall performance of the program obeys a relation in which the product of the time and space used equals the size of the state space. Thus, the speed of the program increases linearly with the amount of memory available. As computer memories become larger and cheaper, we believe that this approach will become increasingly cost-effective.
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Book•
15 Aug 1997TL;DR: Intelligent agents are employed as the central characters in this new introductory text and Nilsson gradually increases their cognitive horsepower to illustrate the most important and lasting ideas in AI.
Abstract: Intelligent agents are employed as the central characters in this new introductory text. Beginning with elementary reactive agents, Nilsson gradually increases their cognitive horsepower to illustrate the most important and lasting ideas in AI. Neural networks, genetic programming, computer vision, heuristic search, knowledge representation and reasoning, Bayes networks, planning, and language understanding are each revealed through the growing capabilities of these agents. The book provides a refreshing and motivating new synthesis of the field by one of AI's master expositors and leading researchers. Artificial Intelligence: A New Synthesis takes the reader on a complete tour of this intriguing new world of AI.
* An evolutionary approach provides a unifying theme
* Thorough coverage of important AI ideas, old and new
* Frequent use of examples and illustrative diagrams
* Extensive coverage of machine learning methods throughout the text
* Citations to over 500 references
* Comprehensive index
Table of Contents
1 Introduction
2 Stimulus-Response Agents
3 Neural Networks
4 Machine Evolution
5 State Machines
6 Robot Vision
7 Agents that Plan
8 Uninformed Search
9 Heuristic Search
10 Planning, Acting, and Learning
11 Alternative Search Formulations and Applications
12 Adversarial Search
13 The Propositional Calculus
14 Resolution in The Propositional Calculus
15 The Predicate Calculus
16 Resolution in the Predicate Calculus
17 Knowledge-Based Systems
18 Representing Commonsense Knowledge
19 Reasoning with Uncertain Information
20 Learning and Acting with Bayes Nets
21 The Situation Calculus
22 Planning
23 Multiple Agents
24 Communication Among Agents
25 Agent Architectures
1,090 citations
TL;DR: A family of heuristic search planners are studied based on a simple and general heuristic that assumes that action preconditions are independent, which is used in the context of best-first and hill-climbing search algorithms, and tested over a large collection of domains.
1,023 citations
Proceedings Article•
22 Jul 2012TL;DR: In this article, a two-level algorithm called Conflict Based Search (CBS) is proposed to solve the multi-agent path finding problem, where at the high level, a search is performed on a tree based on conflicts between agents.
Abstract: In the multi agent path finding problem (MAPF) paths should be found for several agents, each with a different start and goal position such that agents do not collide. Previous optimal solvers applied global A*-based searches. We present a new search algorithm called Conflict Based Search (CBS). CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. In many cases this reformulation enables CBS to examine fewer states than A* while still maintaining optimality. We analyze CBS and show its benefits and drawbacks. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.
517 citations
06 Aug 2009
TL;DR: Artificial Neural Networks Board Games Game Theory Minimaxing Transposition Tables and Memory Memory-Enhanced Test Algorithms Opening Books and Other Set Plays Further Optimizations Turn-Based Strategy Games Supporting Technologies Execution Management Scheduling Anytime Algorithm Level of Detail World Interfacing Communication Getting Knowledge Efficiently Event Managers Polling Stations Sense Management Tools and Content Creation.
Abstract: AI and Games Introduction What Is AI? Model of Game AI Algorithms, Data Structures, and Representations On the Website Layout of the Book Game AI The Complexity Fallacy The Kind of AI in Games Speed and Memory The AI Engine Techniques Movement The Basics of Movement Algorithms Kinematic Movement Algorithms Steering Behaviors Combining Steering Behaviors Predicting Physics Jumping Coordinated Movement Motor Control Movement in the Third Dimension Pathfinding The Pathfinding Graph Dijkstra A* World Representations Improving on A* Hierarchical Pathfinding Other Ideas in Pathfinding Continuous Time Pathfinding Movement Planning Decision Making Overview of Decision Making Decision Trees State Machines Behavior Trees Fuzzy Logic Markov Systems Goal-Oriented Behavior Rule-Based Systems Blackboard Architectures Scripting Action Execution Tactical and Strategic AI Waypoint Tactics Tactical Analyses Tactical Pathfinding Coordinated Action Learning Learning Basics Parameter Modification Action Prediction Decision Learning Naive Bayes Classifiers Decision Tree Learning Reinforcement Learning Artificial Neural Networks Board Games Game Theory Minimaxing Transposition Tables and Memory Memory-Enhanced Test Algorithms Opening Books and Other Set Plays Further Optimizations Turn-Based Strategy Games Supporting Technologies Execution Management Scheduling Anytime Algorithms Level of Detail World Interfacing Communication Getting Knowledge Efficiently Event Managers Polling Stations Sense Management Tools and Content Creation Knowledge for Pathfinding and Waypoint Tactics Knowledge for Movement Knowledge for Decision Making The Toolchain Designing Game AI Designing Game AI The Design Shooters Driving Real-Time Strategy Sports Turn-Based Strategy Games AI-Based Game Genres Teaching Characters Flocking and Herding Games Appendix Books, Periodicals, and Papers Games
472 citations
Cites background or methods from "Finding optimal solutions to Rubik'..."
...Examples of such puzzles are the Rubik’s Cube [Korf, 1997], the 9-puzzle or Sokoban [Junghanns and Schaeffer, 2001]....
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...It is then possible to use it as an admissible heuristic [Korf, 1997]....
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TL;DR: A new search algorithm called Conflict Based Search (CBS), which enables CBS to examine fewer states than A* while still maintaining optimality and shows a speedup of up to a full order of magnitude over previous approaches.
433 citations
Additional excerpts
..., puzzles) as well [28,27]....
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References
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TL;DR: This heuristic depth-first iterative-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifteen Puzzle within practical resource limits.
1,698 citations
Additional excerpts
...…18 243 3,240 43,254 577,368 7,706,988 102,876,480 1,373,243,544 18,330,699,168 244,686,773,808 3,266,193,870,720 43,598,688,377,184 581,975,750,199,168 7,768,485,393,179,328 103,697,388,221,736,960 1,384,201,395,738,071,424 18,476,969,736,848,122,368 246,639,261,965,462,754,048 (IDA*) (Korf 1985a)....
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TL;DR: The macro technique is a new kind of weak method, a method for learning as opposed to problem solving, and introduces a new type of problem structure called operator decomposability.
327 citations
Additional excerpts
...…18 243 3,240 43,254 577,368 7,706,988 102,876,480 1,373,243,544 18,330,699,168 244,686,773,808 3,266,193,870,720 43,598,688,377,184 581,975,750,199,168 7,768,485,393,179,328 103,697,388,221,736,960 1,384,201,395,738,071,424 18,476,969,736,848,122,368 246,639,261,965,462,754,048 (IDA*) (Korf 1985a)....
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TL;DR: A general-purpose algorithm that can solve a number of NP-complete problems in time $T = O(2^{n/2} )$ and space and can be generalized to a fam...
Abstract: In this paper we develop a general-purpose algorithm that can solve a number of NP-complete problems in time $T = O(2^{n/2} )$ and space $S = O(2^{n/4} )$. The algorithm can be generalized to a fam...
194 citations
"Finding optimal solutions to Rubik'..." refers background in this paper
...Schroeppel, Shamir, Fiat et al The first paper to address finding optimal solutions to Rubik’s Cube was (Fiat et al. 1989), which is based on (Schroeppel and Shamir 1981)....
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...(Schroeppel and Shamir 1981) improved on bidirectional search for many problems....
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TL;DR: The checkers program Chinook has won the right to play a 40-game match for the World Checkers Championship against Dr. Marion Tinsley, the first time a program has earned theright to contest for a human World Championship.
186 citations
21 May 1996
TL;DR: For the 15-Puzzle, iterative-deepening A with pattern databases (N=8) reduces the total number of nodes searched on a standard problem set of 100 positions by over 1000-fold.
Abstract: The efficiency of A searching depends on the quality of the lower bound estimates of the solution cost. Pattern databases enumerate all possible subgoals required by any solution, subject to constraints on the subgoal size. Each subgoal in the database provides a tight lower bound on the cost of achieving it. For a given state in the search space, all possible subgoals are looked up, with the maximum cost over all lookups being the lower bound. For sliding tile puzzles, the database enumerates all possible patterns containing N tiles and, for each one, contains a lower bound on the distance to correctly move all N tiles into their correct final location. For the 15-Puzzle, iterative-deepening A with pattern databases (N=8) reduces the total number of nodes searched on a standard problem set of 100 positions by over 1000-fold.
154 citations
"Finding optimal solutions to Rubik'..." refers background or methods in this paper
...The use of such tables, called “pattern databases” is due to (Culberson and Schaeffer 1996), who applied it to the Fifteen Puzzle....
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...The idea of using large tables of precomputed optimal solution lengths for subparts of a combinatorial problem was first proposed by (Culberson and Schaeffer 1996)....
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...(Culberson and Schaeffer 1996) have carried this idea much further....
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...The key idea, due to (Culberson and Schaeffer 1996), is to take a subset of the goals of the original problem, and precompute and store the exact number of moves needed to solve these subgoals from all possible initial states....
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...The algorithm used is iterative-deepening-A* (IDA*), with a lowerbound heuristic function based on large memory-based lookup tables, or “pattern databases” (Culberson and Schaeffer 1996)....
[...]