An admissible and optimal algorithm for searching AND/OR graphs

Abstract. We look at several problems from areas such as network flows, game theory, artificial intelligence, graph theory, integer programming and nonlinear programming and show that they are \. related in that anyone of these problems is solvable in polynomial time iff all the others are, too. At i present, no polynomial time algorithm for these problems is known. These problems extend the equivalence class of problems known as P-Complete. The problem of deciding whether the class of 1 languages accepted by polynomial time nondeterministic Turing machines is the same as that accepted 1 by polynomial time deterministic Turing machines is related to P-Complete problems in that these two classes of languages are the same iff each P-Complete problem has a polynomial deterministic solution.l In view of this, it appears very likely that this equivalence class defines a class of problems that cannot be solved in deterministic polynomial time.

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“…From the above definition of F 1(x'), it follows that 2 ) be a 2-person game with 2 strategies per player and with no equilibrium point:…”

Section: Computationally Related Problemsmentioning

confidence: 99%

Computationally Related Problems

Sahni¹

1974

SIAM J. Comput.

307

126

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“…We present a solution to such problems which performs search in a reduced information state space using a heuristic to guide the search, as with AO* [5]. The key theoretical contribution of this paper is a new algorithm, PAO*, which updates the heuristic value of states throughout the state space in such a way as to reduce the required computation considerably.…”

Section: Introductionmentioning

confidence: 99%

PAO for planning with hidden state

Ferguson

Stentz

Thrun

2004

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004

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Abstract-We describe a heuristic search algorithm for generating optimal plans in a new class of decision problem, characterised by the incorporation of hidden state. The approach exploits the nature of the hidden state to reduce the state space by orders of magnitude. It then interleaves heuristic expansion of the reduced space with forwards and backwards propagation phases to produce a solution in a fraction of the time required by other techniques. Results are provided on an outdoor path planning application.

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“…), and medicine (diagnosing patients, sequencing treatments, etc.). An illustrative list of references for such applications includes [69,72,79,84,98,126,166,220,240,241,252,307,348,354,392,396,421,427]. Sequential decision making is an old subject, but one that has become increasingly important with the need for new models and algorithms as the traditional methods for making decisions sequentially do not scale.…”

Section: Sequential Decision Making Models and Algorithms 28mentioning

confidence: 99%

Computer science and decision theory

Roberts

2008

Ann Oper Res

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This paper reviews applications in computer science that decision theorists have addressed for years, discusses the requirements posed by these applications that place great strain on decision theory/social science methods, and explores applications in the social and decision sciences of newer decision-theoretic methods developed with computer science applications in mind. The paper deals with the relation between computer science and decision-theoretic methods of consensus, with the relation between computer science and game theory and decisions, and with "algorithmic decision theory."

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An admissible and optimal algorithm for searching AND/OR graphs

Cited by 77 publications

References 9 publications

Computationally Related Problems

Computationally Related Problems

PAO for planning with hidden state

Computer science and decision theory

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