We present a polynomial-time path-finding algorithm in AND-OR graphs Given <mml:math alttext="$p$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>  arcs and <mml:math alttext="$n$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> nodes, the complexity of the algorithm is <mml:math alttext="$O\left( {np} \right),$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math> which is superior to the complexity of previously known algorithms.

Mathematical Problems in Engineering

On fast path-finding algorithms in AND-OR graphs

Abstract

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