The Expected Value of Hierarchical Problem-Solving

est case using an abstraction hierarchy in problem-solving can yield an exponential speed-up in search e ciency. Such a speed-up is predicted by various analytical models developed in the literature, and e ciency gains ofthis order have been con rmed empirically. However, these models assume that the Downward Re nement Property (DRP) holds. When this property holds, backtracking never need occur across ion levels. When it fails, search may have to consider many di erent abstract solutions before nding one that can be re ned to a concrete solution. In this paper we provide an analysisof the expected search complexity without assuming the DRP. We nd that l predicts a phase boundary where abstraction no bene t: if the probability that an abstract solution can be re ned is very low or very high, search traction yields signi cant speed up. However, in the phase boundary area where the probability takes on an intermediate value search e ciency is not necessarily improved. The phenomenon of ...

• Type: Conference
• Year: 1992
• Where: AAAI
• Authors: Fahiem Bacchus, Qiang Yang
• Keywords: AAAI 1992, Abstract Solution, Gains Ofthis Order, Intelligent Agents, Phase Boundary