Prediction of Regular Search Tree Growth by Spectral Analysis

  • Authors:
  • Stefan Edelkamp

  • Affiliations:
  • -

  • Venue:
  • KI '01 Proceedings of the Joint German/Austrian Conference on AI: Advances in Artificial Intelligence
  • Year:
  • 2001

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Abstract

The time complexity analysis of the IDA* algorithm has shown that predicting the growth of the search tree essentially relies on only two criteria: The number of nodes in the brute-force search tree for a given depth and the equilibrium distribution of the heuristicestimate. Since the latter can be approximated by random sampling, we accurately predict the number of nodes in the brute-force search tree for large depth in closed form by analyzing the spectrum of the problem graph or one of its factorization.We further derive that the asymptotic brute-force branching factor is in fact the spectral radius of the problem graph and exemplify our considerations in the domain of the (n2 - 1)-Puzzle.