The Backdoor Key: A Path to Understanding Problem Hardness

Yongshao Ruan, Henry Kautz, and Eric Horvitz

We introduce our work on the backdoor key, a concept that shows promise for characterizing problem hardness in backtracking search algorithms. The general notion of backdoors was recently introduced to explain the source of heavy-tailed behaviors in backtracking algorithms. We describe empirical studies that show that the key faction,i.e., the ratio of the key size to the corresponding backdoor size, is a good predictor of problem hardness of ensembles and individual instances within an ensemble for structure domains with large key fraction.

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