On the Markov chain for the move-to-root rule for binary search trees

The move-to-root (MTR) heuristic is a self-organizing rule which attempts to keep a binary search tree in near-optimal form. It is a tree analogue of the move-to-front (MTF) scheme for self-organizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be derived by lumping the MTF chain and give exact formulas for the transition probabilities and stationary distribution for MTR. We also derive the eigenvalues and their multiplicities for MTR. Research for both authors supported by NSF grant DMS-9311367. AMS 1991 subject classifications. Primary 60J10; secondary 68P10, 68P05.