| The study of Self-organizing lists deals with the problem of lowering the average-case asymptotic cost of a list data structure receiving query accesses in Non-stationary Environments (NSEs) with the so-called ``locality of reference'' property. The de facto schemes for Adaptive lists in such Environments are the Move To Front (MTF) and Transposition (TR) rules. However, significant drawbacks exist in the asymptotic accuracy and speed of list re-organization for the MTF and TR rules. This paper improves on these schemes using the design of an Adaptive list data structure as a hierarchical data ``sub''-structure. In this framework, we employ a hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) design, which divides the list data structure into an outer and inner list context. The inner-list context is itself a SLLs containing sub-elements of the list, while the outer-list context contains these sublist partitions as its primitive elements. The elements belonging to a particular sublist partition are determined using reinforcement learning schemes from the theory of Learning Automata. In this paper, we show that the Transitivity Pursuit-Enhanced Object Migration Automata (TPEOMA) can be used in conjunction with the hierarchical SLLs-on-SLLs as the dependence capturing mechanism to learn the probabilistic distribution of the elements in the Environment. The idea of Transitivity builds on the Pursuit concept that injects a noise filter into the EOMA to filter divergent queries from the Environment, thereby increasing the likelihood of training the Automaton to approximate the ``true'' distribution of the Environment. By taking advantage of the Transitivity phenomenon based on the statistical distribution of the queried elements, we can infer ``dependent'' query pairs from non-accessed elements in the transitivity relation. The TPEOMA-enhanced hierarchical SLLs-on-SLLs schemes results in superior performances to the MTF and TR schemes as well as to the EOMA-enhanced hierarchical SLLs-on-SLLs schemes in NSEs. However, the results are observed to have superior performances to the PEOMA-enhanced hierarchical schemes in Environments with a Periodic non-stationary distribution but were inferior in Markovian Switching Environments. |
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