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Better Analysis of GREEDY Binary Search Tree on Decomposable Sequences by Goyal, Navin; Gupta, Manoj is a scholarly article available to read on EtoBox.

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In their seminal paper [Sleator and Tarjan, J.ACM, 1985], the authors conjectured that the splay tree is dynamically optimal binary search tree (BST). In spite of decades of intensive research, the problem remains open. Perhaps a more basic question, which has also attracted much attention, is if there exists any dynamically optimal BST algorithm. One such candidate is GREEDY which is a simple and intuitive BST algorithm [Lucas, Rutgers Tech. Report, 1988; Munro, ESA, 2000; Demaine, Harmon, Iacono, Kane and Patrascu, SODA, 2009]. [Demaine et al., SODA, 2009] showed a novel connection between a geometric problem. Since dynamic optimality conjecture in its most general form remains elusive despite much effort, researchers have studied this problem on special sequences. Recently, [Chalermsook, Goswami, Kozma, Mehlhorn and Saranurak, FOCS, 2015] studied a type of sequences known as $k$-{\em decomposable sequences} in this context, where $k$ parametrizes easiness of the sequence. Using tools from forbidden submatrix theory, they showed that GREEDY takes $n2^{O(k^2)}$ time on this sequence and explicitly raised the question of improving this bound. In this paper, we show that GREEDY take

Author

Goyal, Navin; Gupta, Manoj

Published

2016

Language

EN