Greedy Is an Almost Optimal Deque

In this paper we extend the geometric binary search tree (BST) model of Demaine, Harmon, Iacono, Kane, and Pǎtrascu (DHIKP) to accommodate for insertions and deletions. Within this extended model, we study the online Greedy BST algorithm introduced by DHIKP. Greedy BST is known to be equivalent to a maximally greedy (but inherently offline) algorithm introduced independently by Lucas in 1988 and Munro in 2000, conjectured to be dynamically optimal.

[1]  John Iacono,et al.  In Pursuit of the Dynamic Optimality Conjecture , 2013, Space-Efficient Data Structures, Streams, and Algorithms.

[2]  Rajamani Sundar,et al.  On the deque conjecture for the splay algorithm , 1992, Comb..

[3]  Robert E. Tarjan,et al.  Sequential access in splay trees takes linear time , 1985, Comb..

[4]  Richard Cole,et al.  On the dynamic finger conjecture for splay trees , 1990, STOC '90.

[5]  Richard Cole,et al.  On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences , 1995, SIAM J. Comput..

[6]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[7]  Daniel M. Kane,et al.  The geometry of binary search trees , 2009, SODA.

[8]  Kyle Fox,et al.  Upper Bounds for Maximally Greedy Binary Search Trees , 2011, WADS.

[9]  Alejandro López-Ortiz,et al.  Space-Efficient Data Structures, Streams, and Algorithms Papers in Honor of J. Ian Munro, on the Occasion of His 66th Birthday , 2013 .

[10]  Seth Pettie,et al.  Generalized Davenport-Schinzel sequences and their 0-1 matrix counterparts , 2011, J. Comb. Theory, Ser. A.

[11]  Robert E. Wilber.  Lower Bounds for Accessing Binary Search Trees with Rotations , 1989, SIAM J. Comput..

[12]  Amr Elmasry,et al.  On the sequential access theorem and deque conjecture for splay trees , 2004, Theor. Comput. Sci..

[13]  Richard Cole,et al.  On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof , 2000, SIAM J. Comput..

[14]  Seth Pettie,et al.  Applications of forbidden 0-1 matrices to search tree and path compression-based data structures , 2010, SODA '10.

[15]  Jonathan Derryberry,et al.  Properties of Multi-Splay Trees , 2009 .

[16]  Seth Pettie,et al.  Splay trees, Davenport-Schinzel sequences, and the deque conjecture , 2007, SODA '08.

[17]  J. Ian Munro,et al.  On the Competitiveness of Linear Search , 2000, ESA.