TY - UNPB
T1 - Arithmetic Binary Search Trees: Static Optimality in the Matching Model
AU - Avin, Chen
PY - 2020/12/26
Y1 - 2020/12/26
N2 - Motivated by recent developments in optical switching and reconfigurable network design, we study dynamic binary search trees (BSTs) in the matching model. In the classical dynamic BST model, the cost of both link traversal and basic reconfiguration (rotation) is O(1). However, in the matching model, the BST is defined by two optical switches (that represent two matchings in an abstract way), and each switch (or matching) reconfiguration cost is α while a link traversal cost is still O(1). In this work, we propose Arithmetic BST (A-BST), a simple dynamic BST algorithm that is based on dynamic Shannon-Fano-Elias coding, and show that A-BST is statically optimal for sequences of length Ω(nα log α) where n is the number of nodes (keys) in the tree.
AB - Motivated by recent developments in optical switching and reconfigurable network design, we study dynamic binary search trees (BSTs) in the matching model. In the classical dynamic BST model, the cost of both link traversal and basic reconfiguration (rotation) is O(1). However, in the matching model, the BST is defined by two optical switches (that represent two matchings in an abstract way), and each switch (or matching) reconfiguration cost is α while a link traversal cost is still O(1). In this work, we propose Arithmetic BST (A-BST), a simple dynamic BST algorithm that is based on dynamic Shannon-Fano-Elias coding, and show that A-BST is statically optimal for sequences of length Ω(nα log α) where n is the number of nodes (keys) in the tree.
U2 - https://doi.org/10.48550/arXiv.2012.13698
DO - https://doi.org/10.48550/arXiv.2012.13698
M3 - Preprint
BT - Arithmetic Binary Search Trees: Static Optimality in the Matching Model
ER -