Fringe Analysis of 2-3 Trees with Lazy Parent Split

Abstract

B-trees with lazy parent split (lps) are B-tree variants, according to which parent splits are postponed until a future access of the latter node. This way, the number of splits during an insert is decreased and the number of locks is also decreased. Consequently, better concurrency is achieved. In this paper 2-3 trees with lps are studied. Fringe analysis is used to obtain bounds on some performance metrics of 2-3 trees with lps. The performance metrics of 2-3 tree with lps are compared with those of the classical 2-3 trees. The conclusions are that 2-3 trees with lps have slightly better performance, more keys in the fringe, larger storage utilization and a slightly shorter path length from the root to the leaves.