Maintaining α-balanced trees by partial rebuilding

Abstract

The balance criterion defining the class of α-balanced trees states that the ratio between the shortest and longest paths from a node to a leaf be at least α. We show that a straight-forward use of partial rebuilding for maintenance of α-balanced trees requires an amortized cost of Ω (√ n) per update. By slight modifications of the maintenance algorithms the cost can be reduced to O (log n ) for any value of α, 0 < α < l.

Keywords:

• α-balanced trees
• partial rebuilding
• search trees

^∗This work was partially supported by a grant from the National Swedish Board for Technical Development.

^∗This work was partially supported by a grant from the National Swedish Board for Technical Development.

Notes

^∗This work was partially supported by a grant from the National Swedish Board for Technical Development.