In order to gain maximal efficiency of the concurrent use of search trees the number of nodes to be locked at a time should be as small aa possible, and the locks should be released aa soon aa possible. We propose a new rebalancing method for binary search treea that allows rebalancing to be uncoupled from updating, so as to make updating faster. The trees we use are obtained by relaxing the balance conditions of red-black trees.When not involved with updating, the rebalancing task can be performed as a shadow process being active all the time, or it can be performed outside rush hours, at night, for example.

We consider the separation of rebalancmg from updates m several database structures, such as B-trees for external and AVL-trees for mternal structures We show how this separation can be implemented such that rebalancmg IS performed by local background processes Our solution lmphes that even simple locking schemes (wlthout additional links and copses of certam nodes ) for concurrency control are efficient m the sense that at any time only a small constant number of nodes must be locked

Abstract.Fast hidden line elimination algorithms can be obtained by minor modifications to algorithms developed for reporting intersections of polygons. We show how the same modifications which have been applied to segment trees can be applied to the data structure of Swart and Ladner as well, leading to an O((n+k)logn) time hidden line elimination algorithm (n is the number of boundary edges of the input polygons and k is the number of intersections of the edges on the projection plane). The algorithm improves the fastest previous line-sweep algorithm for the problem by a factor O(Iogn).

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