  The segment tree is an extremely versatile data structure. In this paper, a
new heap based implementation of segment trees is proposed. In such an
implementation of segment tree, the structural information associated with the
tree nodes can be removed completely. Some primary computational geometry
problems such as stabbing counting queries, measure of union of intervals, and
maximum clique size of Intervals are used to demonstrate the efficiency of the
new heap based segment tree implementation. Each interval in a set $S=\{I_1
,I_2 ,\cdots,I_n\}$ of $n$ intervals can be insert into or delete from the heap
based segment tree in $O(\log n)$ time. All the primary computational geometry
problems can be solved efficiently.
