A Note on the Construction of Data Structure "DEAP"

The d&p, recently proposed by Svante Carlsson [2], is an efficient implementation of a doubl*ended priority queue. The deap is a variation of the heap [8] and was proposed as an alternative to the min~max heap [1,4,6]. The operations FindMn and FindMax can be performed in O(1) comparisons, DeleteMin and Delete&x in O(log n) comparisons, Insert in O(log log n) comparisons and Create in O(n) comparisons. In this note we present some new results on the cost of constructing the deap. In particular, for a deap on n elements: l 2.07.. . n 2 log a comparisons are necessary, in the worst and average cases, to construct the deap; this improves the previous lower bound of roughly #n comparisons. 0 2.49.. . n comparisons are sufficient, in the worst case, to construct the deap; this result corrects the originally claimed upper bound of 2.07n comparisons [2], which we here show to be incorrect.