Data-Structural Bootstrapping, Linear Path Compression, and Catenable Heap-Ordered Double-Ended Queues

A deque with heap order is a linear list of elements with real-valued keys that allows insertions and deletions of elements at both ends of the list. It also allows the findmin (alternatively findmax) operation, which returns the element of least (greatest) key, bur it does not allow a general deletemin (deletemax) operation. Such a data structure is also called a mindeque (maxdeque). Whereas implementing heap-ordered deques in constant time per operation is a solved problem, catenating heap-ordered deques in sublogarithmic time has remained open until now. This paper provides an efficient implementation of catenable heap-ordered deques, yielding constant amortized time per operation. The important algorithmic technique employed is an idea that we call data-structural bootstrapping: we abstract heap-ordered deques by representing them by their minimum elements, thereby reducing catenation to simple insertion. The efficiency of the resulting data structure depends upon the complexity elf a special case of path compression that we prove takes linear time