Worst Case Ecient Data Structures for Priority Queues and Deques with Heap Order

An efficient amortized data structure is one that ensures that the average time per operation spent on processing any sequence of operations is small. Amortized data structures typically have very non-uniform response times, i.e., individual operations can be occasionally and unpredictably slow, although the average time over a sequence is kept small by completing most of the other operations quickly. This makes amortized data structures unsuitable in many important contexts, such as real time systems, parallel programs, persistent data structures and interactive software. On the other hand, an efficient worst case data structure guarantees that every operation will be performed quickly. The construction of worst case efficient data structures from amortized ones is a fundamental problem which is also of pragmatic interest. In this report, we have studied two different problems in data structures, namely, the implementation of priority queues and concatenable double ended queues with heap order. We have eliminated amortization from the existing data structures and have proposed new worst case efficient data structures for these problems.