Strictly-Regular Number System and Data Structures

We introduce a new number system that we call the strictlyregular system, which efficiently supports the operations: digit-increment, digit-decrement, cut, concatenate, and add. Compared to other number systems, the strictly-regular system has distinguishable properties. It is superior to the regular system for its efficient support to decrements, and superior to the extended-regular system for being more compact by using three symbols instead of four. To demonstrate the applicability of the new number system, we modify Brodal’s meldable priority queues making deletion require at most 2 lg n+O(1) element comparisons (improving the bound from 7 lg n+O(1)) while maintaining the efficiency and the asymptotic time bounds for all operations.