Weak-Heap Sort

A data structure called a weak-heap is defined by relaxing the requirements for a heap. The structure can be implemented on a 1-dimensional array with one extra bit per data item and can be initialized with n items using exactly n - 1 data element compares. Theoretical analysis and empirical results indicate that it is a competitive structure for sorting. The worst case number of data element comparisons is strictly less than (n - 1) log n + 0.086013n and the expected number is conjectured to be approximately (n - 0.5) log n - 0.413n