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The traditional integer sorting algorithms give a lower bound of O(n log n) expected time without randomization and O(n) with randomization. Recent researches have optimized lower bound for deterministic sorting algorithms. This thesis will present an idea to achieve the complexity of deterministic integer sorting algorithm in O(n log log n log log log n) expected time and linear space. The idea will use Andersson’s exponential tree to perform the sorting with some major modification. Integers will be passed down to exponential tree one at a time but limit the comparison required at each level. The total number of comparison for any integer will be O(log log n log log log n) i.e. total time taken for all integers insertion will be O(n log log n log log log n). The algorithm presented can be compared with the result of Fredman and Willard that sorts n integers in O(n log n / log log n) time in linear space and also with result of Raman that sorts n integers in O(nv(log n log log n)) time in linear space. The algorithm can also be compared with Yijei Han’s result of O(n log log n log log log n) expected time for deterministic linear space integer sorting.

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