ARL, a faster in-place, cache friendly sorting algorithm

This paper introduces a new, faster sorting algorithm (ARL – Adaptive Left Radix) that does in-place, non-stable sorting. Left Radix, often called MSD (Most Significant Digit) radix, is not new in itself, but the adaptive feature and the in-place sorting ability are new features. ARL does sorting with only internal moves in the array, and uses a dynamically defined radix for each pass. ALR is a recursive algorithm that sorts by first sorting on the most significant ‘digits’ of the numbers – i.e. going from left to right. Its space requirements are O(N + logM) and time performance is O(N*log M) – where M is the maximum value sorted and N is the number of integers to sort. The performance of ARL is compared with both with the built in Quicksort algorithm in Java, Arrays.sort(), and with ordinary Radix sorting (sorting from right-to-left). ARL is almost twice as fast as Quicksort if N > 100. This applies to the normal case, a uniformly drawn distribution of the numbers 0:N-1. ARL is also in significantly faster than Quicksort for 8 out of 9 other investigated distributions of the numbers to be sorted. ARL is more cache friendly than Quicksort and also maybe ordinary Radix by generating fewer cache misses. Even though Radix is faster in most cases, ARL becomes faster than Radix for large n (n > 5* 10). Since the space requirement for Radix is twice that of ARL (and Quicksort), this paper proposes ARL as a better general sorting algorithm than Quicksort.