Fault Tolerant Sorting—Theoretical and Empirical Analyses of the Randomized QuickMergesort Algorithm

Abstract

This paper introduces a new paradigm in the design of sorting algorithms, viz., fault tolerance. Fault tolerance is an important concept in modern day computing and design workflows must accommodate this need. In general, there are a number of avenues for faults to occur and techniques to address the same; this paper focusses on only one source of faulty behavior, viz., process termination. Process termination, as a cause of faulty behavior, is important from the perspective of various applications in real-time scheduling. In order to measure the effectiveness of a fault tolerant protocol, it is necessary to define a suitable metric and analyze the performance of the protocol with respect to that metric. We measure the “unsortedness” of an array, as characterized by the number of inversion pairs that remain when the sorting algorithm (process) terminates. This paper proposes a new algorithm for sorting called the Randomized QuickMergesort (RQMS) algorithm. RQMS has a higher degree of fault tolerance than either Randomized Quicksort (RQS) or Mergesort (MS), in that fewer inversion pairs remain when it terminates. Likewise, RQMS has a lower comparison overhead than RQS and is more space-efficient than MS. Our empirical analysis, which was conducted over a wide variety of distributions, conclusively establishes that RQMS is the algorithm of choice, when fault tolerance is paramount in the application.