With re nements to the WEAK-HEAPSORT algorithm we establish the general and practical relevant sequential sorting algorithm RELAXED-WEAK-HEAPSORT executing exactly ndlog ne 2 ne + 1 n log n 0:9n comparisons on any given input. The number of transpositions is bounded by n plus the number of comparisons. Experiments show that RELAXED-WEAK-HEAPSORT only requires O(n) extra bits. Even if this space...

Recently, a new Quicksort variant due to Yaroslavskiy was chosen as standard sorting method for Oracle’s Java 7 runtime library. The decision for the change was based on empirical studies showing that on average, the new algorithm is faster than the formerly used classic Quicksort. Surprisingly, the improvement was achieved by using a dual pivot approach, an idea that was considered not promisi...

We derive CPU time formulae for the two simplest linear time-sorting algorithms, linear probing sort and bucket sort, as a function of the load factor, and show agreement with experimentally measured CPU times. This allows us to compute optimal load factors for each algorithm, whose values have previously been identified only approximately in the literature. We also present a simple model of ca...

Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort algorithm and its variants. Specifically, we study the time complexity of the algorithm and we provide a complete demonstration of the variance of the number of...

The new dual-pivot Quicksort by Vladimir Yaroslavskiy — used in Oracle’s Java runtime library since version 7 — features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less comparisons than classic single-pivot Quicksort implementations. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order sta...

The new dual-pivot Quicksort by Vladimir Yaroslavskiy — used in Oracle’s Java runtime library since version 7 — features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less comparisons than classic single-pivot Quicksort implementations. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order sta...

It is well known that the performance of quicksort can be improved by selecting the median of a sample of elements as the pivot of each partitioning stage. For large samples the partitions are better, but the amount of additional comparisons and exchanges to find the median of the sample also increases. We show in this paper that the optimal sample size to minimize the average total cost of qui...

(Abstract) We present an algorithm to compress hypergraphs into the data structure ZDDs and analyze the computational complexity. Since a ZDD provides an approach to solve large-scale problems that are difficult to compute in a reasonable amount of time and space, it is important to compress hypergraphs efficiently. Our algorithm uses multikey Quicksort given by Bentley and Sedgewick. By conduc...