Like the Selection algorithm, described in several previous blogs, Partition is another algorithm closely related to sorting. Given a single value or an array of values, the Partition algorithm splits the array into sections with useful statistical properties, without sorting it, in linear time – i.e. O(n). Single Value Partition For example, C++ nth_element function […]
Read more "Radix Partition"Selection is an interesting algorithm related to sorting. k-th value Selection, provides the k-th largest value within an unsorted array of values without sorting the array. It does this in linear time, while using comparisons, which is faster than comparison sorting algorithms are capable of. Comparison-based Selection algorithm was developed over 50 years ago. Non-comparison […]
Read more "k[]-th Radix Selection"Problem: You have an array of a billion numeric keys (e.g. 32-bit unsigned integers) and need the largest 11 of them. Solutions: The first two solutions do more work than is necessary, as they sort all of the array elements, including the top 11 elements. This was not required by the problem statement. The whole […]
Read more "Top-K Radix Selection Algorithm"I’ve been optimizing variety of Radix algorithms for over a decade: LSD and MSD Radix Sort, Single Core and Multi-Core, and Radix Selection. Several of these optimization techniques can be applied to all of these algorithms. In this blog, I’ll discuss each of these optimizations and show how much performance is gained, for sequential single […]
Read more "Fastest LSD Radix Sort in C++ on a Single CPU Core"I ran across a research paper recently on Radix Selection where the authors mentioned that LSD Radix Sort is known to have performance issues when sorting arrays of data with certain distributions. They did not elaborate what those distributions were. Also, Professor Sedgewick has mentioned that the worst case for Radix Sort is when the […]
Read more "Optimizations of LSD Radix Sort for Different Input Data Distributions"One performance optimization that was introduced in the Radix Selection algorithm can also be applied to the MSD Radix Sort – combining counting with the permutation phase. This optimization cannot be done during the first digit pass, since counting must be performed first to figure out the bins to permute the data into. However, during […]
Read more "MSD Radix Sort Optimization"In my previous blog post on Radix Selection, the algorithm which returns the k-th largest value from an unsorted array was shown to be significantly faster than sorting, because it performs less work. In this blog, I’ll explore further optimizations to make Radix Sort even faster. More Bits Per Digit Radix Sort (LSD and MSD […]
Read more "Radix Selection Optimizations"There is a closely related algorithm to sorting called Selection, which provides the k-th element from an unsorted array. For example, a 17-th highest test score from a college Physics class, or a 91-st most popular book at the library. One way to accomplish Selection is to sort the array and then access the k-th […]
Read more "Radix Selection Algorithm"The Power Usage of Algorithms in C# blog presents power usage and efficiency of several C# sequential (single core) algorithms is shown. In this blog power usage and efficiency of parallel algorithms is explored. Power Measurement Setup The same setup is used as in Power Usage of Algorithms in C#. Parallel Sorting An array of […]
Read more "Power Usage of Parallel Algorithms in C#"Algorithms power the world – from search to streaming to AI. Each algorithmic domain has a variety of algorithms to choose from, with different run times and characteristics. But how much power do algorithms use? Does power usage vary between algorithms? Are some algorithms more power efficient than others? This blog answers these questions by […]
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Algorithm Performance 