For some computational problems (like sorting), even though the input is given and known (deterministic), it might be helpful to use randomness (probabilitic processes) in the design of the algorithm. This is analogous to the probabilistic method in which we were using probability to prove the existence of a certain object. We’ll see several examples of randomized algorithms in this course, one...

Sorting is one of the most important primitives in various systems, for example, database systems, since it is often the dominant operation in the running time of an entire system. Therefore, there is a long list of work on improving its efficiency. It is also true in the context of secure multi-party computation (MPC), and several MPC sorting protocols have been proposed. However, all existing...

Information theory provides tools and techniques to measure the fundamental limits of predictability. Apart from this formal basis, researchers have attempted to construct so-called ‘optimal’ predictors in order to conduct limits studies for different aspects of program predictability (such as branch outcomes and method return values). This paper reports on two case studies for branch predictio...

In recent years CUDA has become a major architecture for multithreaded computations. Unfortunately, its potential is not yet being commonly utilized because many fundamental problems have no practical solutions for such machines. Our goal is to establish a hybrid multicore/parallel theoretical model that represents well architectures like NVIDIA CUDA, Intel Larabee, and OpenCL as well as admits...

Sorting is a fundamental functionality in libraries, for which efficiency is crucial. Correctness of the highly optimized implementations is often taken for granted. De Gouw et al. have shown that this certainty is deceptive by revealing a bug in the Java Development Kit (JDK) implementation of TimSort. We have formally analysed the other implementation of sorting in the JDK standard library: A...

In this paper we present a Nuprl formalization and proof of Bird’s fusion theorem for trees. We apply the theorem to a derivation of quicksort.

Today there are several efficient algorithms that cope with the popular task of sorting. This paper titled Comparative Performance Study of Improved Heap Sort Algorithm and other sorting Algorithms presents a comparison between classical sorting algorithms and improved heap sort algorithm. To have some experimental data to sustain these comparisons three representative algorithms were chosen (c...

Sorting is known to be one of the fundamental computing problems which continue to attract a great deal of research. It is evident that instruction count requirements of the key sorting algorithms are well understood. However, the cost of executing a sorting algorithm is influenced by factors apart from instruction count such as cache miss and page faults as well. There exist studies of sorting...

Knuth (1973,pp2-3) notes that sorting is estimated to take up 25% of the world’s computer time. With the advent of the microcomputer this may well have changed, but it is nonetheless a both practically and theoretically interesting task. Sorting, in the sense of bringing together related things, has now been subsumed by.the more specific task of ordering, and has spawned an enormous number of s...