Related papers: Zig-zag Sort: A Simple Deterministic Data-Obliviou…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
Consider a clique of n nodes, where in each synchronous round each pair of nodes can exchange O(log n) bits. We provide deterministic constant-time solutions for two problems in this model. The first is a routing problem where each node is…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
We study the self-stabilizing leader election problem in anonymous $n$-nodes networks. Achieving self-stabilization with low space memory complexity is particularly challenging, and designing space-optimal leader election algorithms remains…
As secure processors such as Intel SGX (with hyperthreading) become widely adopted, there is a growing appetite for private analytics on big data. Most prior works on data-oblivious algorithms adopt the classical PRAM model to capture…
The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting $n$ distinct elements in this model. In particular, it…
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…
We present a deterministic sorting algorithm, SPMS (Sample, Partition, and Merge Sort), that interleaves the partitioning of a sample sort with merging. Sequentially, it sorts $n$ elements in $O(n \log n)$ time cache-obliviously with an…
The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around…
Sorting is a fundamental operation across numerous computational domains. Traditionally, this process involves transferring data from main memory to a processing unit for sorting, followed by writing the sorted data back to memory. This…
Many fundamental problems in computational geometry admit no algorithm running in $o(n \log n)$ time for $n$ planar input points, via classical reductions from sorting. Prominent examples include the computation of convex hulls, quadtrees,…
In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The…
In this paper, a sorting technique is presented that takes as input a data set whose primary key domain is known to the sorting algorithm, and works with an time efficiency of O(n+k), where k is the primary key domain. It is shown that the…
Sorting is an essential operation in computer science with direct consequences on the performance of large scale data systems, real-time systems, and embedded computation. However, no sorting algorithm is optimal under all distributions of…
Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
We present the first explicit comparison-based algorithm that sorts the sumset $X + Y = \{x_i + y_j,\ \forall 0 \le i, j < n\}$, where $X$ and $Y$ are sorted arrays of real numbers, in optimal $O(n^2)$ time and comparisons. While Fredman…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…