Related papers: Improved in-place associative integer sorting
Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of…
We consider the fundamental problem of internally sorting a sequence of $n$ elements. In its best theoretical setting QuickMergesort, a combination Quicksort with Mergesort with a Median-of-$\sqrt{n}$ pivot selection, requires at most $n…
We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This…
Building systems with capability of natural language understanding (NLU) has been one of the oldest areas of AI. An essential component of NLU is to detect logical succession of events contained in a text. The task of sentence ordering is…
We describe and analyze Zig-zag Sort--a deterministic data-oblivious sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network.…
One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Natural language semantics can be modeled using the phrase-structured model, which can be represented using a tree-type architecture. As a result, recent advances in natural language processing have been made utilising recursive neural…
Neighborhood graphs are gaining popularity as a concise data representation in machine learning. However, naive graph construction by pairwise distance calculation takes $O(n^2)$ runtime for $n$ data points and this is prohibitively slow…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…
The quantum search algorithm consists of an alternating sequence of selective inversions and diffusion type operations, as a result of which it can find a target state in an unsorted database of size N in only sqrt(N) queries. This paper…
We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n…
It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…
Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In the typical setting investigated till now, each classifier is trained…
In our study we implemented and compared seven sequential and parallel sorting algorithms: bitonic sort, multistep bitonic sort, adaptive bitonic sort, merge sort, quicksort, radix sort and sample sort. Sequential algorithms were…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let…
Learning from the multidimensional data has been an interesting concept in the field of machine learning. However, such learning can be difficult, complex, expensive because of expensive data processing, manipulations as the number of…