Related papers: A note on the complexity of addition
We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…
The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…
In this paper, we focus on the solution of a hard single machine scheduling problem by new heuristic algorithms embedding techniques from machine learning field and scheduling theory. These heuristics transform an instance of the hard…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. We show a linear-time algorithm computing a linear-size representation of all the seeds of a word (the number of seeds might be…
In the subset sum problem we are given n positive integers along with a target integer t. A solution is a subset of these integers summing to t. In this short note we show that for a given subset sum instance there is a proof of size…
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…
The maximal sum of a sequence "A" of "n" real numbers is the greatest sum of all elements of any strictly contiguous and possibly empty subsequence of "A", and it can be computed in "O(n)" time by means of Kadane's algorithm. Letting "A^(x…
We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element's values.
We present a polynomial time algorithm, which solves a nonstandard Variation of the well-known PARTITION-problem: Given positive integers $n, k$ and $t$ such that $t \geq n$ and $k \cdot t = {n+1 \choose 2}$, the algorithm partitions the…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of…
Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and…
In this paper we consider the time and the crossing sequence complexities of one-tape off-line Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n\log n, in…
Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.
We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by…
We consider a matching problem for time series with values in an arbitrary metric space, with the stretching penalty given by the Hellinger kernel. To optimize this matching, we introduce the Elastic Time Warping algorithm with a cubic…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…