Related papers: Summation Problem Revisited -- More Robust Computa…
Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and…
We consider the complexity for computing the approximate sum $a_1+a_2+...+a_n$ of a sorted list of numbers $a_1\le a_2\le ...\le a_n$. We show an algorithm that computes an $(1+\epsilon)$-approximation for the sum of a sorted list of…
We study the following summarization problem: given a parallel composition A=A1||...||An of labelled transition systems communicating with the environment through a distinguished component Ai, efficiently compute a summary Si such that E||A…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Automatic text summarization tools have a great impact on many fields, such as medicine, law, and scientific research in general. As information overload increases, automatic summaries allow handling the growing volume of documents, usually…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems.…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…
Our goal is to find combinations of facts that optimally summarize data sets. We consider this problem in the context of voice query interfaces for simple, exploratory data analysis. Here, the system answers voice queries with a short…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Controllable summarization aims to provide summaries that take into account user-specified aspects and preferences to better assist them with their information need, as opposed to the standard summarization setup which build a single…
Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search,…
The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although…
Entity summarization aims at creating brief but informative descriptions of entities from knowledge graphs. While previous work mostly focused on traditional techniques such as clustering algorithms and graph models, we ask how to apply…
A sum where each of the $N$ summands can be independently chosen from two choices yields $2^N$ possible summation outcomes. There is an $\mathcal{O}(K^2)$-algorithm that finds the $K$ smallest/largest of these sums by evading the…
AI systems typically make decisions and find patterns in data based on the computation of aggregate and specifically sum functions, expressed as queries, on data's attributes. This computation can become costly or even inefficient when…