Related papers: Summation Problem Revisited -- More Robust Computa…
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of…
In this paper, we investigate the problem of assessing statistical methods and effectively summarizing results from simulations. Specifically, we consider problems of the type where multiple methods are compared on a reasonably large test…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…
Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
The \emph{top-$k$-sum} operator computes the sum of the largest $k$ components of a given vector. The Euclidean projection onto the top-$k$-sum sublevel set serves as a crucial subroutine in iterative methods to solve composite…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large…
An emerging class of data systems partition their data and precompute approximate summaries (i.e., sketches and samples) for each segment to reduce query costs. They can then aggregate and combine the segment summaries to estimate results…
Tabular data provide answers to a significant portion of search queries. However, reciting an entire result table is impractical in conversational search systems. We propose to generate natural language summaries as answers to describe the…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
This paper describes a new median algorithm and a median approximation algorithm. The former has O(n) average running time and the latter has O(n) worst-case running time. These algorithms are highly competitive with the standard algorithm…