Related papers: Selective algorithm processing of subset sum distr…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
We consider a monopolist seller facing a single buyer with additive valuations over n heterogeneous, independent items. It is known that in this important setting optimal mechanisms may require randomization [HR12], use menus of infinite…
The unit selection problem aims to identify objects, called units, that are most likely to exhibit a desired mode of behavior when subjected to stimuli (e.g., customers who are about to churn but would change their mind if encouraged). Unit…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We consider the Modular Subset Sum problem: given a multiset $X$ of integers from $\mathbb{Z}_m$ and a target integer $t$, decide if there exists a subset of $X$ with a sum equal to $t \pmod{m}$. Recent independent works by Cardinal and…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
The submodular function maximization is an attractive optimization model that appears in many real applications. Although a variety of greedy algorithms quickly find good feasible solutions for many instances while guaranteeing…
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…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…