Related papers: Towards universally optimal sorting algorithms
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable…
Topological sorting is an important technique in numerous practical applications, such as information retrieval, recommender systems, optimization, etc. In this paper, we introduce a problem of generalized topological sorting with…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
We consider a recently introduced framework in which fairness is measured by worst-case outcomes across groups, rather than by the more standard differences between group outcomes. In this framework we provide provably convergent…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
We consider stochastic convex optimization with a strongly convex (but not necessarily smooth) objective. We give an algorithm which performs only gradient updates with optimal rate of convergence.
We generalize the classical nuts and bolts problem to a setting where the input is a collection of $n$ nuts and $m$ bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
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…
It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems,…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…