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It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…
We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for finding control policies are unlikely to or simply don't have guarantees of finding policies within a constant factor or a…
Bender et al. (SPAA 2013) have proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Given that calibration costs, it…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
The best arm identification problem requires identifying the best alternative (i.e., arm) in active experimentation using the smallest number of experiments (i.e., arm pulls), which is crucial for cost-efficient and timely decision-making…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
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…