Related papers: Exact Algorithms via Monotone Local Search
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 consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and…
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
This article analyzes the stochastic runtime of a Cross-Entropy Algorithm on two classes of traveling salesman problems. The algorithm shares main features of the famous Max-Min Ant System with iteration-best reinforcement. For simple…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained…
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the…
Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can be stated about optimal solutions if an objective function is…
This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…
The 0-1 integer linear programming feasibility problem is an important NP-complete problem. This paper proposes a continuous-time dynamical system for solving that problem without getting trapped in non-solution local minima. First, the…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…
In the Exact Matching problem, we are given a graph whose edges are colored red or blue and the task is to decide for a given integer k, if there is a perfect matching with exactly k red edges. Since 1987 it is known that the Exact Matching…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…
We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…