Related papers: Exact Algorithms via Monotone Local Search
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day…
In parameterized complexity, it is a natural idea to consider different generalizations of classic problems. Usually, such generalization are obtained by introducing a "relaxation" variable, where the original problem corresponds to setting…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
For many hard computational problems, simple algorithms that run in time $2^n \cdot n^{O(1)}$ arise, say, from enumerating all subsets of a size-$n$ set. Finding (exponentially) faster algorithms is a natural goal that has driven much of…
In many real-world problems and applications, finding only a single element, even though the best, among all possible candidates, cannot fully meet the requirements. We may wish to have a collection where each individual is not only…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and a parameter $\alpha>1$, and the goal is to design an $\alpha$-approximation algorithm with the…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and…
Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact exponential time algorithms. The…
In the Set Cover problem, we are given a set system with each set having a weight, and we want to find a collection of sets that cover the universe, whilst having low total weight. There are several approaches known (based on greedy…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…