Related papers: Towards the sampling Lov\'asz Local Lemma

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…

We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

We consider the following conditional linear regression problem: the task is to identify both (i) a $k$-DNF condition $c$ and (ii) a linear rule $f$ such that the probability of $c$ is (approximately) at least some given bound $\mu$, and…

We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is…

Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…

In classic distributed graph problems, each instance on a graph specifies a space of feasible solutions (e.g. all proper ($\Delta+1$)-list-colorings of the graph), and the task of distributed algorithm is to construct a feasible solution…

We present a sublinear time algorithm that gives random local access to the uniform distribution over satisfying assignments to an arbitrary k-SAT formula $\Phi$, at exponential clause density. Our algorithm provides memory-less query…

Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…

In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…

We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An…

Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded…

Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…

We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…

For many random Constraint Satisfaction Problems, by now, we have asymptotically tight estimates of the largest constraint density for which they have solutions. At the same time, all known polynomial-time algorithms for many of these…

Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula $F$ with $n$ variables and clause density $\alpha$. Assume that the probability that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that…

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

We introduce and study constrained Markov Decision Processes (cMDPs) with anytime constraints. An anytime constraint requires the agent to never violate its budget at any point in time, almost surely. Although Markovian policies are no…