Related papers: Superconstant Inapproximability of Decision Tree L…
The Steiner tree problem is one of the classic and most fundamental $\mathcal{NP}$-hard problems: given an arbitrary weighted graph, seek a minimum-cost tree spanning a given subset of the vertices (terminals). Byrka \emph{et al}. proposed…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…
We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is…
We show that, assuming NP $\not\subseteq$ $\cap_{\delta > 0}$DTIME$\left(\exp{n^\delta}\right)$, the shortest vector problem for lattices of rank $n$ in any finite $\ell_p$ norm is hard to approximate within a factor of $2^{(\log n)^{1 -…
Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by…
r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
Scheduling with assignment restrictions is an important special case of scheduling unrelated machines which has attracted much attention in the recent past. While a lower bound on approximability of 3/2 is known for its most general…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time p_{ij} if processed on…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Sequential learning models situations where agents predict a ground truth in sequence, by using their private, noisy measurements, and the predictions of agents who came earlier in the sequence. We study sequential learning in a social…
The best algorithm for approximating Steiner tree has performance ratio $\ln(4)+\epsilon \approx 1.386$ [J. Byrka et al., \textit{Proceedings of the 42th Annual ACM Symposium on Theory of Computing (STOC)}, 2010, pp. 583-592], whereas the…
Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution…
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…