Related papers: Local Search for Weighted Tree Augmentation and St…
Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to…
Wattenhofer [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the…
This paper studies the estimation of the conditional density f (x, $\times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $\in$ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with…
Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP…
Random Forest's performance can be matched by a single slow-growing tree (SGT), which uses a learning rate to tame CART's greedy algorithm. SGT exploits the view that CART is an extreme case of an iterative weighted least square procedure.…
We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…
Non-asymptotic analysis of quasi-Newton methods have gained traction recently. In particular, several works have established a non-asymptotic superlinear rate of $\mathcal{O}((1/\sqrt{t})^t)$ for the (classic) BFGS method by exploiting the…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
The priority model was introduced to capture "greedy-like" algorithms. Motivated by the success of advice complexity in the area of online algorithms, the fixed priority model was extended to include advice, and a reduction-based framework…
Motivated by online decision-making in time-varying combinatorial environments, we study the problem of transforming offline algorithms to their online counterparts. We focus on offline combinatorial problems that are amenable to a constant…
This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in…
This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two…
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X_n \subset X which can be used to approximate the elements of F. The best possible error we can achieve for such an…
We show that a very simple modification of the Pure Greedy Algorithm for approximating functions by sparse sums from a dictionary in a Hilbert or more generally a Banach space has optimal convergence rates on the class of convex…
A promising approach for obtaining improved approximation algorithms for Steiner tree is to use the bidirected cut relaxation (BCR). The integrality gap of this relaxation is at least $36/31$, and it has long been conjectured that its true…
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…
We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is $\Theta(\log n)$. Moreover, we prove that the same result also holds for graphic, Euclidean, and rectilinear instances of the…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
Inspired by the network routing literature \cite{aggarwal1996efficient}, we develop what we call a ``Pre-Emptive Greedy Algorithm" to embed bounded degree induced trees in sparse expanders. This generalises a powerful and central result of…
We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the…