Related papers: The Primal-Dual Greedy Algorithm for Weighted Cove…
Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Set Cover is a classic NP-hard problem; as shown by Slav\'{i}k (1997) the greedy algorithm gives an approximation ratio of $\ln n - \ln \ln n + \Theta(1)$. A series of works by Lund \& Yannakakis (1994), Feige (1998), Moshkovitz (2015) have…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
A major problem in data augmentation is to ensure that the generated new samples cover the search space. This is a challenging problem and requires exploration for data augmentation policies to ensure their effectiveness in covering the…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…
Given an unweighted graph $G$, the *minimum $r$-dominating set problem* asks for the smallest-cardinality subset $S$ such that every vertex in $G$ is within radius $r$ of some vertex in $S$. While the $r$-dominating set problem on planar…
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…
In the Shortest Common Superstring problem, one needs to find the shortest superstring for a set of strings. This problem is APX-hard, and many approximation algorithms were proposed, with the current best approximation factor of 2.466.…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the…
In this paper, with the parametric symmetric coercive elliptic boundary value problem as an example of the primal-dual variational problems satisfying the strong duality, we develop primal-dual reduced basis methods (PD-RBM) with robust…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g.,…