Related papers: Reducing Matroid Optimization to Basis Search
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…
We address optimization of nonlinear functions of the form $f(Wx)$, where $f:\R^d\to \R$ is a nonlinear function, $W$ is a $d\times n$ matrix, and feasible $x$ are in some large finite set $F$ of integer points in $\R^n$. One motivation is…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…
In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of…
Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…
Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
We consider a fast approximation algorithm for the linear matroid intersection problem. In this problem, we are given two $r \times n$ matrices $M_1$ and $M_2$, and the objective is to find a largest set of columns that are linearly…
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…
We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…
In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation…