Related papers: Approximation Algorithms for Size-Constrained Non-…
The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint. We study the problem of designing truthful mechanisms…
Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle…
Maximizing submodular functions has been increasingly used in many applications of machine learning, such as data summarization, recommendation systems, and feature selection. Moreover, there has been a growing interest in both submodular…
We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…
Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…
We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.' (1) If the constraint is specified by a monadic…
We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling…
Cardinality constrained submodular function maximization, which aims to select a subset of size at most $k$ to maximize a monotone submodular utility function, is the key in many data mining and machine learning applications such as data…
We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-\epsilon$. It is shown that every randomized streaming algorithm for this problem needs space $\Omega(\log n + \log b -…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often…
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…
We revisit the MaxSAT problem in the data stream model. In this problem, the stream consists of $m$ clauses that are disjunctions of literals drawn from $n$ Boolean variables. The objective is to find an assignment to the variables that…
Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
We present a polynomial time algorithm for online maximization of $k$-submodular maximization. For online (nonmonotone) $k$-submodular maximization, our algorithm achieves a tight approximate factor in an approximate regret. For online…
We provide a deterministic algorithm that outputs an $O(n^{3/4} \log n)$-approximation for the Longest Common Subsequence (LCS) of two input sequences of length $n$ in near-linear time. This is the first deterministic approximation…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…