Related papers: On Submodular Search and Machine Scheduling
We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…
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…
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 study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
We study \emph{combinatorial procurement auctions}, where a buyer with a valuation function $v$ and budget $B$ wishes to buy a set of items. Each item $i$ has a cost $c_i$ and the buyer is interested in a set $S$ that maximizes $v(S)$…
Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…
We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions…
We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
Meta-Learning has gained increasing attention in the machine learning and artificial intelligence communities. In this paper, we introduce and study an adaptive submodular meta-learning problem. The input of our problem is a set of items,…
We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…
In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm…
In submodular covering problems, we are given a monotone, nonnegative submodular function $f: 2^N \rightarrow\mathbb{R}_+$ and wish to find the min-cost set $S\subseteq N$ such that $f(S)=f(N)$. This captures SetCover when $f$ is a coverage…