Related papers: The Submodular Santa Claus Problem
We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. The leader's aim is to optimize a linear objective function…
Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
Cooperative games are an important class of problems in game theory, where the goal is to distribute a value among a set of players who are allowed to cooperate by forming coalitions. An outcome of the game is given by an allocation vector…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…
We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario…
It is generally believed that submodular functions -- and the more general class of $\gamma$-weakly submodular functions -- may only be optimized under the non-negativity assumption $f(S) \geq 0$. In this paper, we show that once the…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
Budget feasible mechanism design studies procurement combinatorial auctions where the sellers have private costs to produce items, and the buyer(auctioneer) aims to maximize a social valuation function on subsets of items, under the budget…
In this work, we study the Stochastic Budgeted Multi-round Submodular Maximization (SBMSm) problem, where we aim to adaptively maximize the sum, over multiple rounds, of a monotone and submodular objective function defined on subsets of…
In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice? In this paper, we develop the first linear-time algorithm for…
We study a problem related to submodular function optimization and the exact matching problem for which we show a rather peculiar status: its natural LP-relaxation can have fractional optimal vertices, but there is always also an optimal…