相关论文: Combinatorial Algorithm for Restricted Max-Min Fai…
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed,…
In the max-min allocation problem a set $P$ of players are to be allocated disjoint subsets of a set $R$ of indivisible resources, such that the minimum utility among all players is maximized. We study the restricted variant, also known as…
We study the Maximum Budgeted Allocation problem, which is the problem of assigning indivisible items to players with budget constraints. In its most general form, an instance of the MBA problem might include many different prices for the…
We study the max-min fair allocation problem in which a set of $m$ indivisible items are to be distributed among $n$ agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item $j$…
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…
We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of $m$ indivisible goods to $n$ players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known…
The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we…
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…
We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
We study a novel problem of fairness in ranking aimed at minimizing the amount of individual unfairness introduced when enforcing group-fairness constraints. Our proposal is rooted in the distributional maxmin fairness theory, which uses…
Graph Balancing is the problem of orienting the edges of a weighted multigraph so as to minimize the maximum weighted in-degree. Since the introduction of the problem the best algorithm known achieves an approximation ratio of $1.75$ and it…
We study an online version of the max-min fair allocation problem for indivisible items. In this problem, items arrive one by one, and each item must be allocated irrevocably on arrival to one of $n$ agents, who have additive valuations for…
Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
We consider the problem of allocating indivisible goods fairly among n agents who have additive and submodular valuations for the goods. Our fairness guarantees are in terms of the maximin share, that is defined to be the maximum value that…
In this paper, we consider the restricted case of the problem and improve the current best approximation ratio by presenting a polynomial time 12-approximation algorithm using linear programming and semi-definite programming. Our algorithm…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…