Related papers: On the Configuration LP for Maximum Budgeted Alloc…
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…
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…
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 consider the classical problem of Scheduling on Unrelated Machines. In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time $p_{ij}$ of a job $j$…
We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
In the restricted Santa Claus problem we are given resources $\mathcal R$ and players $\mathcal P$. Every resource $j\in\mathcal R$ has a value $v_j$ and every player $i$ desires a set $\mathcal R(i)$ of resources. We are interested in…
In the problem of Submodular Max-Min Allocation, we are given a set of items, a set of players, and monotone submodular valuation functions that represent the satisfaction of a player with a certain subset of items. The goal is to find an…
Assortment optimization concerns the problem of selling items with fixed prices to a buyer who will purchase at most one. Typically, retailers select a subset of items, corresponding to an "assortment" of brands to carry, and make each…
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem…
We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization…
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 $j$…
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…
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…
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…
Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…
We study procurement games where each seller supplies multiple units of his item, with a cost per unit known only to him. The buyer can purchase any number of units from each seller, values different combinations of the items differently,…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…