Arash Asadpour

An approximation algorithm for max-min fair allocation of indivisible goods

In this paper we give the first approximation algorithm for the problem of max-min fair allocation of indivisible goods. The approximation ratio of our algorithm is Ω1√k log3 k. As a part of our algorithm, we design an iterative method for rounding a fractional matching on a tree which might be of independent interest.

Santa claus meets hypergraph matchings

We consider the restricted assignment version of the problem of max-min fair allocation of indivisible goods, also known as the Santa Claus problem. There are m items and n players. Every item has some nonnegative value, and every player is interested in only some of the items. The goal is to distribute the items to the players in a way that maximizes the minimum of the sum of the values of the items given to any player. It was previously shown via a nonconstructive proof that uses the Lovász local lemma that the integrality gap of a certain configuration LP for the problem is no worse than some (unspecified) constant. This gives a polynomial-time algorithm to estimate the optimum value of the problem within a constant factor, but does not provide a polynomial-time algorithm for finding a corresponding allocation. We use a different approach to analyze the integrality gap. Our approach is based upon local search techniques for finding perfect matchings in certain classes of hypergraphs. As a result, we prove that the integrality gap of the configuration LP is no worse than 1/4. Our proof provides a local search algorithm which finds the corresponding allocation, but is nonconstructive in the sense that this algorithm is not known to converge to a local optimum in a polynomial number of steps.

An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods

In this paper, we give the first approximation algorithm for the problem of max-min fair allocation of indivisible goods. An instance of this problem consists of a set of

Stochastic Submodular Maximization

k

Santa Claus Meets Hypergraph Matchings

people and

Maximizing Stochastic Monotone Submodular Functions

m

Online Resource Allocation with Limited Flexibility

indivisible goods. Each person has a known linear utility function over the set of goods which might be different from the utility functions of other people. The goal is to distribute the goods among the people and maximize the minimum utility received by them. The approximation ratio of our algorithm is

Concise Bid Optimization Strategies with Multiple Budget Constraints

\Omega(\frac{1}{\sqrt{k}\log^{3}k})

An O(log n/log log n)-approximation algorithm for the asymmetric traveling salesman problem

. As a crucial part of our algorithm, we design and analyze an iterative method for rounding a fractional matching on a tree which might be of independent interest. We also provide better bounds when we are allowed to exclude a small fraction of the people from the problem.

On the Inefficiency Ratio of Stable Equilibria in Congestion Games

We study stochastic submodular maximization problem with respect to a cardinality constraint. Our model can capture the effect of uncertainty in different problems, such as cascade effects in social networks, capital budgeting, sensor placement, etc. We study non-adaptive and adaptive policies and give optimal constant approximation algorithms for both cases. We also bound the adaptivity gap of the problem between 1.21 and 1.59.