Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity
Proceedings of the 8th ACM conference on Electronic commerce
On allocations that maximize fairness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Santa Claus Meets Hypergraph Matchings
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximation Algorithms for the Max-Min Allocation Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
MaxMin allocation via degree lower-bounded arborescences
Proceedings of the forty-first annual ACM symposium on Theory of computing
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
On Low-Envy Truthful Allocations
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Maximizing the minimum load for selfish agents
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Fair Division under Ordinal Preferences: Computing Envy-Free Allocations of Indivisible Goods
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
New Constructive Aspects of the Lovász Local Lemma
Journal of the ACM (JACM)
Egalitarian allocations of indivisible resources: theory and computation
CIA'06 Proceedings of the 10th international conference on Cooperative Information Agents
Santa claus meets hypergraph matchings
ACM Transactions on Algorithms (TALG)
Quasi-polynomial local search for restricted max-min fair allocation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximate Mechanism Design without Money
ACM Transactions on Economics and Computation
Autonomous Agents and Multi-Agent Systems
Annals of Mathematics and Artificial Intelligence
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The problem of allocating divisible goods has enjoyed a lot of attention in both mathematics (e.g. the cake-cutting problem) and economics (e.g. market equilibria). On the other hand, the natural requirement of indivisible goods has been somewhat neglected, perhaps because of its more complicated nature. In this work we study a fairness criterion, called the Max-Min Fairness problem, for k players who want to allocate among themselves m indivisible goods. Each player has a specified valuation function on the subsets of the goods and the goal is to split the goods between the players so as to maximize the minimum valuation. Viewing the problem from a game theoretic perspective, we show that for two players and additive valuations the expected minimum of the (randomized) cut-and-choose mechanism is a 1/2-approximation of the optimum. To complement this result we show that no truthful mechanism can compute the exact optimum.We also consider the algorithmic perspective when the (true) additive valuation functions are part of the input. We present a simple 1/(m - k + 1) approximation algorithm which allocates to every player at least 1/k fraction of the value of all but the k - 1 heaviest items. We also give an algorithm with additive error against the fractional optimum bounded by the value of the largest item. The two approximation algorithms are incomparable in the sense that there exist instances when one outperforms the other.