Min-max optimization of several classical discrete optimization problems
Journal of Optimization Theory and Applications
Approximating the weight of shallow Steiner trees
Discrete Applied Mathematics
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems
Theoretical Computer Science
Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem
Theoretical Computer Science
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Minimum spanning tree with hop restrictions
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Logical Preference Representation and Combinatorial Vote
Annals of Mathematics and Artificial Intelligence
Multicriteria Optimization
Approximation algorithms for the bi-criteria weighted MAX-CUT problem
Discrete Applied Mathematics
Fairness Measures for Resource Allocation
SIAM Journal on Computing
Bi-objective scheduling algorithms for optimizing makespan and reliability on heterogeneous systems
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Journal of Artificial Intelligence Research
The Efficiency of Fair Division
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
On the approximability of robust spanning tree problems
Theoretical Computer Science
The efficiency of fair division with connected pieces
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Operations Research
Operations Research Letters
The 2-hop spanning tree problem
Operations Research Letters
Approximating k-hop minimum-spanning trees
Operations Research Letters
A fully polynomial bicriteria approximation scheme for the constrained spanning tree problem
Operations Research Letters
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We consider optimization problems in a multiagent setting where a solution is evaluated with a vector. Each coordinate of this vector represents an agent's utility for the solution. Due to the possible conflicts, it is unlikely that one feasible solution is optimal for all agents. Then, a natural aim is to find solutions that maximize the satisfaction of the least satisfied agent, where the satisfaction of an agent is defined as his relative utility, i.e., the ratio between his utility for the given solution and his maximum possible utility. This criterion captures a classical notion of fairness since it focuses on the agent with lowest relative utility. We study worst-case bounds on this ratio: for which ratio a feasible solution is guaranteed to exist, i.e., to what extend can we find a solution that satisfies all agents? How can we build these solutions in polynomial time? For several optimization problems, we give polynomial-time deterministic algorithms which (almost always) achieve the best possible ratio.