A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
An O(log*n) approximation algorithm for the asymmetric p-center problem
Journal of Algorithms
K-pair delay constrained minimum cost routing in undirected networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Multiobjective query optimization
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Bicriterion Single Machine Scheduling with Resource Dependent Processing Times
SIAM Journal on Optimization
An improved FPTAS for restricted shortest path
Information Processing Letters
Two O (log* k)-Approximation Algorithms for the Asymmetric k-Center Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
A FPTAS for Approximating the Unrelated Parallel Machines Scheduling Problem with Costs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Modeling of Transport Risk for Hazardous Materials
Operations Research
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
A PTAS for weight constrained Steiner trees in series-parallel graphs
Theoretical Computer Science
On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems
Theoretical Computer Science
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
Multicriteria Optimization
Efficiently computing succinct trade-off curves
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Multicriteria Global Minimum Cuts
Algorithmica
Approximately dominating representatives
Theoretical Computer Science
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Decision-making based on approximate and smoothed Pareto curves
Theoretical Computer Science
Bi-objective scheduling algorithms for optimizing makespan and reliability on heterogeneous systems
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the twenty-fourth annual symposium on Computational geometry
Theory of Computing Systems
Hitting sets when the VC-dimension is small
Information Processing Letters
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Approximation complexity of min-max (regret) versions of shortest path, spanning tree, and knapsack
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Complexity of the min-max (regret) versions of cut problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
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We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of biobjective problems (containing many important widely studied problems such as shortest paths, spanning tree, matching, and many others), we can compute in polynomial time an $\epsilon$-Pareto set that contains at most twice as many solutions as the minimum set. Furthermore we show that the factor of 2 is tight for these problems; i.e., it is NP-hard to do better. We present upper and lower bounds for three or more objectives, as well as for the dual problem of computing a specified number $k$ of solutions which provide a good approximation to the Pareto curve.