Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Multiobjective query optimization
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Bicriterion Single Machine Scheduling with Resource Dependent Processing Times
SIAM Journal on Optimization
An improved FPTAS for restricted shortest path
Information Processing Letters
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
Asymmetric k-center is log* n-hard to approximate
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficient approximation of optimization queries under parametric aggregation constraints
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Approximately dominating representatives
ICDT'05 Proceedings of the 10th international conference on Database Theory
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Decision-making based on approximate and smoothed Pareto curves
Theoretical Computer Science
Succinct approximate convex pareto curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
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
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
How good is the Chord algorithm?
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Supervised design space exploration by compositional approximation of Pareto sets
Proceedings of the 48th Design Automation Conference
Decision making based on approximate and smoothed pareto curves
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximately dominating representatives
ICDT'05 Proceedings of the 10th international conference on Database Theory
Efficiency-revenue trade-offs in auctions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Approximation quality of the hypervolume indicator
Artificial Intelligence
A fast approximation-guided evolutionary multi-objective algorithm
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Trade-off (aka Pareto) curves are typically used to represent the trade-off among different objectives in multiobjective optimization problems. Although trade-off curves are exponentially large for typical combinatorial optimization problems (and infinite for continuous problems), it was observed in Papadimitriou and Yannakakis [On the approximability of trade-offs and optimal access of web sources, in: Proc. 41st IEEE Symp. on Foundations of Computer Science, 2000] that there exist polynomial size ε approximations for any ε 0, and that under certain general conditions, such approximate ε-Pareto curves can be constructed in polynomial time. In this paper we seek general-purpose algorithms for the efficient approximation of trade-off curves using as few points as possible. In the case of two objectives, we present a general algorithm that efficiently computes an ε-Pareto curve that uses at most 3 times the number of points of the smallest such curve; we show that no algorithm can be better than 3-competitive in this setting. If we relax ε to any ε' ε, then we can efficiently construct an ε'-curve that uses no more points than the smallest ε-curve. With three objectives we show that no algorithm can be c-competitive for any constant c unless it is allowed to use a larger ε value. We present an algorithm that is 4-competitive for any ε' (1 + ε)2 - 1. We explore the problem in high dimensions and give hardness proofs showing that (unless P=NP) no constant approximation factor can be achieved efficiently even if we relax ε by an arbitrary constant.