Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
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STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
The vehicle routing problem
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Constrained TSP and Low-Power Computing
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
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SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Parameterized Approximability of TSP with Deadlines
Theory of Computing Systems
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SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Reoptimization of the Metric Deadline TSP
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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Theoretical Computer Science
Reoptimization of the metric deadline TSP
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SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Improved approximations for TSP with simple precedence constraints
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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PAKDD'12 Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
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Journal of Discrete Algorithms
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The aim of this paper is to investigate the approximability of some generalized versions of TSP which typically arise in practical applications. The most important generalization is TSP with time windows, where some vertices have to be visited after some specified opening time, but before some deadline. Our main results are as follows (assuming P ≠NP) 1. In contrast to the constant approximability of metric TSP, there is no polynomial-time o(|V|)-approximation algorithm for metric TSP with time windows 2. Metric TSP with as few as two time windows is not approximable within ratio 2–ε 3. There is no polynomial-time o(|V|)-approximation algorithm for TSP with a single time window and arbitrarily small violations of the triangle inequality 4. Metric TSP with a prescribed linear order on some vertices can be solved in polynomial time with a constant approximation guarantee, even if the triangle inequality is violated by a constant factor