Introduction to algorithms
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Introduction to the theory of complexity
Introduction to the theory of complexity
Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset 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
Performance Guarantees for the TSP with a Parameterized Triangle Inequality
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Nearly linear time approximation schemes for Euclidean TSP and other geometric problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
An explicit lower bound for TSP with distances one and two
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Algorithmics – is there hope for a unified theory?
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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The investigation of the possibility to efficiently compute approximations of hard optimization problems is one of the central and most fruitful areas of current algorithm and complexity theory. The aim of this paper is twofold. First, we introduce the notion of stability of approximation algorithms. This notion is shown to be of practical as well as of theoretical importance, especially for the real understanding of the applicability of approximation algorithms and for the determination of the border between easy instances and hard instances of optimization problems that do not admit any polynomial-time approximation. Secondly, we apply our concept to the study of the traveling salesman problem. We show how to modify the Christofides algorithm for Δ-TSP to obtain efficient approximation algorithms with constant approximation ratio for every instance of TSP that violates the triangle inequality by a multiplicative constant factor. This improves the result of Andreae and Bandelt [AB95].