The traveling salesman problem with distances one and two
Mathematics of Operations Research
On linear time minor tests with depth-first search
Journal of Algorithms
Journal of the ACM (JACM)
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
A tight analysis of the greedy algorithm for set cover
Journal of Algorithms
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Approximation Hardness of TSP with Bounded Metrics
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Finding a Path of Superlogarithmic Length
SIAM Journal on Computing
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating the maximum clique minor and some subgraph homeomorphism problems
Theoretical Computer Science
On finding spanning trees with few leaves
Information Processing Letters
Note: On the complexity of approximating the Hadwiger number
Theoretical Computer Science
Hadwiger's conjecture is decidable
Proceedings of the forty-first annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Structural properties of hard metric TSP inputs
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Inapproximability of maximal strip recovery
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
Improved approximations for TSP with simple precedence constraints
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an approximation of this type that is better than known inapproximability lower bounds for either of the two individual optimization problems forming the pair. In particular, we find either a (1 + ε)-approximation to (1, 2)-TSP or a 1/ε-approximation to maximum independent set, from a given graph, in linear time. We show a similar paired approximation result for finding either a coloring or a long path. However, no such tradeoff exists in some other cases: for set cover and hitting set problems defined from a single set family, and for clique and independent set problems on the same graph, it is not possible to find an approximation when both problems are combined that is better than the best approximation for either problem on its own.