Completeness in approximation classes
Information and Computation
Computational Complexity
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
P-Complete Approximation Problems
Journal of the ACM (JACM)
Structure in Approximation Classes
SIAM Journal on Computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theoretical Computer Science
Survey: A survey on the structure of approximation classes
Computer Science Review
Hi-index | 5.23 |
We present a reduction that allows us to establish completeness results for several approximation classes mainly beyond APX. Using it, we extend one of the basic results of S. Khanna, R. Motwani, M. Sudan, and U. Vazirani (On syntactic versus computational views of approximability, SIAM J. Comput. 28 (1998) 164-191) by proving sufficient conditions for getting complete problems for the whole Log-APX, the class of problems approximable within ratios that are logarithms of the size of the instance, as well as for any approximability class beyond APX. We also introduce a new approximability class, called Poly-APX(Δ), dealing with graph-problems approximable with ratios functions of the maximum degree Δ of the input-graph. For this class also, using the proposed reduction, we establish complete problems.