Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Approximation algorithms
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Efficient approximation of min set cover by moderately exponential algorithms
Theoretical Computer Science
Exact algorithms for exact satisfiability and number of perfect matchings
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Improved approximation bounds for the minimum rainbow subgraph problem
Information Processing Letters
Collective spatial keyword querying
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Discrete Applied Mathematics
Capacitated domination faster than O(2n)
Information Processing Letters
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Fast algorithms for min independent dominating set
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Parameterized approximation algorithms for hitting set
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Approximating MAX SAT by moderately exponential and parameterized algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Algorithms for dominating clique problems
Theoretical Computer Science
Efficient algorithms for the max k-vertex cover problem
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Fast algorithms for min independent dominating set
Discrete Applied Mathematics
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
Lift-and-Project methods for set cover and knapsack
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
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The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order O(c^n), but with the constant c as small as possible. In this work we extend this line of research and we investigate whether the constant c can be made even smaller when one allows constant factor approximation. In fact, we describe a kind of approximation schemes-trade-offs between approximation factor and the time complexity. We use general transformations from exponential-time exact algorithms to approximations that are faster but still exponential-time. For example, we show that for any reduction rate r, one can transform any O^*(c^n)-time^1 algorithm for Set Cover into a (1+lnr)-approximation algorithm running in time O^*(c^n^/^r). We believe that results of that kind extend the applicability of exact algorithms for NP-hard problems.