Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximation algorithms
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Parameterized approximation of dominating set problems
Information Processing Letters
Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
An approximation algorithm for the maximum leaf spanning arborescence problem
ACM Transactions on Algorithms (TALG)
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Kernelization through tidying: a case study based on s-plex cluster vertex deletion
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized approximation algorithms for hitting set
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Parameterized approximability of the disjoint cycle problem
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Kernelization algorithms for d-hitting set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parameterized Complexity
Parameterized Complexity and Approximation Algorithms
The Computer Journal
The Computer Journal Special Issue on Parameterized Complexity
The Computer Journal
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
A novel parameterised approximation algorithm for minimum vertex cover
Theoretical Computer Science
Hi-index | 0.00 |
We motivate and describe a new parameterized approximation paradigm which studies the interaction between performance ratio and running time for any parametrization of a given optimization problem. As a key tool, we introduce the concept of α-shrinking transformation, for α≥1. Applying such transformation to a parameterized problem instance decreases the parameter value, while preserving approximation ratio of α (or α-fidelity). For example, it is well-known that Vertex Cover cannot be approximated within any constant factor better than 2 [24] (under usual assumptions). Our parameterized α-approximation algorithm for k-Vertex Cover, parameterized by the solution size, has a running time of 1.273(2−α)k, where the running time of the best FPT algorithm is 1.273k [10]. Our algorithms define a continuous tradeoff between running times and approximation ratios, allowing practitioners to appropriately allocate computational resources. Moving even beyond the performance ratio, we call for a new type of approximative kernelization race. Our α-shrinking transformations can be used to obtain kernels which are smaller than the best known for a given problem. For the Vertex Cover problem we obtain a kernel size of 2(2−α)k. The smaller "α-fidelity" kernels allow us to solve exactly problem instances more efficiently, while obtaining an approximate solution for the original instance. We show that such transformations exist for several fundamental problems, including Vertex Cover, d-Hitting Set, Connected Vertex Cover and Steiner Tree. We note that most of our algorithms are easy to implement and are therefore practical in use.