René van Bevern , Artem M. Kirilin , Daniel A. Skachkov , Pavel V. Smirnov , Oxana Yu. Tsidulko
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引用次数: 1
Abstract
The NP-hard Multiple Hitting Set problem is the problem of finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasibility of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Data) architectures.
期刊介绍：
The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions.
Research areas include traditional subjects such as:
• Theory of algorithms and computability
• Formal languages
• Automata theory
Contemporary subjects such as:
• Complexity theory
• Algorithmic Complexity
• Parallel & distributed computing
• Computer networks
• Neural networks
• Computational learning theory
• Database theory & practice
• Computer modeling of complex systems
• Security and Privacy.
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