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- W3037864488 abstract "We analyze a reduction rule for computing kernels for the hitting set problem: In a hypergraph, the link of a set c of vertices consists of all edges that are supersets of c. We call such a set critical if its link has certain easy-to-check size properties. The rule states that the link of a critical c can be replaced by c. It is known that a simple linear-time algorithm for computing hitting set kernels (number of edges) at most k^d (k is the hitting set size, d is the maximum edge size) can be derived from this rule. We parallelize this algorithm and obtain the first AC⁰ kernel algorithm that outputs polynomial-size kernels. Previously, such algorithms were not even known for artificial problems. An interesting application of our methods lies in traditional, non-parameterized approximation theory: Our results imply that uniform AC⁰-circuits can compute a hitting set whose size is polynomial in the size of an optimal hitting set." @default.
- W3037864488 created "2020-07-02" @default.
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- W3037864488 date "2020-01-01" @default.
- W3037864488 modified "2023-10-09" @default.
- W3037864488 title "Kernelizing the Hitting Set Problem in Linear Sequential and Constant Parallel Time" @default.
- W3037864488 doi "https://doi.org/10.4230/lipics.swat.2020.9" @default.
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