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Daniel A. Skachkov

Publications and source records attributed to Daniel A. Skachkov.

2 recordsLinked to original sources
arXiv2023

A quadratic-order problem kernel for the traveling salesman problem parameterized by the vertex cover number

The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with $τ^2+τ$ vertices for GTSP, where $τ$ is the vertex cover number of the input graph. Any $α$-approximate solution for the problem kernel also gives an $α$-approximate solution for the original instance, for any $α\geq1$.

cs.DS↗
arXiv2023

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

The NP-hard Multiple Hitting Set problem is 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 feasability of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Date) architectures.

cs.DS↗