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Oxana Yu. Tsidulko

Publications and source records attributed to Oxana Yu. Tsidulko.

5 recordsLinked to original sources
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.

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arXiv2021

The Hierarchical Chinese Postman Problem: the slightest disorder makes it hard, yet disconnectedness is manageable

The Hierarchical Chinese Postman Problem is finding a shortest traversal of all edges of a graph respecting precedence constraints given by a partial order on classes of edges. We show that the special case with connected classes is NP-hard even on orders decomposable into a chain and an incomparable class. For the case with linearly ordered (possibly disconnected) classes, we get 5/3-approximations and fixed-parameter algorithms by transferring results from the Rural Postman Problem.

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arXiv2020

On approximate data reduction for the Rural Postman Problem: Theory and experiments

Given an undirected graph with edge weights and a subset $R$ of its edges, the Rural Postman Problem (RPP) is to find a closed walk of minimum total weight containing all edges of $R$. We prove that RPP is WK[1]-complete parameterized by the number and cost $d$ of edges traversed additionally to the required ones. Thus, in particular, RPP instances cannot be polynomial-time compressed to instances of size polynomial in $d$ unless the polynomial-time hierarchy collapses. In contrast, denoting by $b\leq 2d$ the number of vertices incident to an odd number of edges of $R$ and by $c\leq d$ the number of connected components formed by the edges in $R$, we show how to reduce any RPP instance $I$ to an RPP instance $I'$ with $2b+O(c/\varepsilon)$ vertices in $O(n^3)$ time so that any $α$-approximate solution for $I'$ gives an $α(1+\varepsilon)$-approximate solution for $I$, for any $α\geq 1$ and $\varepsilon>0$. That is, we provide a polynomial-size approximate kernelization scheme (PSAKS). We experimentally evaluate it on wide-spread benchmark data sets as well as on two real snow plowing instances from Berlin. On instances with few connected components, the number of vertices and required edges is reduced to about $50\,\%$ at a $1\,\%$ solution quality loss. We also make first steps towards a PSAKS for the parameter $c$.

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arXiv2019

Parameterized algorithms and data reduction for the short secluded $s$-$t$-path problem

Given a graph $G=(V,E)$, two vertices $s,t\in V$, and two integers $k,\ell$, the Short Secluded Path problem is to find a simple $s$-$t$-path with at most $k$ vertices and $\ell$ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number, treewidth, feedback vertex number, and feedback edge number. In particular, we completely settle the question of the existence of problem kernels with size polynomial in these parameters and their combinations with $k$ and $\ell$. We also obtain a $2^{O(w)}\cdot \ell^2\cdot n$-time algorithm for graphs of treewidth $w$, which yields subexponential-time algorithms in several graph classes.

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