Research output per year
Research output per year
Steven Chaplick, Fedor V. Fomin, Petr A. Golovach, Dusan Knop^{*}, Peter Zeman
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
We obtain new polynomial kernels and compression algorithms for PATH COVER and CYCLE COVER, the well-known generalizations of the classical HAMILTONIAN PATH and HAMILTONIAN CYCLE problems. Our choice of parameterization is strongly influenced by the work of Biro, Hujter, and Tuza, who in 1992 introduced H-graphs, intersection graphs of connected subgraphs of a subdivision of a fixed (multi) graph H. In this work, we turn to proper H-graphs, where the containment relationship between the representations of the vertices is forbidden. As the treewidth of a graph measures how similar the graph is to a tree, the size of graph H is the parameter measuring the closeness of the graph to a proper interval graph. We prove the following results.
- PATH COVER admits a kernel of size O(parallel to H parallel to(8)), that is, we design an algorithm that for an n-vertex graph G and an integer k >= 1, in time polynomial in n and parallel to H parallel to, outputs a graph G' of size O(parallel to H parallel to(8)) and k'
- CYCLE COVER admits a compression of size O(parallel to H parallel to(10)) into another problem, called PRIZE COLLECTING CYCLE COVER, that is, we design an algorithm that, in time polynomial in n and parallel to H parallel to, outputs an equivalent instance of PRIZE COLLECTING CYCLE COVER of size O(parallel to H parallel to(10)).
In all our algorithms we assume that a proper H-decomposition is given as a part of the input.
Original language | English |
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Title of host publication | Algorithms and Data Structures. WADS 2019 |
Editors | Z. Friggstad, JR Sack, M. Salavatipour |
Publisher | Springer, Cham |
Pages | 296-310 |
Number of pages | 15 |
ISBN (Electronic) | 978-3-030-24766-9 |
ISBN (Print) | 978-3-030-24765-2 |
DOIs | |
Publication status | Published - 2019 |
Externally published | Yes |
Series | Lecture Notes in Computer Science |
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Volume | 11646 |
ISSN | 0302-9743 |
Research output: Contribution to journal › Article › Academic › peer-review