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We explore this direction for the classic\n                    <jats:sc>Feedback Vertex Set<\/jats:sc>\n                    problem on undirected graphs, leading to a new type of graph structure called\n                    <jats:italic>antler decomposition<\/jats:italic>\n                    , which identifies vertices that belong to an optimal solution. It is an analogue of the celebrated\n                    <jats:italic>crown decomposition<\/jats:italic>\n                    which has been used for\n                    <jats:sc>Vertex Cover<\/jats:sc>\n                    . We develop the graph structure theory around such decompositions and develop fixed-parameter tractable algorithms to find them, parameterized by the number of vertices for which they witness presence in an optimal solution. This reduces the search space of fixed-parameter tractable algorithms parameterized by the solution size that solve\n                    <jats:sc>Feedback Vertex Set<\/jats:sc>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/978-3-030-86838-3_1","type":"book-chapter","created":{"date-parts":[[2021,9,19]],"date-time":"2021-09-19T18:05:30Z","timestamp":1632074730000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Preprocessing to Reduce the Search Space: Antler Structures for Feedback Vertex Set"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2767-8140","authenticated-orcid":false,"given":"Huib","family":"Donkers","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8204-1268","authenticated-orcid":false,"given":"Bart M. 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