"3" . . . . . . "21"^^ . "RIV/00216224:14330/08:00024875!RIV10-GA0-14330___" . . "RIV/00216224:14330/08:00024875" . . . . . "2"^^ . . . . "Finding branch-decomposition and rank-decomposition" . . "Finding branch-decomposition and rank-decomposition" . "1"^^ . . . "P(GA201/08/0308), S, Z(MSM0021622419)" . "Finding branch-decomposition and rank-decomposition"@en . "Finding branch-decomposition and rank-decomposition"@en . "14330" . "Hlin\u011Bn\u00FD, Petr" . "graph; matroid; rank-width; clique-width; branch-width; fixed parameter tractable algorithm"@en . "38" . "0097-5397" . . "Oum, Sang-il" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "[C3041CC3A400]" . . "We present a new algorithm that can output the rank-decomposition of width at most $k$ of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most $k$ if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run in time $O(n^3)$ for each fixed value of $k$ where $n$ is the number of vertices / elements of the input." . . "We present a new algorithm that can output the rank-decomposition of width at most $k$ of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most $k$ if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run in time $O(n^3)$ for each fixed value of $k$ where $n$ is the number of vertices / elements of the input."@en . . "368050" . "SIAM Journal on Computing" . . "000258895100012" .