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- W2949662246 abstract "We investigate the complexity of counting trees, forests and bases of matroids from a parameterized point of view. It turns out that the problems of computing the number of trees and forests with $k$ edges are $# W[1]$-hard when parameterized by $k$. Together with the recent algorithm for deterministic matrix truncation by Lokshtanov et al. (ICALP 2015), the hardness result for $k$-forests implies $# W[1]$-hardness of the problem of counting bases of a matroid when parameterized by rank or nullity, even if the matroid is restricted to be representable over a field of characteristic $2$. We complement this result by pointing out that the problem becomes fixed parameter tractable for matroids represented over a fixed finite field." @default.
- W2949662246 created "2019-06-27" @default.
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- W2949662246 date "2016-11-06" @default.
- W2949662246 modified "2023-09-27" @default.
- W2949662246 title "Parameterized counting of trees, forests and matroid bases" @default.
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