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- W3212280309 abstract "Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural parameter called defect. Roughly speaking, it measures the efficiency of the moves used in the shortest untangling sequence of Reidemeister moves. We show that the II- moves in a shortest untangling sequence can be essentially performed greedily. Using that, we show that this problem belongs to W[P] when parameterized by the defect. We also show that this problem is W[P]-hard by a reduction from Minimum axiom set." @default.
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- W3212280309 date "2021-11-09" @default.
- W3212280309 modified "2023-09-27" @default.
- W3212280309 title "Parameterized complexity of untangling knots." @default.
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