2 research outputs found
The Complexity of Finding Tangles
We study the following combinatorial problem. Given a set of y-monotone
curves, which we call wires, a tangle determines the order of the wires on a
number of horizontal layers such that the orders of the wires on any two
consecutive layers differ only in swaps of neighboring wires. Given a multiset
of swaps (that is, unordered pairs of wires) and an initial order of the
wires, a tangle realizes if each pair of wires changes its order exactly as
many times as specified by . Finding a tangle that realizes a given multiset
of swaps and uses the least number of layers is known to be NP-hard. We show
that it is even NP-hard to decide if a realizing tangle exists