We provide a $O(|\delta| \log |Q|)$-time algorithm computing a co-lex total preorder when the input is a Wheeler NFA, and an algorithm with the same time complexity computing the smallest-width co-lex partial order of any DFA.

We show that, for acyclic graphs, considering the width of the graph yields advances in our understanding of its approximability. For the non-negative version, we show that a popular heuristic is a $O( \log |X|)$-approximation on graphs satisfying two properties related to the width (satisfied by e.g., series-parallel graphs), and strengthen its worst-case approximation ratio for sparse graphs. For the negative version, we give a $(\lceil \log \Vert X \Vert \rceil +1)$-approximation using a power-of-two approach, combined with parity fixing arguments and a decomposition of unitary flows ($\Vert X \Vert \leq 1$) into at most width paths.

computer science by Yo! Baba from the Noun Project

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