User talk:Francisbach

Time-expanded graphs as a k-shortest-path problem
See second paragraph of my 2015 survey http://bulletin.eatcs.org/index.php/beatcs/article/download/322/304 for a brief explanation of the time-expanded graph and its use in converting k-best state sequence problems in weighted automata into k-best path problems in graphs. Searching Google scholar for "k-shortest" "time-expanded" finds hundreds of references. This approach requires that the automaton be deterministic (otherwise you get multiple sequences representing the same string); the reference you keep trying to add appears to be following exactly this approach after converting a nondeterministic automaton to a deterministic one. —David Eppstein (talk) 18:32, 20 June 2022 (UTC)


 * For deterministic automata the problem is trivial. The reference mentioned is not converting the input into a deterministic one, rather it is doing this on-the-fly, which is critical. Also, the input is a weighted automaton. The URL for the survey you indicated does not seem to be authored by you. Also, I searched for "expanded" or "time-expanded" and found no instance of these terms in that document. Francisbach (talk) 11:57, 21 June 2022 (UTC)
 * The first page gives the column editor; my name is below the title of the individual column on the second page. Also, my pointer to "second paragraph" was inaccurate; sorry. I meant the second paragraph of the k-shortest-paths section, section 3. Here, let me quote it for you:
 * Many problems of hypothesis generation in natural language processing and speech recognition can also be formulated as k-best optimization problems [20, 35, 38, 45 – 48, 54, 68, 99, 119, 120, 161, 162, 174]. The Viterbi decoding technique for Markov models, commonly used to model these problems, can also be formulated as a search for a path in an associated graph, with a vertex for each pair of a time step and a Markov state, and the k-best beam search technique used for multiple hypothesis generation in these problems can be interpreted as a special case of a k-shortest-path algorithm.
 * As for weights, there is no difficulty in applying weights to a time-expanded graph.
 * I am not entirely opposed to mentioning these applications in the article here. What I am opposed to is reporting it as if it is a new and different problem that only the reference you give was capable of solving, when in fact many researchers have applied standard k-shortest-path methods to solve it. It falsifies the scholarly record to do so. —David Eppstein (talk) 20:32, 21 June 2022 (UTC)