Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
S. Hart , Tel Aviv University
Davenport-Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport-Schinzel sequence composed of n symbols is (n /spl alpha/(n)), where /spl alpha/ (n) is the functional inverse of Ackermann's function, and is thus very slow growing. This is achieved by establishing an equivalence between such sequences and generalized path compression schemes on rooted trees, and then by analyzing these schemes.
S. Hart, M. Sharir, "Nonlinearity Of Davenport-Schinzel Sequences And Of A Generalized Path Compression Scheme", FOCS, 1984, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 1984, pp. 313-319, doi:10.1109/SFCS.1984.715930