TY - GEN
T1 - Nonlinearity of davenport-schinzel sequences and of a generalized path compression scheme
AU - Hart, Sergiu
AU - Sharir, Micha
N1 - Publisher Copyright:
© 1984 IEEE.
PY - 1984
Y1 - 1984
N2 - 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 Θ(nα(n)),where α(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.
AB - 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 Θ(nα(n)),where α(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.
UR - http://www.scopus.com/inward/record.url?scp=85115253717&partnerID=8YFLogxK
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AN - SCOPUS:85115253717
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 313
EP - 319
BT - 25th Annual Symposium on Foundations of Computer Science, FOCS 1984
PB - IEEE Computer Society
T2 - 25th Annual Symposium on Foundations of Computer Science, FOCS 1984
Y2 - 24 October 1984 through 26 October 1984
ER -