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 -