 
Summary: JOURNAL OF COMPUTER AND SYSTEM SCIENCES 37, 118129 (1988)
Meanders and Their Applications in
Lower Bounds Arguments
NOGA ALON*
Department of Mathematics, Sackler Faculty of Exact Sciences,
Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
and Bell Communications Research,
Morristown, New Jersey 07960
AND
WOLFGANG MAASS?
Department of Mathematics, Statistics, and Computer Science,
University of Illinois at Chicago,
Chicago, Illinois 60680
Received August 1, 1987
The notion of a meander is introduced and studied. Roughly speaking, a meander is a
sequence of integers (drawn from the set N= {I, 2, .... n}) that wanders back and forth
between various subsets of N a lot. Using Ramsey theoretic proof techniques we obtain sharp
lower bounds on the minimum length of meanders that achieve various levels of wandering.
We then apply these bounds to improve existing lower bounds on the length of constant width
branching programs for various symmetric functions. In particular, an Q (n log n) lower bound
