Abstract:
We give a number of new lower bounds in the cell probe model with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations.
We study the signed prefix sum problem: given a string of length n of
zeroes and signed ones, compute the sum of its ith prefix during updates.
We show a lower bound of 
time per operations,
even if the prefix sums are bounded by 
during all
updates. We also show that if the update time is bounded by the product of
the worst-case update time and the answer to the query, then the update time
must be 
.
These results
allow us to prove lower bounds for a variety of seemingly unrelated dynamic
problems. We give a lower bound for the dynamic planar point location in
monotone subdivisions of per operation. We give a
lower bound for the dynamic transitive closure problem on upward planar
graphs with one source and one sink of 
per
operation. We give a lower bound of for the dynamic membership problem of any Dyck language with two or
more letters. This implies the same lower bound for the dynamic word problem
for the free group with k generators. We also give lower bounds for the
dynamic prefix majority and prefix equality problems.
Available as PostScript, PDF, DVI.