  We consider computing the longest palindrome in a text of length $n$ in the
streaming model, where the characters arrive one-by-one, and we do not have
random access to the input. While computing the answer exactly using sublinear
memory is not possible in such a setting, one can still hope for a good
approximation guarantee.
  We focus on the two most natural variants, where we aim for either additive
or multiplicative approximation of the length of the longest palindrome. We
first show that there is no point in considering Las Vegas algorithms in such a
setting, as they cannot achieve sublinear space complexity. For Monte Carlo
algorithms, we provide a lowerbound of $\Omega(\frac{n}{E})$ bits for
approximating the answer with additive error $E$, and $\Omega(\frac{\log
n}{\log(1+\varepsilon)})$ bits for approximating the answer with multiplicative
error $(1+\varepsilon)$ for the binary alphabet. Then, we construct a generic
Monte Carlo algorithm, which by choosing the parameters appropriately achieves
space complexity matching up to a logarithmic factor for both variants. This
substantially improves the previous results by Berenbrink et al. (STACS 2014)
and essentially settles the space complexity.
