  The genome rearrangement problem computes the minimum number of operations
that are required to sort all elements of a permutation. A block-interchange
operation exchanges two blocks of a permutation which are not necessarily
adjacent and in a prefix block-interchange, one block is always the prefix of
that permutation. In this paper, we focus on applying prefix block-interchanges
on binary and ternary strings. We present upper bounds to group and sort a
given binary/ternary string. We also provide upper bounds for a different
version of the block-interchange operation which we refer to as the `restricted
prefix block-interchange'. We observe that our obtained upper bound for
restricted prefix block-interchange operations on binary strings is better than
that of other genome rearrangement operations to group fully normalized binary
strings. Consequently, we provide a linear-time algorithm to solve the problem
of grouping binary normalized strings by restricted prefix block-interchanges.
We also provide a polynomial time algorithm to group normalized ternary strings
by prefix block-interchange operations. Finally, we provide a classification
for ternary strings based on the required number of prefix block-interchange
operations.
