We construct the Compressed Form array data structure (CF array) that supports the array interface while requiring$\mathcal{O}(n)$bits of space to store$n$integers from the range$\{1,2, \ldots$, poly$(n)\}$, under the smoothness condition that large integers are spaced proportionally to their values:$\forall i \neq j,\lfloor\log \min \{A[i], A[j]\}\rfloor \leq\lfloor\log\vert j-i\vert \rfloor$.

Palindromes are sequences of characters that read the same forward and backward and have fascinated computer scientists for centuries due to their unique properties. The exploration of palindromes sheds light on fundamental principles of pattern recognition, sequence alignment, and combinatorics, making them a crucial concept in theoretical and applied disciplines. We introduce a novel method for compressing palindromic structures in strings, establishing upper and lower bounds for their efficient representation. We do so by presenting a data structure capable of storing all maximal palindromes (Manacher array) in sublinear space with near-optimal access time. Our approach reduces the memory overhead of storing palindromes, offering a new avenue for optimizing compression algorithms in text processing applications.