Sharing results is more efficient than having each child potentially waste a lot of time generating redundant data. On the other hand, the information may not be important enough, or have sufficient long-term value, to merit being stored on disk. In this scenario, Inter-Process Communication (IPC) is a useful tool to have around.
This topic is non-specific to mod_perl and big enough to fill several books on its own. A non-exhaustive list of the modules to look at includes IPC::SysV, IPC::Shareable, IPC::Semaphore, IPC::ShareLite, Apache::Session, and Cache::Cache. And of course make sure to read the perlipc manpage. Also refer to the books listed in Section 17.3 at the end of this chapter.