 Largest free memory block

The largest free memory block is the longest contiguous free region available within a specified allocation pool and address space. If free-block lengths are $s_1,\dots ,s_n$,For an empty free-block set, take $L_{\max }=0$. The largest block and total free capacity answer different questions: a contiguous request can fail even when $F_{\mathrm{free}}$ exceeds its size. This is the central layout issue in external memory fragmentation.^[ref]

For free lengths24,40 and16 bytes, $F_{\mathrm{free}}=80$ bytes and $L_{\max }=40$ bytes. A48-byte contiguous request fails in that fixed, nonmoving pool before metadata and memory alignment are considered. Coalescing an additional freed separator can increase $L_{\max }$ without requiring the allocator to obtain another region from the operating system.

Raw extent length can overstate payload capacity. For a block $[a,b)$, an illustrative header requirement $h$ and payload alignment $A$, choose aligned payload startThe aligned free-block capacity in this simple layout is $\max (b-p,0)$. A32-byte block starting at0 with an8-byte header and16-byte payload alignment has $p=16$ and only16 bytes of payload capacity. A24-byte payload therefore fails despite a raw32-byte extent. Actual allocator layouts can impose further constraints.

The quantity also depends on the allocation layer. A large virtually contiguous block need not occupy contiguous physical page frames. Comparing $L_{\max }$ values without specifying virtual versus physical space, allocator pool and usable payload convention can therefore mix distinct fragmentation problems.