Traditional comparison sorting algorithms like QuickSort rely heavily on conditional branching (if-else data divergence), recursive call stacks, and random memory access patterns, making them notoriously inefficient on SIMD/SIMT architectures like GPUs. Bitonic Merge Sort is an oblivious comparison network algorithm: the sequence of comparisons is identical regardless of the input data. Every thread executes the exact same mathematical instruction sequence at every stage, eliminating thread divergence. It maps perfectly to massive parallel GPU compute workgroups, sorting millions of elements across thousands of shader cores in sub-millisecond times.

In WebGPU compute shaders, global storage buffers (VRAM) have high latency (hundreds of clock cycles). However, each compute workgroup has access to fast on-chip shared memory declared with "var shared_data: array". For sort stages where the comparison span fits within the workgroup size (up to 256 or 512 elements), all compare-and-swap operations execute entirely in shared registers synchronized with workgroupBarrier(), avoiding round-trips to global VRAM and boosting memory throughput by over 10x.

A prefix sum takes an input array [a0, a1, a2, ...] and outputs running totals [0, a0, a0+a1, ...]. Guy Blelloch's workgroup-parallel algorithm computes this in O(N) operations and O(log N) depth using two phases: an Up-Sweep (reduce phase building a binary summation tree) and a Down-Sweep (clearing root to 0 and traversing down). In WebGPU, parallel scan is the foundational engine for stream compaction (filtering dead particles), building radix trees, dynamic allocation of variable-sized geometry, and spatial hash grid binning.

3D Gaussian Splatting requires rendering hundreds of thousands to millions of semi-transparent 3D ellipsoids. To produce mathematically correct alpha blending without visual tearing, all Gaussians must be sorted strictly back-to-front relative to the camera on every single frame at 60fps. Transferring millions of Gaussian depth keys back to the CPU to call JavaScript Array.sort() stalls the rendering pipeline and destroys framerates. Bitonic sort running directly on WebGPU compute shaders sorts 1,000,000 Gaussians in under 2 milliseconds directly in VRAM.