Prefix Sharing Is a Sorting Problem

תקציר מקורי באנגליתarXiv:2609.13692v1 Announce Type: cross Abstract: LLM serving reuses KV cache by exact prefix match, so when a prompt is assembled from a set of reusable pieces -- retrieved passages, tool definitions, few-shot exemplars -- the order chosen for those pieces determines how much computation can be shared. Every deployed system fixes that order by a single global convention. We prove this is optimal only when requests contain at most two pieces, and asymptotically wrong in general. Our main result is a structure theorem: the minimum prefix-trie cost equals min_H sum_x w(x) t_x(H) over binary hierarchies H on the requests, where t_x(H) is the canonical decomposition size of the set of requests needing chunk x. Choosing chunk orders is therefore equivalent to choosing one hierarchy over request