'route-dependent' is a compound of English 'route' and 'dependent'. 'route' originates from Old French 'route' (meaning 'way, road'), and 'dependent' ultimately comes from Latin 'dependēns' (from 'dependēre'), where 'de-' meant 'down/from' and 'pendere' meant 'to hang'.

'route' changed from Old French 'route' and Middle English 'route' and became modern English 'route'; 'dependent' derived from Latin 'dependere' through Old French into Middle English and became modern English 'dependent'. The compound 'route-dependent' is a modern English formation used especially in technical and descriptive contexts (20th century onward).

Individually, 'route' originally meant 'way/road' and 'dependent' meant 'hanging/down from' (figuratively 'relying on'); combined in modern usage they mean 'relying on or varying with the route' (no substantial shift from component meanings, but specialized as a compound adjective).