Yes, I would say the relationship is the opposite. Data structures imply a set of algorithms based on the promises of the data structure implementation. Algorithms themselves are free-floating things that can be reasoned about just as well in a C program as an instruction flow diagram as a Turing machine program. Take for instance an algorithm to divide two 32-bit integers. Or an algorithm that computes the max in a sequence (which is an abstraction) of numbers. There is no data structure, unless the argument is that a memory cell is itself a data structure.
