Linking algorithm is an implementation of a system model - the set of rules and assumptions that include (but are not limited to) how to construct markets in time and space, how to handle multioutput processes, allocate credit for recyclable materials, etc.
There are currently a large number of system models used in life cycle assessment, and in environmental product declarations and footprinting.
Ecoinvent publishes three different versions, each with their own system model: Allocation Cut-Off by Classification; Substitution, Consequential, Long-Term and Allocation at the Point of Substitution (APOS).
However, for the general community it can be difficult to examine all the explicit and unspoken assumptions and choices that each system model includes. Intermediate steps of the linking are also not available.