A computer architecture for collapsing dependency graphs for colliding store and load instructions. Many-to-one mappings are provided between logical registers and physical registers, so that more than one logical register may map to the same physical register. For a load instruction that is predicted to collide with an earlier in-flight store instruction, the destination logical register of the load instruction is mapped to the same physical register to which the source logical register of the earlier in-flight store instruction is mapped. A many-to-one mapping may be realized by associating a counter with each physical register, so that the value of a counter indicates whether its associated physical counter is free.