This has been covered elsewhere for earlier versions but the solution doesn't seem to fix this issue. I'm getting the following error when I update from Playa 4.4.5 to 4.5.1, on EE 2.7.2:
A Database Error Occurred
enter preformatted text here`Error Number: 1060
Duplicate column name 'parent_element_id'
ALTER TABLE exp_playa_relationships ADD parent_element_id VARCHAR(255) NULL AFTER parent_var_id
Filename: third_party/playa/ft.playa.php
Line Number: 488