The Real life data is often dirty. To clean the data, efficient algorithms for detecting errors have to be in place. Errors in the data are typically detected as violations of constraints (Data quality rules), such as Functional Dependencies (FDs), Denial Constraints, and Conditional Functional Dependencies (CFDs). When the data is in a centralized database, it is known that two SQL queries be adequate to detect its violations of a set of CFDs. It is increasingly common to find data partitioned vertically or horizontally, and distributed across different sites. This is highlighted by the recent interests in SaaS of Cloud computing, Map Reduce, and columnar DBMS. In the distributed settings, however, it is much harder to detect errors in the data. To find violations in both settings, it is necessary to ship data from one site to another. It is NP-complete, to find violations of CFDs, with minimum data shipment, in a distributed relation that is partitioned either horizontally or vertically. So, the proposed work introduces such incremental algorithms for vertically and horizontally partitioned data, and show that the algorithms are absolute. Further, propose an optimization technique for the incremental algorithm over vertical partitions to reduce data shipment for error detection.