The Sudoku completion problem with rectangular hole pattern is NP-complete

The sudoku completion problem is a special case of the latin square completion problem andboth problems are known to beNP-complete. However, in the case of a rectangular hole pattern – i.e. each column (or row) is either full or empty of symbols – it is known that the latin square completion problem can be solved in polynomial time. Conversely, we prove in this paper that the same rectangular hole pattern still leaves the sudoku completion problem NP-complete. © 2012 Elsevier B.V. All rights reserved.