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

Abstract

The sudoku completion problem is a special case of the latin square completion problem and both problems are known to be NP-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.

The research was partially supported by the Spanish CICYT, MICINN and MINECO Projects MTM2010-21580-C02-01, ARINF (TIN2009-14704-C03-01), and TASSAT (TIN2010-20967-C04-03).