Greedy Defining Sets in Latin Squares

A Greedy Defining Set is a set of entries in a Latin square with the property that when the square is systematically filled in with a greedy algorithm, the greedy algorithm succeeds. Let g(n) be the smallest Greedy Defining Set for any Latin square of order n. We give theorems on the upper bounds of g(n) and a table listing upper bounds of g(n) for small values of n. For a circulant Latin square, we find that the size of the smallest Greedy Defining Set is (n(n-1) 6 .

• Type: Journal
• Year: 2008
• Where: ARSCOM
• Authors: Manouchehr Zaker
• Keywords: ARSCOM 2008, Greedy, Greedy Algorithm, Greedy Defining