Efficient Packing of Unit Squares in a Square

Let s(N) denote the edge length of the smallest square in which one can pack N unit squares. A duality method is introduced to prove that s(6) = s(7) = 3. Let nr be the smallest integer n such that s(n2 + 1) n + 1/r. We use an explicit construction to show that nr 27r3 /2+O(r2 ), and also that n2 43.

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Michael J. Kearney, Peter Shiu
• Keywords: COMBINATORICS 2002, Duality Method, Edge Length, Smallest Square