We study the problem of cutting a number of pieces of the same length from n rolls of different lengths so that the remaining part of each utilized roll is either sufficiently short or sufficiently long. A piece is sufficiently short, if it is shorter than a pre-specified threshold value d min, so that it can be thrown away as it cannot be used again for cutting future orders. And a piece is sufficiently long, if it is longer than a pre-specified threshold value d max (with d max¿>¿d min), so that it can reasonably be expected to be usable for cutting future orders of almost any length. We show that this problem, faced by a curtaining wholesaler, is solvable in O(n log n) time by analyzing a non-trivial class of allocation problems.
|Title of host publication||Algorithms - ESA 2005 : 13th annual european symposium, Palma de Mallorca, Spain, October 3-6, 2005 : proceedings|
|Editors||G.S. Brodal, S. Leonardi|
|Place of Publication||Berlin|
|Publication status||Published - 2005|
|Name||Lecture Notes in Computer Science|