## Containment Algorithms for Nonconvex Polygons with Applications to Layout (1995)

Citations: | 13 - 6 self |

### BibTeX

@TECHREPORT{Daniels95containmentalgorithms,

author = {Karen McIntosh Daniels},

title = {Containment Algorithms for Nonconvex Polygons with Applications to Layout},

institution = {},

year = {1995}

}

### OpenURL

### Abstract

Layout and packing are NP-hard geometric optimization problems of practical importance for which finding a globally optimal solution is intractable if P!=NP. Such problems appear in industries such as aerospace, ship building, apparel and shoe manufacturing, furniture production, and steel construction. At their core, layout and packing problems have the common geometric feasibility problem of containment: find a way of placing a set of items into a container. In this thesis, we focus on containment and its applications to layout and packing problems. We demonstrate that, although containment is NP-hard, it is fruitful to: 1) develop algorithms for containment, as opposed to heuristics, 2) design containment algorithms so that they say "no" almost as fast as they say "yes", 3) use geometric techniques, not just mathematical programming techniques, and 4) maximize the number of items for which the algorithms are practical. Our approach to containment is based on a new restrict/evaluate...