1. Asanka Herath Buddhika Kottahachchi
Polygon Packing
Asanka Herath Buddhika Kottahachchi

2. What?
Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing translation and rotation.

3. Why? It has important applications in the apparel industry
Pieces of material (polygons) need to be cut out of rolls of material to be assembled together as items of clothing
Considerable amounts of material is wasted as a result of not having an optimal layout for making the cuts
NP-hard problem.
Current approaches use heuristics with varying degrees of efficiency. Room for improvement.

4. Exploiting Parallel Processing
Process multiple candidate layouts simultaneously
Split resources to work on different approaches (…)
Fast heuristics to determine initial layouts
Slower relaxed placement methods to optimize initial layouts
Share information about current bounds and current optimal solution to reduce search space
Implementation: C and MPI

5. Anyone been here before?
Lots of existing literature
Referred to as
Nesting Problem
Marker Maker’s Problem
Many related problems (…)
Our method would follow work done by Benny Kaejr Nielsen and Allan Odgaard (Copenhagen, Denmark)
Commercial implementations (…)
At least one attempt at a parallel library for solving nesting problems

6. Related problems Can be categorized as Decision Problems
Decide whether a given set of shapes fit within a given shape
Knapsack Problem
Given a set of shapes and a region, find a placement of a subset of shapes that maximizes the utilization (area covered) of the region.
Bin packing problem.
Given a set of shapes and a set of regions, minimize the number of regions needed to place all shapes.
Strip packing problem.
Given a set of shapes and a width W, minimize the length of a rectangular region with width W such that all shapes are contained in the region.

7. Commercial Implementations

8. Questions?