Design and implementation of a parallel solution to the cutting stock problem

The constrained 2-D cutting stock problem is an irregular problem with dynamic data structures, highly variable amounts of computation per task, and unpredictable amounts and patterns of communication. This paper describes the design and implementation of a parallel solution to this problem on a cluster of workstations and a distributed memory multicomputer. The key element of our parallel solution is the replication of an important data structure on all processors. By exploiting properties of the cutting stock problem which allow the use of relaxed consistency mechanisms, our approach is able to reduce the overheads for communication and synchronization in comparison to approaches that partition this data structure among processors. A token-based lazy release consistency protocol is used to ensure mutual exclusion and maintain consistency, and a randomized work-stealing protocol is employed to dynamically balance work among processors. Good speedups are reported for three benchmark problems executed on two distributed memory platforms: a cluster of workstations interconnected by a 10 Mbps Ethernet and an Intel Paragon. keywords: two-dimensional cutting stock, irregular problems, workstation clusters, dynamic load balancing, relaxed consistency, distributed memory multicomputer