Memory Mangement in the PoSSo Solver

Abstract

A uniform general purpose garbage collector may not always provide optimal performance. Sometimes an algorithm exhibits a predictable pattern of memory usage that could be exploited, delaying as much as possible the intervention of the collector. This requires a collector whose strategy can be customized to the need of an algorithm. We present a dynamic memory management framework which allows such customization, while preserving the convenience of automatic collection in the normal case. The Customizable Memory Management (CMM) organizes memory in multiple heaps, each one encapsulating a particular storage discipline. The default heap for collectable objects uses the technique of mostly copying garbage collection, providing good performance and memory compaction. Customization of the collector is achieved through object orientation by specialising the collector methods for each heap class. We describe how the CMM has been exploited in the implementation of the Buchberger algorithm, by using a special heap for temporary objects created during polynomial reduction. The solution drastically reduces the overall cost of memory allocation in the algorithm.

Monomial representations for Gröbner bases computations

“…a = 0 + 12 se + : : : + m , 1 2 m , 1se ; b = 0 + 12 se + : : : + m , 1 2 m , 1se b a = m,1 + m,22 se + : : : + 0 2 m , 1se ; b b = m,1 + m,22 se + : : : + 0 2 m , 1se ; b + a mod 2 sw = 0 + 12 se + : : : + m , 1 2 m , 1se ; b , a mod 2 sw = 0 + 12 se + : : : + m , 1 Firstly, stricter bounds on the values of the single exponents have to be assured i.e., the exponent v alues need to be less than 2 se,1 instead of 2 se .…”