Pruning with Modular Arithmetic in NP problems
نویسندگان
چکیده
Using modular arithmetic we introduce a simple bound which applies to a wide range of bin-packing like problems. This bound must hold if a problem is to be soluble. When it fails, search can therefore be pruned. We show the value of such pruning in a greedy backtracking algorithm for number partitioning problems. As the bound can be used when solving inexact as well as exact partitioning problems, we can prune search in optimisation as well as decision problems. We demonstrate that modular pruning reduces search in a state of the art optimisation procedure for number partitioning. Finally, we show that more sophisticated use of our bound can lead to further reductions in search.
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