Symmetry Breaking During Search (SBDS) adds conditional symmetry breaking constraints (which are nogoods) dynamically upon backtracking to avoid exploring symmetrically equivalents of visited search space. The constraint store is proliferated with numerous such individual nogoods which are weak in constraint propagation. We introduce the notion of increasing nogoods, and give a global constraint of a sequence of increasing nogoods, incNGs. Reasoning globally with increasing nogoods allows extra prunings. We prove formally that nogoods accumulated for a given symmetry at a search node in SBDS and its variants are increasing. Thus we can maintain only one increasing-nogoods global constraint for each given symmetry during search. We give a polynomial time filtering algorithm for incNGs and also an efficient incremental counterpart which is stronger than GAC on each individual nogood. We demonstrate with extensive experimentation how incNGs can increase propagation and speed up search against SBDS, its variants, SBDD and carefully tailored static methods.
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