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<p>Variable aggregation is a common method for creating computationally efficient linear programming model of exponentially large problem. This paper demonstrates that aggregation alone is not the only factor that improves the bound on the probability of the union of events. Yang et al. introduced a new, finer aggregation method that, intuitively, should result in tighter bounds. However, when we study this aggregation method on its own without the additional constraints proposed by Yang et al., its upper bound is identical to those proposed by (Prékopa, A and Gao, L in Discrete Appl. Math, 145(3):444–454, 2005) and (Kwerel, Seymour M in J. Am. Statistical Association 70(350):472–479, 1975). This finding suggests that additional valid inequalities, not just the aggregation method, should be carefully considered to tighten the bounds.</p>

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Variable aggregation and its effect on union bounding problem

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Joonhee Lee

摘要

Variable aggregation is a common method for creating computationally efficient linear programming model of exponentially large problem. This paper demonstrates that aggregation alone is not the only factor that improves the bound on the probability of the union of events. Yang et al. introduced a new, finer aggregation method that, intuitively, should result in tighter bounds. However, when we study this aggregation method on its own without the additional constraints proposed by Yang et al., its upper bound is identical to those proposed by (Prékopa, A and Gao, L in Discrete Appl. Math, 145(3):444–454, 2005) and (Kwerel, Seymour M in J. Am. Statistical Association 70(350):472–479, 1975). This finding suggests that additional valid inequalities, not just the aggregation method, should be carefully considered to tighten the bounds.