The equal sum partition problem has infinite unsolvable families for n/k ratios in (2, 24/7) despite the slack condition, while linear partitions with strong slack are solvable via randomized rounding of the fractional relaxation with exponentially small failure probability.
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On the Equal Sum Partition Problem
The equal sum partition problem has infinite unsolvable families for n/k ratios in (2, 24/7) despite the slack condition, while linear partitions with strong slack are solvable via randomized rounding of the fractional relaxation with exponentially small failure probability.