A Theorem on Partitioning a Sorted List of Numbers with an Application to VLSI Floorplanning
نویسنده
چکیده
Given a finite nonincreasing sequence of positive numbers a1 ≥ a2 ≥ . . . ≥ an > 0, select index j such that the absolute value of the difference between the sum of the first j terms and the sum of the remaining n− j terms is minimized. An analysis shows that the ratio of these two sums is then bounded between γ ≡ max{2, β} and 1/γ, where β is the maximum pairwise ratio of successive terms in the original sequence, β ≡ maxi ai+1/ai. An application of this result to zero-dead-space VLSI floorplanning is described.
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