Computation and Storage in the Cloud by Dong Yuan & Yun Yang & Jinjun Chen

Author:Dong Yuan & Yun Yang & Jinjun Chen
Language: eng
Format: epub
ISBN: 9780124078796
Publisher: Elsevier Inc.
Published: 2013-01-04T05:00:00+00:00

Lemma 5.1

In the PSS of a DDG_LS, for three MCSSs, if any two of them are adjacent to each other, then the three partition lines between every two MCSSs intersect at one point.

In the statement of Lemma 5.1, two MCSSs are adjacent, meaning that the corresponding areas of the two MCSSs in the PSS are adjacent. Figure 5.15 shows an example of Lemma 5.1. We assume that Si,i′, Sj,j′ and Sk,k′ be three MCSSs, where SCRi,i′<SCRj,j′<SCRk,k′ as shown in Figure 5.15A, and any two of Si,i′, Sj,j′, Sk,k′ are adjacent as shown in Figure 5.15B. Based on the positions of the first and last stored data sets, we calculate the three partition lines as follows:

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