Algorithms and Dynamic Data Structures for Basic Graph Optimization Problems.
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![Figure 5.2: An illustration of the query (x 1 y u)[z, 2 j ], where we are given j, x 1 , x 2 , and y, but not z.](https://thumb-us.123doks.com/thumbv2/123dok_us/931926.2620792/91.918.339.640.119.204/figure-illustration-query-x-y-u-z-given.webp)
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![Figure 5.7: The a and b represent vertices on the path xy [x 0 , y 0 ], and the black line denotes the path ay and xb](https://thumb-us.123doks.com/thumbv2/123dok_us/931926.2620792/100.918.297.687.397.490/figure-represent-vertices-path-black-line-denotes-path.webp)
![Figure 5.9: When u is before u 0 and c l v u goes through u 0 in Case II.2, as shown in the dash line of (A), we can see c l v u is shorter than the subpath from c l to v in xy [x 0 , y 0 ]](https://thumb-us.123doks.com/thumbv2/123dok_us/931926.2620792/106.918.294.686.110.413/figure-goes-case-shown-dash-line-shorter-subpath.webp)
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