Improved Time Bounds for the Maximum Flow Problem
Improved Time Bounds for the Maximum Flow Problem
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In our eReader you can find the full English version of the book. Read Improved Time Bounds for the Maximum Flow Problem Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Improved Time Bounds for the Maximum Flow Problem
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This improvement is analogous to the bound Edmonds and Karp derived for their capacity-scaling transportation algorithm [4]. The argument is as follows. The algorithm maintains the invariant that the total excess on active vertices is at most nU* . Let phase j be the first phase such that A ^ {/*. Then the total iixrcase in due to phase changes up to and including the change from phase y - 1 to phase ; is at most n 2) 2n/2'~* = 0(n ). The total increase in due to later phase changes is O (n^ lo...gt/*). D Having described the scaling algorithm, we consider the question of whether its running time can be improved by reducing the number of nonsaturating pushes. The proof of Lemma 3. 1 bounds the number of nonsaturating pushes by estimating the total increase in the potential . Observe that there is an imbalance in this estimate: 0{n^ log* U) of the increase is due to phase changes, whereas only O(n^) is due to relabelings. Our plan is to improve this estimate by decreasing the contribution of the phase changes, at the cost of increasing the contribution of the relabelings.
What to read after Improved Time Bounds for the Maximum Flow Problem?
You can find similar books in the "Read Also" column, or choose other free books by Ravindra K Ahuja to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This improvement is analogous to the bound Edmonds and Karp derived for their capacity-scaling transportation algorithm [4]. The argument is as follows. The algorithm maintains the invariant that the total excess on active vertices is at most nU* . Let phase j be the first phase such that A ^ {/*. Then the total iixrcase in due to phase changes up to and including the change from phase y - 1 to phase ; is at most n 2) 2n/2'~* = 0(n ). The total increase in due to later phase changes is O (n^ lo...gt/*). D Having described the scaling algorithm, we consider the question of whether its running time can be improved by reducing the number of nonsaturating pushes. The proof of Lemma 3. 1 bounds the number of nonsaturating pushes by estimating the total increase in the potential . Observe that there is an imbalance in this estimate: 0{n^ log* U) of the increase is due to phase changes, whereas only O(n^) is due to relabelings. Our plan is to improve this estimate by decreasing the contribution of the phase changes, at the cost of increasing the contribution of the relabelings.
What to read after Improved Time Bounds for the Maximum Flow Problem?
You can find similar books in the "Read Also" column, or choose other free books by Ravindra K Ahuja to read onlineMoreLess
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