Network flows: theory, algorithms, and by Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin

By Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin

Bringing jointly the vintage and the modern features of the sector, this entire advent to community flows presents an integrative view of thought, algorithms, and purposes. It deals in-depth and self-contained remedies of shortest direction, greatest circulation, and minimal rate movement difficulties, together with an outline of latest and novel polynomial-time algorithms for those middle types. For pros operating with community flows, optimization, and community programming.

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Additional resources for Network flows: theory, algorithms, and applications(conservative)

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Bˆn−1 ) The received word (r0 , r1 , . . , rn−1 ) of length n at the output of the channel is decoded into the code word (bˆ0 , bˆ1 , . . , bˆn−1 ) of length n or the information word uˆ = (uˆ 0 , uˆ 1 , . . , uˆ k−1 ) of length k respectively. 2: Decoding of an (n, k) block code the decoded code word and decoded information word are given by bˆ = (bˆ0 , bˆ1 , . . , bˆn−1 ) and uˆ = (uˆ 0 , uˆ 1 , . . , uˆ k−1 ) respectively. 3. Without further algebraic properties of the (n, k) block code, the encoding can be carried out by a table look-up procedure.

BM } with M = q k q-nary code words of length n and minimum Hamming distance d by B(n, k, d). The minimum weight of the block code B is defined as min wt(b). 4. Weight Distribution The so-called weight distribution W (x) of an (n, k) block code B = {b1 , b2 , . . , bM } describes how many code words exist with a specific weight. Denoting the number of code words with weight i by wi = |{b ∈ B : wt(b) = i}| 2 In view of the linear block codes introduced in the following, we assume here that all possible information words u = (u0 , u1 , .

N For the purpose of error correction, the minimum distance decoding can be implemented by a majority decoding scheme. The decoder emits the information symbol uˆ 0 which appears most often in the received word. The weight distribution of a repetition code is simply given by W (x) = 1 + (q − 1) x n . Although this repetition code is characterised by a low code rate R, it is used in some communication standards owing to its simplicity. For example, in the short-range wireless communication system BluetoothTM a triple repetition code is used as part of the coding scheme of the packet header of a transmitted baseband packet (Bluetooth, 2004).

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