Flow network

Given the flow network below with labels (capacity, flow), let (S) be the source and (T) be the sink.

Build the residual network from the given (capacity, flow) labels. Consider this as the initial residual network and evaluate the statements:

I. In the initial residual network, the path S -> B -> E -> F -> T is an augmenting path with bottleneck 3.
II. In the initial residual network, there is no augmenting path. The current flow is already maximum.
III. Starting from the initial residual network, after performing any best single-path augmentation (i.e., any augmenting path with maximum bottleneck possible), there still exists an augmenting path with bottleneck 1.
IV. The value of the current flow in the given network (before any new augmentation) is 13.

Choose the correct alternative:

A) I and III only
B) I and IV only
C) II and III only
D) I, III, and IV
E) None of the above

Original idea by: Thiago Soares Laitz

Comentários

  1. Joao Meidanis28 de setembro de 2025 às 17:19

    Boa questão, mas não gostei das capacidades virem antes dos fluxos. Em geral, a literatura vai ao contrário disso. E a resposta acaba sendo (E), certo? Pois III é falsa, usando SBET.

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