Virtual Labs

In a flow network, what does the 'Capacity Constraint' imply for any edge (u, v)?

a: The flow must be equal to the capacity Explanation

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b: The flow must be greater than or equal to the capacity Explanation

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c: The flow cannot exceed the capacity of the edge Explanation

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d: The flow must be a prime number Explanation

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What is the 'Flow Conservation' rule for an intermediate node?

a: Total incoming flow must equal total outgoing flow Explanation

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b: Incoming flow must be greater than outgoing flow Explanation

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c: All nodes must have at least one unit of flow Explanation

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d: Nodes store flow like a reservoir Explanation

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If the total flow leaving the source is 15 units, what must be the total flow entering the sink?

a: It depends on the number of edges Explanation

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b: Exactly 15 units Explanation

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c: Less than 15 units due to friction Explanation

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d: At least 30 units Explanation

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Which of the following best describes a 'Source' node in a flow network?

a: A node where all edges are incoming Explanation

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b: A node with no incoming edges (net producer of flow) Explanation

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c: A node that cannot be connected to the sink Explanation

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d: The node with the highest index Explanation

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In a directed graph used for flow networks, an edge (u, v) means:

a: Flow can travel from u to v and v to u Explanation

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b: Flow can only travel from u to v Explanation

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c: u and v are the same node Explanation

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d: The edge has no capacity Explanation

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What happens if a node has more flow entering than leaving?

a: It violates flow conservation (unless it is the sink) Explanation

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b: The extra flow is deleted Explanation

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c: The algorithm runs faster Explanation

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d: The node changes color Explanation

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Can an edge have a negative capacity?

a: Yes, for reverse flow Explanation

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b: No, capacity must be non-negative Explanation

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c: Only if the graph has cycles Explanation

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d: Only in the residual graph Explanation

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If an edge has a capacity of 10 and a current flow of 4, how much more flow can it handle?

a: 10 units Explanation

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b: 4 units Explanation

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c: 6 units Explanation

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d: 14 units Explanation

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The Maximum Flow problem is a classic problem in which field?

a: Sorting algorithms Explanation

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b: Network Optimization Explanation

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c: Database normalization Explanation

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d: Operating system scheduling Explanation

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True or False: A flow network can have multiple sources and sinks.

a: True (they can be converted to a single source/sink model) Explanation

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b: False (only one of each is allowed) Explanation

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Ford - Fulkerson Algorithm