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5. Compute the maximum flow and the minimum cut
capacity in the flow network below with source s and sink t
. Capacities of arcs are indicated next to the arc in
(parenthesis). When computing the flows you can indicate
the flow on an arc, for example on arc xy with the notation
10/15 meaning the flow is 10 and the capacity of arc xy is
15. Show the residual network at each iteration, the
augmenting path, and the current flow after the
augmentation. Finally show the minimum cut. Recall that
the Max-Flow Min-Cut theorem states that the value of the
maximum flow is equal to the minimum cut capacity in the
flow network. G=(V,A) V={s, A, B, C, D, E, F, t}
A={sA(500), sB(500), sC(500), AB(80), AD(200), BC(50),
BE(300), CF(250), DE(50), Dt(500), EA(100), EC(100),
EF(80), Et(100), Ft(500)}
Solution
Some directed networks have a transparent starting (called
the source) and a transparent finish (called the sink).
These networks also can be thought-about as having flow.
every node has associate quantity of flow (total weight of
all edges incoming at the vertex) associated an outflow
(total weight of all edges going away the vertex). Flow
networks have a large style of applications together with
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planning, dependableness frameworks, traffic flow, system
flows for systems together with electricity, water, gas and
information.
The maximum flow through the node is that the smallest
of those values. we are able to assume logically
concerning why this could be the case. Neither the sink
node nor the supply node have most values, solely the
intermediate ones.
Some directed networks have a transparent starting (called
the source) and a transparent finish (called the sink).
These networks also can be thought-about as having flow.
every node has associate quantity of flow (total weight of
all edges incoming at the vertex) associated an outflow
(total weight of all edges going away the vertex). Flow
networks have a large style of applications together with
planning, dependableness frameworks, traffic flow, system
flows for systems together with electricity, water, gas and
information.
The maximum flow through the node is that the smallest
of those values. we are able to assume logically
concerning why this could be the case. Neither the sink
node nor the supply node have most values, solely the
intermediate ones.
Some directed networks have a transparent starting (called
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the source) and a transparent finish (called the sink).
These networks also can be thought-about as having flow.
every node has associate quantity of flow (total weight of
all edges incoming at the vertex) associated an outflow
(total weight of all edges going away the vertex). Flow
networks have a large style of applications together with
planning, dependableness frameworks, traffic flow, system
flows for systems together with electricity, water, gas and
information.
The maximum flow through the node is that the smallest
of those values. we are able to assume logically
concerning why this could be the case. Neither the sink
node nor the supply node have most values, solely the
intermediate ones.
Some directed networks have a transparent starting (called
the source) and a transparent finish (called the sink).
These networks also can be thought-about as having flow.
every node has associate quantity of flow (total weight of
all edges incoming at the vertex) associated an outflow
(total weight of all edges going away the vertex). Flow
networks have a large style of applications together with
planning, dependableness frameworks, traffic flow, system
flows for systems together with electricity, water, gas and
information.
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The maximum flow through the node is that the smallest
of those values. we are able to assume logically
concerning why this could be the case. Neither the sink
node nor the supply node have most values, solely the
intermediate ones.
Some directed networks have a transparent starting (called
the source) and a transparent finish (called the sink).
These networks also can be thought-about as having flow.
every node has associate quantity of flow (total weight of
all edges incoming at the vertex) associated an outflow
(total weight of all edges going away the vertex). Flow
networks have a large style of applications together with
planning, dependableness frameworks, traffic flow, system
flows for systems together with electricity, water, gas and
information.
The maximum flow through the node is that the smallest
of those values. we are able to assume logically
concerning why this could be the case. Neither the sink
node nor the supply node have most values, solely the
intermediate ones.
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### Unformatted Attachment Preview

5. Compute the maximum flow and the minimum cut capacity in the flow network below with source s and sink t . Capacities of arcs are indicated next to the arc in (parenthesis). When computing the flows you can indicate the flow on an arc, for example on arc xy with the notation 10/15 meaning the flow is 10 and the capacity of arc xy is 15. Show the residual network at each iteration, the augmenting path, and the current flow after the augmentation. Finally show the minimum cut. Recall that the Max-Flow Min-Cut theorem states that the value of the maximum flow is equal to the minimum cut capacity in the flow network. G=(V,A) V={s, A, B, C, D, E, F, t} A={sA(500), sB(500), sC(500), AB(80), AD(200), BC(50), BE(300), CF(250), DE(50), Dt(500), EA(100 ), EC(100), EF(80), Et(100), Ft(500)} Solution Some directed networks have a transparent starting (called the source) and a transparent finish (called the sink). These networks also can be thought -about as having flow. every node has associate quantit y of flow (total weight of all edges incoming at the vertex) associated an outflow (total weight of all edges going away the vertex). Flow networks have a large style of applications together with planning, dependableness frameworks, traffic flow, system flows for systems together with electricity, water, gas and information. The maximum flow through the node is that the smallest of those values. we are able to assume logically concerning why this could be the case. Neither the sink node nor the supply node have most values, solely the intermediate ones. Some directed networks have a transparent starting (called the source) and a transparent finish (called the sink). These networks also can be thought -about as having flow. every node has associate quantity o f flow (total weight of all edges incoming at the vertex) associated an outflow (total weight of all edges going away the vertex). Flow networks have a large style of applications together with planning, dependableness frameworks, traffic flow, system flows for systems together with electricity, water, gas and information. The maximum flow through the node is that the smallest of those values. we are able to assume logically concerning why this could be the case. Neither the sink node nor the supply node ha ve most values, solely the intermediate ones. Some directed networks have a transparent starting (called the source) and a transparent finish (called the sink). These networks also can be thought -about as having flow. every node has associate quantity of f low (total weight of all edges incoming at the vertex) associated an outflow (total weight of all edges going away the vertex). Flow networks have a large style of applications together with planning, dependableness frameworks, traffic flow, system flows for systems together with electricity, water, gas and information. The maximum flow through the node is that the smallest of those values. we are able to assume logically concerning why this could be the case. Neither the sink node nor the supply node have most values, solely the intermediate ones. Some directed networks have a transparent starting (called the source) and a transparent finish (called the sink). These networks also can be thought -about as having flow. every node has associate quantity of flow (total weight of all edges incoming at the vertex) associated an outflow (total weight of all edges going away the vertex). Flow networks have a large style of applications together with planning, dependableness frameworks, traffic flow, system flows for systems together with electricity, water, gas and information. The maximum flow through the node is that the smallest of those values. we are able to assume logically concerning why this could be the case. Neither the sink node nor the supply node have mos t values, solely the intermediate ones. Some directed networks have a transparent starting (called the source) and a transparent finish (called the sink). These networks also can be thought -about as having flow. every node has associate quantity of flow (t otal weight of all edges incoming at the vertex) associated an outflow (total weight of all edges going away the vertex). Flow networks have a large style of applications together with planning, dependableness frameworks, traffic flow, system flows for systems together with electricity, water, gas and information. The maximum flow through the node is that the smallest of those values. we are able to assume logically concerning why this could be the case. Neither the sink node nor the supply node have most v alues, solely the intermediate ones. Name: Description: ...
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