Design of “balancing” networks with loopbacks
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Say that you have a network of conveyor belts with nodes, where each node is a 2-lane crossover switch (2 in, 2 out, either straight-through or crossed-over).
Beneš networks work to solve the problem nicely when there are $2^N$ inputs and outputs, but are somewhat lacking in, say, the case of a 14->6 lane network.
It seems somewhat evident that any non-$2^N$ lane network will require some variety of loops in the balancing network, in order to handle ratios like 1/3.
Is there any established mathematical basis for non-$2^N$ networks of this nature?
graph-theory applications network-flow
asked Nov 18 at 17:58
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Say that you have a network of conveyor belts with nodes, where each node is a 2-lane crossover switch (2 in, 2 out, either straight-through or crossed-over).
Beneš networks work to solve the problem nicely when there are $2^N$ inputs and outputs, but are somewhat lacking in, say, the case of a 14->6 lane network.
It seems somewhat evident that any non-$2^N$ lane network will require some variety of loops in the balancing network, in order to handle ratios like 1/3.
Is there any established mathematical basis for non-$2^N$ networks of this nature?
graph-theory applications network-flow
asked Nov 18 at 17:58
Stack Tracer
1063
"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Say that you have a network of conveyor belts with nodes, where each node is a 2-lane crossover switch (2 in, 2 out, either straight-through or crossed-over).
Beneš networks work to solve the problem nicely when there are $2^N$ inputs and outputs, but are somewhat lacking in, say, the case of a 14->6 lane network.
It seems somewhat evident that any non-$2^N$ lane network will require some variety of loops in the balancing network, in order to handle ratios like 1/3.
Is there any established mathematical basis for non-$2^N$ networks of this nature?
graph-theory applications network-flow
asked Nov 18 at 17:58
Stack Tracer
1063
Say that you have a network of conveyor belts with nodes, where each node is a 2-lane crossover switch (2 in, 2 out, either straight-through or crossed-over).
Beneš networks work to solve the problem nicely when there are $2^N$ inputs and outputs, but are somewhat lacking in, say, the case of a 14->6 lane network.
It seems somewhat evident that any non-$2^N$ lane network will require some variety of loops in the balancing network, in order to handle ratios like 1/3.
Is there any established mathematical basis for non-$2^N$ networks of this nature?
graph-theory applications network-flow
graph-theory applications network-flow
asked Nov 18 at 17:58
Stack Tracer
1063
asked Nov 18 at 17:58
Stack Tracer
1063
asked Nov 18 at 17:58
Stack Tracer
1063
asked Nov 18 at 17:58
Stack Tracer
1063
asked Nov 18 at 17:58
Stack Tracer
1063
1063
"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36
add a comment |
"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36
"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36
add a comment |
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"Beneš networks work to solve the problem nicely" - what problem? You've given a description of the network of conveyor belts, but not the problem that you're trying to solve.
– Misha Lavrov
Nov 18 at 19:48
@MishaLavrov Not sure what's unclear about it, but let's try this as an alternative explanation: how do I design an N->M balancing network for systems of this type.
– Stack Tracer
Nov 18 at 21:56
If you're hoping for an audience of people who already know what an "N->M balancing network" is to answer your question, that's fine. You're more likely to get an answer if you translate that to a graph-theoretic statement so someone who's merely fluent in graph theory can attempt to answer your question. But you know better than I do if there is a simple description. (Wikipedia doesn't help and in fact I'm unconvinced that it's talking about the same concept.)
– Misha Lavrov
Nov 18 at 22:00
@MishaLavrov, I have no real idea how to translate this into a graph-theoretic statement (and get the feeling that if I did, I wouldn't need to ask how to solve the problem).
– Stack Tracer
Nov 19 at 2:36