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Question:

 

have there been any serious (meaning by a reputated mathematician) attempts to solve the euclidean TSP in the complex plane by interpreting the $(x,y)$ coordinates of the real plane as complex numbers and then applying function-theoretic methods?

To be more concrete:
it would be an obvious idea to interpret the $(x,y)$ coordinates of the real instance as the complex zeroes or poles of some complex function and then try to express simple closed tours e.g. as certain conformal mappings of the unit circle.
As it is often the case, that a real-analytic problem is easier solved in the complex plane, it seems justified to put some hope into an easier solution of the ETSP by transferring it to the complex plane or, maybe even to quaternian space.

Question:

 

have there been any serious (meaning by a reputated mathematician) attempts to solve the euclidean TSP in the complex plane by interpreting the $(x,y)$ coordinates of the real plane as complex numbers and then applying function-theoretic methods?

To be more concrete:
it would be an obvious idea to interpret the $(x,y)$ coordinates of the real instance as the complex zeroes or poles of some complex function and then try to express simple closed tours e.g. as certain conformal mappings of the unit circle.
As it is often the case, that a real-analytic problem is easier solved in the complex plane, it seems justified to put some hope into an easier solution of the ETSP by transferring it to the complex plane or, maybe even to quaternian space.

Question:

have there been any serious (meaning by a reputated mathematician) attempts to solve the euclidean TSP in the complex plane by interpreting the $(x,y)$ coordinates of the real plane as complex numbers and then applying function-theoretic methods?

To be more concrete:
it would be an obvious idea to interpret the $(x,y)$ coordinates of the real instance as the complex zeroes or poles of some complex function and then try to express simple closed tours e.g. as certain conformal mappings of the unit circle.
As it is often the case, that a real-analytic problem is easier solved in the complex plane, it seems justified to put some hope into an easier solution of the ETSP by transferring it to the complex plane or, maybe even to quaternian space.

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Manfred Weis
Manfred Weis
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Attempts to Solve the Euclidean TSP in the Complex Plane

Question:

have there been any serious (meaning by a reputated mathematician) attempts to solve the euclidean TSP in the complex plane by interpreting the $(x,y)$ coordinates of the real plane as complex numbers and then applying function-theoretic methods?

To be more concrete:
it would be an obvious idea to interpret the $(x,y)$ coordinates of the real instance as the complex zeroes or poles of some complex function and then try to express simple closed tours e.g. as certain conformal mappings of the unit circle.
As it is often the case, that a real-analytic problem is easier solved in the complex plane, it seems justified to put some hope into an easier solution of the ETSP by transferring it to the complex plane or, maybe even to quaternian space.