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Mathematically we will show that total cases for ETSP are reducible to Cn^5 from n!, which means that the solution becomes polynomial.
Our solution is geometrical in nature and assumes ETSP on topologically equivalent maps.
For a start we assume that maps available are topologically correct i.e. in which relative distances matter and no scaling is required. The emphasis is on the property exhibited by each point and its relative position.
For e.g. in Fig 1 below
d(A1A2) < d (A1A3 ) < d (A1A4 ) etc.
Here d(Ai Aj ) is usual distance function measuring distance between any arbitrary points Ai and Aj relative to distance between other arbitrary points Am and An (say).
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Space for Fig.1
These maps are topological maps only. We again state that the distances are relative only and emphasis is on the property exhibited by each point not on their actual position.
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POINTS ON THE PERIPHERY OF CONVEX POLYGON
