![Free-eBooks.net](/resources/img/logo-nfe.png)
![All New Design](/resources/img/allnew.png)
326
327
328
329
330
331
332
333
334
335
336
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).
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
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.
357
358
POINTS ON THE PERIPHERY OF CONVEX POLYGON