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14Hamiltonian2_10_v2

14Hamiltonian2_10_v2 - ENGG1007 oundations of Computer...

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Unformatted text preview: ENGG1007 oundations of Computer Science Foundations of Computer Science Graphs Graphs Hamiltonian Graphs 2 Hamiltonian Graphs 2 Professor Francis Chin, Dr SM Yiu November 15/17, 2010 Chapter 9.5 1 ENGG1007 FCS otating Drum otating Drum Rotating Drum Rotating Drum First bit Third bit 2 Second bit ENGG1007 FCS otating Drum Positioning revisited otating Drum Positioning revisited Rotating Drum Positioning revisited Rotating Drum Positioning revisited The 2 n positions of the drum can be etermined by the contacts of ngs determined by the contacts of n rings. The innermost ring is for the first bit, …and the outermost ring for the 111 000 110 001 101 010 last bit. 100 011 Third bit Errors might easily be introduced at First bit Second bit the position transition. For example: 001 to 010, we might have 001 ____ 001 000 001 011 3 010 Perfect transition 010 Gap introduces error 010 Overlap introduces error ENGG1007 FCS otating Drum Positioning revisited otating Drum Positioning revisited Rotating Drum Positioning revisited Rotating Drum Positioning revisited Errors might easily be introduced at 111 000 110 001 101 010 the transition from one position to the next if the change of the bit positions is more than one bit. 100 011 Third bit EG. Transition between 111 and 000. Any bit representation is possible. First bit Second bit 1 100 000 101 001 111 011 110 010 Thus the bit representations of two djacent positions should not differ 100 111 101 4 adjacent positions should not differ too much (with only 1 bit transition). ENGG1007 FCS ray Code ray Code Gray Code Gray Code Consider bit strings {000,001,010,011,100,101,110,111} Can you permute them so that adjacent bit strings defer by one bit only? 110 Transform to G(V,E), where V = set of bit strings, 100 101 111 E = { (x,y) if x and y differ by 1 bit } 000 001 010 011 is easy to see that G is a hypercube....
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