September 2014
Intermediate to advanced
320 pages
10h 24m
English
Content preview from Complex Networks
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Algorithms and Complexity
47
(a) G(V,E)
(b) G'(V,E')
Figure 3.12: Reduction from independent set to clique
by checking the proposed solution S in G whether IND is a clique in G
′
. Figure 3.13
displays the reduction relationships between the fundamental NPC problems.
Once a problem is found to be NPC, there is no need to search for a solution in
P. The possible approaches for the solution are as follows:
We may use the exponential solution if there is one, for small values of input.
We can use heuristics which can lead to a solution in polynomial time. As an
example, the heuristic to find the minimal VC could be always choosing the
highest degree vertex ...
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