Backtracking Maximal Clique

1
Backtracking Maximal Clique
Backtrack_Clique(X, l) if (l 0) Cl
V else Cl Cl-1 n Axl-1 n Bxl-1 for each x
in Cl xl x Nl1 Axl n Nl if(Nl1 !
) Backtrack_Clique(X, l1) else print(x
0, , xl)
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Maximal Clique Example
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Generic Backtrack Search

• backtrack(X, c, n)
• compute candidates for level c
• for each candidate x
• if(x1, , xc-1, x) is acceptable // point 1
• xc x
• if(c lt n)
• backtrack(X, c1, n) // point 2
• else
• process solution // point 3

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4-Queens Search Tree
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Backtrack Estimation

• Backtrack_estimate(x1,,xc-1, c, n)
• compute candidates for level c
• for each candidate x
• if(x1, , xc-1, x) is acceptable
• record(x)
• dc
• estimatec scale dc
• scale scale dc
• xc random acceptable candidate
• if(c lt n)
• backtrack_estimate(x1,,xc, c1, n)
• else
• process solution