Module11_08 - Backtracking and Branch and Bound Module 11...

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Backtracking and Branch and Bound Module 11 CSE5311 Fall 2008 Kumar CSE5311 Backtracking ± Using Backtracking ± Large instances of difficult combinatorial problems can be solved ± Worst case complexity of Backtracking can be exponential ± Typically, a path is taken to check if a solution can be reached ± If not, the path is abandoned and another path taken ± The process is repeated until the solution is arrived at
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Kumar CSE5311 N-Queens problem ± Place n-queens on an n × n chess board so that no two queens attack each other. ± A queen can attack another if the latter is on the same row, column or diagonal Q 1 Q 2 Q 3 Q 4 Kumar CSE5311 Q 0 1
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Kumar CSE5311 Q 0 1 Q Q 2 Kumar CSE5311 Q 0 1 Q Q 2 Q Q 2
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Kumar CSE5311 Q 0 1 Q Q 2 Q Q 2 Kumar CSE5311 Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 0 1 2 3 4 5 6 7 8
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Kumar CSE5311 Hamiltonian Circuit Problem a d e b f c a b c d e f Start at a vertex and visit all the other vertices in the graph exactly once and return to the start vertex Kumar CSE5311 Hamiltonian Circuit Problem a d e b f c a b c d e f e d f
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Kumar CSE5311 Hamiltonian Circuit Problem a d e b f c a b c
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This document was uploaded on 11/18/2009.

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Module11_08 - Backtracking and Branch and Bound Module 11...

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