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AC-3 with 4-queen

This is the illustration of the AC-3 algorithm for four queens from exhaustive study of essential constraint satisfaction problem techniques based on N-Queens problem by Md. Ahsan Ayub, Kazi A Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir and Rakib Ibna Hamid.

I am confused whether this is pure AC-3 or AC-3 with backtracking. Which one is it?

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The Fig. 5 in the question depicts AC-algorithm with backtracking.

In fact, without backtracking, checking arc-consistency alone can hardly solve the 4-Queen problem. Unless it happens that choices made so far will be extended to a desired configuration, any algorithm to solve CSP have to backtrack so as to check other possibilities.

Here is a relevant excerpt from the article.

Conversely, if it does not become possible to place a Queen at the pointed column, like in Fig. 5(c), backtracker will backtrack the previous assigned Queen’s column to reassign the conflicted Queen to a newly safe cell at the same column. Then, it will, at first, clear the constraints it created by calling the implemented modular function.

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  • $\begingroup$ if so,this article is used the algorithm of kti.mff.cuni.cz/~bartak/constraints/propagation.html ,is it? @Apass.Jack $\endgroup$ – Cecelia Feb 13 '19 at 1:24
  • $\begingroup$ Not sure what you meant (your sentence seems broken). If you meant that that articles also explains the idea that backtracking goes hand in hand with (arc) consistency checking, yes. $\endgroup$ – John L. Feb 13 '19 at 1:30
  • $\begingroup$ if so,the pseudo code in fig5 is [procedure AC3-BT(cv) Q <- {(Vi,Vcv) in arcs(G),i<cv}; consistent <- true; while not Q empty & consistent select and delete any arc (Vk,Vm) from Q; consistent <- REVISE(Vk,Vm) endwhile return consistent end AC3-BT] $\endgroup$ – Cecelia Feb 13 '19 at 1:40
  • $\begingroup$ The pure AC-3 algorithm puts all arcs in queue.If AC-3 combines with backtracking ,how to put arcs in queue? $\endgroup$ – Cecelia Feb 13 '19 at 3:59
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    $\begingroup$ Write the variable assignments with backtracking mechanism as pseudocode or programming code first. Then add AC3 as another procedure to that. $\endgroup$ – John L. Feb 13 '19 at 4:05

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