A repeated-update problem in the DeltaBlue algorithm

We observe a repeated-update problem in the process of updating walkabout strengths of the DeltaBlue algorithm, which is known as a fast constraint solving method based on local propagation. According to the basic references on the DeltaBlue algorithm, the time complexity of the planning phase is described as O(MN) for a constraint problem such that the number of constraints is N and the maximum number of methods a constraint has is M. We, however, point out that the time complexity is not O(MN) using a very simple example. In this example, the time complexity is exponential order for N. Then we present a corrected DeltaBlue algorithm whose time complexity is O(EN²) for a constraint problem such that the number of constraints is N and the maximum number of variables a constraint has is E. Finally we measure the performance of the corrected DeltaBlue algorithm using two benchmarks.