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This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates estimation accuracy. We propose a general approach for making any sorting algorithm anytime and introduce two new algorithms: multizip sort and Corsort. Simulations showcase the superior performance of both algorithms compared to existing methods. Multizip sort keeps a low global complexity, while Corsort produces intermediate estimates surpassing previous algorithms.