An Exact Exponential Branch-and-Merge Algorithm for the Single Machine Total Tardiness Problem

Abstract : This paper proposes an exact exponential algorithm for the single machine total tardiness problem. It exploits the structure of a basic branch-and-reduce framework based on the well known Lawler's decomposition property that solves the problem with worst-case complexity O * (3^n) in time and polynomial space. The proposed algorithm, called branch-and-merge, is an improvement of the branch-and-reduce technique with the embedding of a node merging operation. Its time complexity converges to O * (2^n) keeping the space complexity polynomial. This improves upon the best-known complexity result for this problem provided by dynamic programming across the subsets with O * (2^n) worst-case time and space complexity. The branch-and-merge technique is likely to be generalized to other sequencing problems with similar decomposition properties.
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Michele Garraffa, Lei Shang, Federico Della Croce, Vincent T'Kindt. An Exact Exponential Branch-and-Merge Algorithm for the Single Machine Total Tardiness Problem. 2017. ⟨hal-01477835⟩

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