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By Definition 2(2) and (4), any subhyperpath from s to (v_i) must contain the set (pi _{sv_i}) of hyperarcs returned by the procedure Backtrack listed in Algorithm 1.
These schemes are shown to (1) further reduce the average complexity of the backtrack search procedure, (2) enable our system to efficiently solve problems that could not be solved otherwise due to excessive computation cost, and (3) be more effective at solving job shop scheduling problems than other look-back schemes advocated in the literature.
Blazewicz et al. mainly focused on how to improve the backtracking procedure of the Smith-Waterman algorithm [ 24].
It is formulated as a bilevel integer programming and it uses the backtracking procedure to satisfy the blending and the manufacturing rules.
To reduce computational effort during the backtrack procedure, TWIN relies on an integer wavelet tree auxiliary data structure which allows the algorithm to focus on just those optical fragments within the current FM-index interval that are consistent with the current query fragment.
Recurrence formulas imply that the backtracking procedure does not create twice the same node: each formula computes the cost for v v between pairs of nodes where at least one is a descendant of v or v.
Blazewicz et. al. [ 25] were the first to perform the backtracking procedure inside a kernel function.
It can be seen that the backtracking procedure proposed in this work decreases the run time of the dynamic programming part by up to 45.8% (N = 40) in the case of 10 codes and 48% (N = 80) in the case of 20 codes.
The backtracking procedure classically follows each cost on the chosen line in the recurrence formulas, creating adjacency trees from root to leaves.
Backtrack the trellis to determine the MLSE solution.
Note that by virtue of the backtracking procedure, it becomes unnecessary to compute the other 20 combinations that yield, which all have higher weights.
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