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Fig. 4 | Algorithms for Molecular Biology

Fig. 4

From: Sparse RNA folding revisited: space-efficient minimum free energy structure prediction

Fig. 4

Ideas of the space-efficient backtracking procedure and its requirements. We illustrate concepts sketching the upper-triangular V-matrix in different algorithm phases. The dark-grey lower triangle is unused. The stored rows i..\(i+M\) are shown as light-grey area; the light-grey boxes represent the candidates. a Evaluation phase of sparse MFE folding without space-efficient trace-back; the algorithm stores the last \(M+1\) rows and the candidates. b Space-efficient trace-back (red arrow) in the basic algorithm fails, since trace continuations cannot be efficiently retrieved in general; eventually, the trace reaches a non-candidate entry (filled circle), which is not in memory. c Naive sparse MFE folding with trace-back stores all trace arrows (black arrows) to candidates (boxes) and non-candidates (circles). d SparseMFEFold removes arrows to candidates and applies garbage collection to fundamentally reduce the space requirements

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