Maximum Subarray Problem in 1D and 2D via Weighted Paths in Directed Acyclic Graphs

Yann Barsamian 1, 2
2 CAMUS - Compilation pour les Architectures MUlti-coeurS
Inria Nancy - Grand Est, ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie
Abstract : The Maximum Subarray Problem was encountered by Ulf Grenander for maximum likelihood estimation in pattern analysis. We are given a vector (or matrix) of numbers, and we have to find the contiguous sub-vector (or sub-matrix) which has the maximum sum of numbers in it. Apart from the original application, the problem also arises for example in biological sequence analysis. We present here a linear-time algorithm in one dimension which is different from the one known due to Kadane, and present a way of extending it to two dimensions. To achieve the latter, we provide a new technique, the red-blue graphs, which encodes all the contiguous sub-matrices of an m × n matrix in size O(m × n).
Type de document :
Pré-publication, Document de travail
2016
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Soumis le : lundi 11 septembre 2017 - 14:57:45
Dernière modification le : mardi 17 avril 2018 - 09:04:21

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Yann Barsamian. Maximum Subarray Problem in 1D and 2D via Weighted Paths in Directed Acyclic Graphs. 2016. 〈hal-01585324〉

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