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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).
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https://hal.archives-ouvertes.fr/hal-01585324
Contributor : Yann Barsamian <>
Submitted on : Monday, September 11, 2017 - 2:57:45 PM
Last modification on : Saturday, October 27, 2018 - 1:23:53 AM

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  • HAL Id : hal-01585324, version 1

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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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