Maximum Subarray Problem in 1D and 2D via Weighted Paths in Directed Acyclic Graphs - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

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

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).
Fichier principal
Vignette du fichier
MSP-DAG.pdf (163.88 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01585324 , version 1 (11-09-2017)

Identifiers

  • HAL Id : hal-01585324 , version 1

Cite

Yann Barsamian. Maximum Subarray Problem in 1D and 2D via Weighted Paths in Directed Acyclic Graphs. 2016. ⟨hal-01585324⟩
174 View
1087 Download

Share

Gmail Facebook X LinkedIn More