Reconstructing Convex Matrices by Integer Programming Approaches

  • Alain Billionnet
  • Fethi Jarray
  • Ghassen Tlig
  • Ezzedine Zagrouba


We consider the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of adjacent ones. We reformulate the problem by using integer programming and we develop approximate solutions based on linearization and convexification techniques.


Discrete Tomography (DT) Integer programming Convexification Linearization 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Alain Billionnet
    • 1
  • Fethi Jarray
    • 1
  • Ghassen Tlig
    • 1
    • 2
  • Ezzedine Zagrouba
    • 2
  1. 1.CEDRIC-CNAMParisFrance
  2. 2.Faculté des Sciences de Tunis El ManarEl Manar IITunisie

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