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Sparse Integer Programming Is Fixed-Parameter Tractable

Author

Listed:
  • Friedrich Eisenbrand

    (EPFL SB MATH DISOPT, 1015 Lausanne, Switzerland)

  • Christoph Hunkenschröder

    (Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany)

  • Kim-Manuel Klein

    (Institut für Theoretische Informatik, Universität zu Lübeck, 23538 Lübeck, Germany)

  • Martin Koutecký

    (Computer Science Institute, Faculty of Mathematics and Physics, Charles University, 118 00 Praha 1, Czech Republic)

  • Asaf Levin

    (Faculty of Data and Decision Sciences, Technion – Israel Institute of Technology, Technion City, Haifa 3200003, Israel)

  • Shmuel Onn

    (Faculty of Data and Decision Sciences, Technion – Israel Institute of Technology, Technion City, Haifa 3200003, Israel)

Abstract

We study the general integer programming problem where the number of variables n is a variable part of the input. We consider two natural parameters of the constraint matrix A : its numeric measure a and its sparsity measure d . We present an algorithm for solving integer programming in time g ( a , d ) poly ( n , L ) , where g is some computable function of the parameters a and d , and L is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by a and d , and is solvable in polynomial time for every fixed a and d . Our results also extend to nonlinear separable convex objective functions.

Suggested Citation

  • Friedrich Eisenbrand & Christoph Hunkenschröder & Kim-Manuel Klein & Martin Koutecký & Asaf Levin & Shmuel Onn, 2025. "Sparse Integer Programming Is Fixed-Parameter Tractable," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 2141-2156, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:2141-2156
    DOI: 10.1287/moor.2023.0162
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