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A compact representation for minimizers of k-submodular functions

Author

Listed:
  • Hiroshi Hirai

    (The University of Tokyo)

  • Taihei Oki

    (The University of Tokyo)

Abstract

A k-submodular function is a generalization of submodular and bisubmodular functions. This paper establishes a compact representation for minimizers of a k-submodular function by a poset with inconsistent pairs (PIP). This is a generalization of Ando–Fujishige’s signed poset representation for minimizers of a bisubmodular function. We completely characterize the class of PIPs (elementary PIPs) arising from k-submodular functions. We give algorithms to construct the elementary PIP of minimizers of a k-submodular function f for three cases: (i) a minimizing oracle of f is available, (ii) f is network-representable, and (iii) f arises from a Potts energy function. Furthermore, we provide an efficient enumeration algorithm for all maximal minimizers of a Potts k-submodular function. Our results are applicable to obtain all maximal persistent labelings in actual computer vision problems. We present experimental results for real vision instances.

Suggested Citation

  • Hiroshi Hirai & Taihei Oki, 2018. "A compact representation for minimizers of k-submodular functions," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 709-741, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-017-0142-0
    DOI: 10.1007/s10878-017-0142-0
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