About strongly polynomial time algorithms for quadratic optimization over submodular constraints


We present new strongly polynomial algorithms for special cases of convex separable quadratic minimization over submodular constraints. The main results are: an O(NM log(N 2/M)) algorithm for the problemNetwork defined on a network onM arcs andN nodes; an O(n logn) algorithm for thetree problem onn variables; an O(n logn) algorithm for theNested problem, and a linear time algorithm for theGeneralized Upper Bound problem. These algorithms are the best known so far for these problems. The status of the general problem and open questions are presented as well.

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This research has been supported in part by ONR grant N00014-91-J-1241.

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Hochbaum, D.S., Hong, S. About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Mathematical Programming 69, 269–309 (1995). https://doi.org/10.1007/BF01585561

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  • Quadratic programming
  • Submodular constraints
  • Kuhn-Tucker conditions
  • Lexicographically optimal flow
  • Parametric maximum flow