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Mathematical Programming

, Volume 69, Issue 1–3, pp 269–309 | Cite as

About strongly polynomial time algorithms for quadratic optimization over submodular constraints

  • Dorit S. Hochbaum
  • Sung-Pil Hong
Article

Abstract

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(N2/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.

Keywords

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

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Copyright information

© The Mathematical Programming Society, Inc. 1995

Authors and Affiliations

  • Dorit S. Hochbaum
    • 1
    • 2
  • Sung-Pil Hong
    • 2
  1. 1.School of Business AdministrationUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of IEORUniversity of CaliforniaBerkeleyUSA

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