Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Decomposable multi-parameter matroid optimization problems
Theoretical Computer Science - Latin American theoretical informatics
Inverse parametric sequence alignment
Journal of Algorithms
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
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We present a weighted version of Megiddo's multidimensional search technique and use it to obtain faster algorithms for certain convex optimization problems in $\Reals^d$, for fixed $d$. This leads to speed-ups by a factor of $\log^d n$ for applications such as solving the Lagrangian duals of matroidal knapsack problems and of constrained optimum subgraph problems on graphs of bounded tree-width.