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- W2568921000 abstract "A divide-and-conquer strategy based on variations of the Lipton-Tarjan planar separatortheorem has been one of the most common approaches for solving planar graph problems formore than 20 years. We present a new framework for designing fast subexponential exact and parameterized algorithms on planar graphs. Our approach is based on geometric properties of planar branch decompositions obtained by Seymour & Thomas, combined with refined techniques of dynamic programming on planar graphs based on properties of non-crossing partitions. Compared to divide-and-conquer algorithms, the main advantages of our method are a) it is a generic method which allows to attack broad classes of problems; b) the obtained algorithms provide a better worst case analysis. To exemplify our approach we show how to obtain an O(26.903√n) time algorithm solving weighted HAMILTONIAN CYCLE. We observe how our technique can be used to solve PLANAR GRAPH TSP in time O(29.8594√n). Our approach can be used to design parameterized algorithms as well. For example we introduce the first 2O(√ k)nO(1) time algorithm for parameterized Planar k-cycle by showing that for a given k we can decide if a planar graph on n vertices has a cycle of length at least k in time O(213.6√kn + n3)." @default.
- W2568921000 created "2017-01-13" @default.
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- W2568921000 date "2006-01-01" @default.
- W2568921000 modified "2023-10-16" @default.
- W2568921000 title "Efficient Exact Algorithms on Planar Graphs: Exploiting Sphere Cut Decompositions" @default.
- W2568921000 hasPublicationYear "2006" @default.
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