| Summary: | 碩士 === 國立清華大學 === 資訊系統與應用研究所 === 103 === Planarization of clustered graph is a series of operations to transform the underlying graph by creation of degree four crossing dummies such that the result becomes a c-planar clustered graph. The heuristic for planarization consists of two stages: finding a subgraph by discarding some edges, and then reinsert discarded edges back through planarization operations. The edge reinsertion stage generally involves path finding on certain gadgets. The criteria of planarization is to minimize the number of incurred crossing dummies.
The classic method for planarization of clustered graph deal with this problem by starting from a maximal c-planar sub-clustered graph and then repetitively doing single edge insertion while maintaining cluster boundary cycles. But the modeling of cluster boundary cycles put unnecessary constraint on the cyclic ordering of outgoing edges of each cluster, hence prohibit some potentially good embeddings in which better solution can be found.
The thesis proposes an improved heuristic algorithm for planarization of clustered graph. In the thesis, the modeling of cluster boundary cycles breaks into modeling of boundary points and boundary edges, and the modeling of boundary edges are deferred after edge reinsertion stage has been finished. Moreover, shortcut gadgets are augmented to the gadget such that searching a shortest weighted path on the augmented gadget is effectively finding an optimal solution for single edge insertion amongst more embeddings at once.
The proposed method is both theoretically and experimentally examined. Theoretically that the proposed method finds an optimal solution for single edge insertion among a certain type embedding set for a c-connected clustered graph. And experimentally that the proposed method does outperform the classic method in the sense that the overall average of incurred crossings is reduced to about 89.1% in the experiment.
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