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On the Complexity of Embedding of Graphs into Grids with Minimum Congestion
Akira MATSUBAYASHI Shuichi UENO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1996/04/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
NP-completeness, graph embedding, congestion, grid, VLSI layout,
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It is known that the problem of determining, given a planar graph G with maximum vertex degree at most 4 and integers m and n, whether G is embeddable in an m n grid with unit congestion is NP-hard. In this paper, we show that it is also NP-complete to determine whether G is embeddable in ak n grid with unit congestion for any fixed integer k 3. In addition, we show a necessary and sufficient condition for G to be embeddable in a 2 grid with unit congestion, and show that G satisfying the condition is embeddable in a 2 |V(G)| grid. Based on the characterization, we suggest a linear time algorithm for recognizing graphs embeddable in a 2 grid with unit congestion.