On the Complexity of Minimum Congestion Embedding of Acyclic Graphs into Ladders

Akira MATSUBAYASHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.5   pp.1218-1226
Publication Date: 2001/05/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
graph embedding,  graph layout,  VLSI layout,  grid,  

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Summary: 
It is known that the problem of determining, given a planar graph G and an integer m, whether there exists a congestion-1 embedding of G into an m k-grid is NP-complete for a fixed integer k 3. It is also known that the problem for k = 3 is NP-complete even if G is restricted to an acyclic graph. The complexity of the problem for k = 2 was left open. In this paper, we show that for k = 2, the problem can be solved in polynomial time if G is restricted to a tree, while the problem is NP-complete even if G is restricted to an acyclic graph.