Computer Science – Data Structures and Algorithms
Scientific paper
2001-01-27
SIAM Journal on Discrete Mathematics, 12(3):317--325, 1999
Computer Science
Data Structures and Algorithms
Scientific paper
Let G be an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge. If G is triangulated, we can encode it using {4/3}m-1 bits, improving on the best previous bound of about 1.53m bits. In case exponential time is acceptable, roughly 1.08m bits have been known to suffice. If G is triconnected, we use at most (2.5+2\log{3})\min\{n,f\}-7 bits, which is at most 2.835m bits and smaller than the best previous bound of 3m bits. Both of our schemes take O(n) time for encoding and decoding.
He Xin
Kao Ming-Yang
Lu Hsueh-I
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