Minimum-area h-v drawings of complete binary trees

The number, , of rooted plane binary trees of height ≤ h with n internal nodes is shown to satisfyuniformly for δ−1(log n)−1/2 ≤ β ≤ δ(log n)1/2, where and δ is a positive constant. An asymptotic formula for is derived for h = cn, where 0 < c < 1. Bounds for are also derived for large and small heights. The methods apply to any simple family of trees, and the general asymptotic results are stated.

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Forest management strategies for dealing with fire-related uncertainty when managing two forest seral stages

Canadian Journal of Forest Research ◽

10.1139/x10-212 ◽

2011 ◽

Vol 41 (2) ◽

pp. 309-320 ◽

Cited By ~ 12

Author(s):

David W. Savage ◽

David L. Martell ◽

B. Mike Wotton

Keyword(s):

Forest Management ◽

Simulation Model ◽

Sustainable Forest Management ◽

Management Strategies ◽

Fire Regimes ◽

Analysis Tool ◽

Planning Model ◽

Minimum Area ◽

Forest Management Planning ◽

Planning Models

Ecological values are an important aspect of sustainable forest management, but little attention has been paid to maintaining these values when using traditional linear programming (LP) forest management planning models in uncertain planning environments. We embedded an LP planning model that specifies when and how much to harvest in a simulation model of a “managed” flammable forest landscape. The simulation model was used to evaluate two strategies for dealing with fire-related uncertainty when managing mature and old forest areas. The two seral stage areas were constrained in the LP planning model to a minimum of 10% of the total forest area and the strategies were evaluated under four representative fire regimes. We also developed a risk analysis tool that can be used by forest managers that wish to incorporate fire-related uncertainty in their decision-making. We found that use of the LP model would reduce the areas of the mature and old forest to their lower bound and fire would further reduce the seral areas below those levels, particularly when the mean annual burn fraction exceeds 0.45% per annum. Increasing the minimum area required (i.e., the right-hand side of the constraint) would increase the likelihood of satisfying the minimum area requirements.

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