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Positive attitude, tree-width etc

A few days ago I was listening to a lecture given by Shripad Dharmadhikari. He is an IITB alumnus, he has set up Manthan Adhyayan Kendra, a centre for research in energy and water related issues. He has also been associated with Narmada Bachao Andolan for around twelve years. Through his talk, he highlighted the energy crisis that India is doomed to face in another two decades or so. He mentioned that in another decade or so, no river in India will be flowing freely. That is, there will be dams, often cascaded dams, on every major river in India. Imagine the kids of next generation trying to find wild and wilderness in India! May be his estimates are not accurate, may be there are more than 3-4 decades before India energy crisis. However, his data and his description of the current state of affairs seemed very scary. Just hearing this made me rather depressed. I wondered how he manages to muster enough energy, courage and at the same time positive attitude every morning and keep working in energy/water related issues. For that matter, I wonder how people who dedicate themselves to help the society, especially Indian society, manage to do so without getting discouraged.

On this note I would like to mention something about my mother. She has now started living her retired life. For about a year or so she was trying to figure out what she wants to do with her time in the next few years. After many careful considerations she has started teaching in a school for special kids. When she was considering this option I certainly thought it was a great thing to do, but I was a bit worried for her. What if concerns for the kids and helplessness of their parents fill her with depression? I mentioned my worries before she made her final decision. She brushed them off  with much confidence and added: "I will feel happy that I am at least doing something." I totally admired her response. It made me proud and happy. It was a simple and honest thought. I am happy to mention that she has been teaching a batch of 8 special kids in a school and she keeps telling me many funny anecdotes about each kid. She has learned many tricks to help them concentrate, help them remember. She has created many work books, picture books. In all, she has been having a good time.

I guess, helping a cause cannot be done without having a very positive spirit, a clarity of thought to come to terms with all the extant problems and a strong will to circumvent them. I am probably stating the obvious. But let me! It always helps to get reminded of the basic principles.

Now, going back to the tree-width problem. I am now able to get a tree decomposition of depth O(log^2 n) and width 2 for any tree by a very simple proof. The question is: can I bring it down to depth O(log n) and width say 7 or 8? To know the definition of tree decomposition and the definition of treewidth check: http://en.wikipedia.org/wiki/Tree_decomposition





Comments

Hans Bodlaender said…
Yes, my old work with Torben Hagerup shows that one can find a tree decomposition of width 2 of a tree with depth O(log n).
Hans Bodlaender
Nutan said…
Dear Hans Bodlaender, thank you for the information. Now that I know it can be done, I should try to do it again! In any case, if I fail, I will look up the reference. Thanks once again, for stopping by.

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