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A report I submitted for a networks course. Survey on IP Traceback

Lot of theory people have been working on a field named Data Stream algorithms. They basically store a part of the stream to keep some properties of the stream like top-k frequent items. I think the concepts from data streams algorithms can be applied in IP Traceback problem. If I get time, I will think about it. If you are interested let me know.
Abstract :

Abstract—The rising threat of DoS, and DDoS has made IP Traceback an important problem. Instead of preventing systems, we have to deploy mechanism to actually trace the culprit. In this way the attackers will be discouraged. People are working on mechanisms to defend against DDoS. We need mechanisms which are easy to deploy and which require less manegement work. In this report, we discuss the current scenario of IP Traceback mechanisms. We make a simple matrix on which we analyze different mechanisms.

I just figured that its very easy to keep standard deviation of each subtree in a binary tree. And this made me think of a problem. I don’t know if people have already been working on it or not. But its an interesting problem. Suppose I have a large data of numbers. And someone asks me to give him k numbers so that they have the same average. How do I do that?

Let me express it in mathematical form. You are given ‘n’ numbers, . Give me ‘k’ numbers out of these ‘n’ numbers so that their average is nearest to