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The Scientific World Journal
Volume 2013, Article ID 960348, 10 pages
Research Article

Knee Point Search Using Cascading Top-k Sorting with Minimized Time Complexity

1Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China
2China Organizational Name Administration Center, Beijing 100028, China
3Department of Information Science and Applications, Asia University, Taichung 41354, Taiwan

Received 20 May 2013; Accepted 20 July 2013

Academic Editors: Z. Cai and Y. Deng

Copyright © 2013 Zheng Wang and Shian-Shyong Tseng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Anomaly detection systems and many other applications are frequently confronted with the problem of finding the largest knee point in the sorted curve for a set of unsorted points. This paper proposes an efficient knee point search algorithm with minimized time complexity using the cascading top-k sorting when a priori probability distribution of the knee point is known. First, a top-k sort algorithm is proposed based on a quicksort variation. We divide the knee point search problem into multiple steps. And in each step an optimization problem of the selection number k is solved, where the objective function is defined as the expected time cost. Because the expected time cost in one step is dependent on that of the afterwards steps, we simplify the optimization problem by minimizing the maximum expected time cost. The posterior probability of the largest knee point distribution and the other parameters are updated before solving the optimization problem in each step. An example of source detection of DNS DoS flooding attacks is provided to illustrate the applications of the proposed algorithm.