Bilinear separation of two sets in n-space
Computational Optimization and Applications
Time Series Segmentation for Context Recognition in Mobile Devices
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
A Dynamic Programming Algorithm for Linear Text Segmentation
Journal of Intelligent Information Systems
Unimodal Segmentation of Sequences
ICDM '04 Proceedings of the Fourth IEEE International Conference on Data Mining
Algorithm Design
Random separation: a new method for solving fixed-cardinality optimization problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity
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We divide a string into k segments, each with only one sort of symbols, so as to minimize the total number of exceptions. Motivations come from machine learning and data mining. For binary strings we develop a linear-time algorithm for any k. Key to efficiency is a special-purpose data structure, called W-tree, which reflects relations between repetition lengths of symbols. Existence of algorithms faster than obvious dynamic programming remains open for non-binary strings. Our problem is also equivalent to finding weighted independent sets of prescribed size in paths. We show that this problem in bounded-degree graphs is FPT.