On the Complexity of Optimal Multisplitting

Tapio Elomaa, Juho Rousu

Research output: Chapter in Book/Report/Conference proceedingChapter or book articleProfessional


Dynamic programming has been studied extensively, e.g., in computational geometry and string matching. It has recently found a new application in the optimal multisplitting of numerical attribute value domains.We reflect the results obtained earlier to this problem and study whether they help to shed a new light on the inherent complexity of this time-critical subtask of machine learning and data mining programs. The concept of monotonicity has come up in earlier research. It helps to explain the different asymptotic time requirements of optimal multisplitting with respect to different attribute evaluation functions. As case studies we examine Training Set Error and Average Class Entropy functions. The former has a linear-time optimization algorithm, while the latter—like most well-known attribute evaluation functions—takes a quadratic time to optimize. It is shown that neither of them fulfills the strict monotonicity condition, but computing optimal Training Set Error values can be decomposed into monotone subproblems.
Original languageEnglish
Title of host publicationFoundations of Intelligent Systems
Subtitle of host publication12th International Symposium, ISMIS 2000 Charlotte, NC, USA, October 11–14, 2000 Proceedings
EditorsZbigniew W. Ras, Setsuo Ohsuga
Place of PublicationBerlin - Heidelberg
ISBN (Electronic)978-3-540-39963-6
ISBN (Print)978-3-540-41094-2
Publication statusPublished - 2000
MoE publication typeD2 Article in professional manuals or guides or professional information systems or text book material
Event12th Int. Symp. ISMIS 2000, Charlotte, NC, Oct. 2000 -
Duration: 1 Jan 2000 → …

Publication series

SeriesLecture Notes in Computer Science


Conference12th Int. Symp. ISMIS 2000, Charlotte, NC, Oct. 2000
Period1/01/00 → …


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