Algorithms for a class of isotonic regression problems

P. M. Pardalos, G. Xue

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


The isotonic regression problem has applications in statistics, operations research, and image processing. In this paper a general framework for the isotonic regression algorithm is proposed. Under this framework, we discuss the isotonic regression problem in the case where the directed graph specifying the order restriction is a directed tree with n vertices. A new algorithm is presented for this case, which can be regarded as a generalization of the PAV algorithm of Ayer et al. Using a simple tree structure such as the binomial heap, the algorithm can be implemented in O(n log n) time, improving the previously best known O(n2) time algorithm. We also present linear time algorithms for special cases where the directed graph is a path or a star.

Original languageEnglish (US)
Pages (from-to)211-222
Number of pages12
JournalAlgorithmica (New York)
Issue number3
StatePublished - Mar 1999
Externally publishedYes


  • Binomial heap
  • Isotonic regression
  • Linear time algorithms

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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