JSAI International Symposium on Artificial Intelligence

JSAI-isAI 2014: New Frontiers in Artificial Intelligence pp 317-330 | Cite as

Mapping Kernels Between Rooted Labeled Trees Beyond Ordered Trees

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9067)

Abstract

In this paper, we investigate several mapping kernels to count all of the mappings between two rooted labeled trees beyond ordered trees, that is, cyclically ordered trees such as biordered trees, cyclic-ordered trees and cyclic-biordered trees, and degree-bounded unordered trees. Then, we design the algorithms to compute a top-down mapping kernel, an LCA-preserving segmental mapping kernel, an LCA-preserving mapping kernel, an accordant mapping kernel and an isolated-subtree mapping kernel for biordered trees in O(nm) time and ones for cyclic-ordered and cyclic-biordered trees in O(nmdD) time, where n is the number of nodes in a tree, m is the number of nodes in another tree, D is the maximum value of the degrees in two trees and d is the minimum value of the degrees in two trees. Also we design the algorithms to compute the above kernels for degree-bounded unordered trees in O(nm) time. On the other hand, we show that the problem of computing label-preserving leaf-extended top-down mapping kernel and label-preserving bottom-up mapping kernel is #P-complete.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Kouichi Hirata
    • 1
  • Tetsuji Kuboyama
    • 2
  • Takuya Yoshino
    • 1
  1. 1.Kyushu Institute of TechnologyIizukaJapan
  2. 2.Gakushuin UniversityToshimaJapan

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