FPT algorithms for embedding into low complexity graphic metrics

Arijit Ghosh, Sudeshna Kolay, Gopinath Mishra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The METRIC EMBEDDING problem takes as input two metric spaces (X,DX) and (Y,DY), and a positive integer d. The objective is to determine whether there is an embedding F: X → Y such that the distortion dF ≤ d. Such an embedding is called a distortion d embedding. In parameterized complexity, the METRIC EMBEDDING problem is known to be W-hard and therefore, not expected to have an FPT algorithm. In this paper, we consider the GEN-GRAPH METRIC EMBEDDING problem, where the two metric spaces are graph metrics. We explore the extent of tractability of the problem in the parameterized complexity setting. We determine whether an unweighted graph metric (G, DG) can be embedded, or bijectively embedded, into another unweighted graph metric (H,DH), where the graph H has low structural complexity. For example, H is a cycle, or H has bounded treewidth or bounded connected treewidth. The parameters for the algorithms are chosen from the upper bound d on distortion, bound Δ on the maximum degree of H, treewidth α of H, and the connected treewidth αc of H. Our general approach to these problems can be summarized as trying to understand the behavior of the shortest paths in G under a low distortion embedding into H, and the structural relation the mapping of these paths has to shortest paths in H.

Original languageEnglish
Title of host publication26th European Symposium on Algorithms, ESA 2018
EditorsHannah Bast, Grzegorz Herman, Yossi Azar
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770811
StatePublished - 1 Aug 2018
Externally publishedYes
Event26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland
Duration: 20 Aug 201822 Aug 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference26th European Symposium on Algorithms, ESA 2018


  • Dynamic programming
  • FPT
  • Metric embedding
  • Metric spaces

ASJC Scopus subject areas

  • Software


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