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Reconstruction of Trees from Jumbled and Weighted Subtrees

Authors: Dénes Bartha, Peter Burcsi, and Zsuzsanna Lipták

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)


Abstract
Let T be an edge-labeled graph, where the labels are from a finite alphabet Sigma. For a subtree U of T the Parikh vector of U is a vector of length |Sigma| which specifies the multiplicity of each label in U. We ask when T can be reconstructed from the multiset of Parikh vectors of all its subtrees, or all of its paths, or all of its maximal paths. We consider the analogous problems for weighted trees. We show how several well-known reconstruction problems on labeled strings, weighted strings and point sets on a line can be included in this framework. We present reconstruction algorithms and non-reconstructibility results, and extend the polynomial method, previously applied to jumbled strings [Acharya et al., SIAM J. on Discr. Math, 2015] and weighted strings [Bansal et al., CPM 2004], to deal with general trees and special tree classes.

Cite as

Dénes Bartha, Peter Burcsi, and Zsuzsanna Lipták. Reconstruction of Trees from Jumbled and Weighted Subtrees. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bartha_et_al:LIPIcs.CPM.2016.10,
  author =	{Bartha, D\'{e}nes and Burcsi, Peter and Lipt\'{a}k, Zsuzsanna},
  title =	{{Reconstruction of Trees from Jumbled and Weighted Subtrees}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.10},
  URN =		{urn:nbn:de:0030-drops-60861},
  doi =		{10.4230/LIPIcs.CPM.2016.10},
  annote =	{Keywords: trees, paths, Parikh vectors, reconstruction problems, homometric sets, polynomial method, jumbled strings, weighted strings}
}
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