License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2020.7
URN: urn:nbn:de:0030-drops-133102
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13310/
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Chandrasekaran, Karthekeyan ; Grigorescu, Elena ; Istrate, Gabriel ; Kulkarni, Shubhang ; Lin, Young-San ; Zhu, Minshen

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree

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LIPIcs-IPEC-2020-7.pdf (0.6 MB)

Abstract

A heapable sequence is a sequence of numbers that can be arranged in a min-heap data structure. Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011) as a generalization of the well-studied longest increasing subsequence problem and its complexity still remains open. An equivalent formulation of the longest heapable subsequence problem is that of finding a maximum-sized binary tree in a given permutation directed acyclic graph (permutation DAG). In this work, we study parameterized algorithms for both longest heapable subsequence and maximum-sized binary tree. We introduce alphabet size as a new parameter in the study of computational problems in permutation DAGs and show that this parameter with respect to a fixed topological ordering admits a complete characterization and a polynomial time algorithm. We believe that this parameter is likely to be useful in the context of optimization problems defined over permutation DAGs.

BibTeX - Entry

@InProceedings{chandrasekaran_et_al:LIPIcs:2020:13310,
  author =	{Karthekeyan Chandrasekaran and Elena Grigorescu and Gabriel Istrate and Shubhang Kulkarni and Young-San Lin and Minshen Zhu},
  title =	{{Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13310},
  URN =		{urn:nbn:de:0030-drops-133102},
  doi =		{10.4230/LIPIcs.IPEC.2020.7},
  annote =	{Keywords: maximum binary tree, heapability, permutation directed acyclic graphs}
}

Keywords: maximum binary tree, heapability, permutation directed acyclic graphs
Collection: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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