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

Authors Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, Minshen Zhu

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ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • maximum binary tree
  • heapability
  • permutation directed acyclic graphs

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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.

Cite As Get BibTex

Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, and Minshen Zhu. Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.IPEC.2020.7

Author Details

Karthekeyan Chandrasekaran
  • University of Illinois, Urbana-Champaign, IL, USA
Elena Grigorescu
  • Purdue University, West Lafayette, IN, USA
Gabriel Istrate
  • West University of Timişoara, Romania
  • e-Austria Research Institute, Timişoara, Romania
Shubhang Kulkarni
  • University of Illinois, Urbana-Champaign, IL, USA
Young-San Lin
  • Purdue University, West Lafayette, IN, USA
Minshen Zhu
  • Purdue University, West Lafayette, IN, USA

Funding

  • Chandrasekaran, Karthekeyan: Supported by NSF CCF-1814613 and NSF CCF-1907937.
  • Grigorescu, Elena: Supported by NSF CCF-1910659 and NSF CCF-1910411.
  • Istrate, Gabriel: Supported by a grant of the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI project number PN-III-P4-ID-PCE-2016-0842, within PNCDI III.
  • Lin, Young-San: Supported by NSF CCF-1910411.
  • Zhu, Minshen: Supported by NSF CCF-1910659.

References

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