2026-08-07T05:21:35Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13310 2024-03-06T10:51:40Z ddc:004 open_access

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree Chandrasekaran, Karthekeyan Grigorescu, Elena Istrate, Gabriel Kulkarni, Shubhang Lin, Young-San Zhu, Minshen maximum binary tree heapability permutation directed acyclic graphs 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Karthekeyan Chandrasekaran and Elena Grigorescu and Gabriel Istrate and Shubhang Kulkarni and Young-San Lin and Minshen Zhu 2020 Is Part Of LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2020.7 urn:nbn:de:0030-drops-133102 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.7 eng https://creativecommons.org/licenses/by/3.0/legalcode