文章基本信息

标题：Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree
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作者：Karthekeyan Chandrasekaran ; Elena Grigorescu ; Gabriel Istrate 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：180
页码：1-16
DOI：10.4230/LIPIcs.IPEC.2020.7
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：maximum binary tree; heapability; permutation directed acyclic graphs