TY - GEN
T1 - Fixed-parameter algorithms for longest heapable subsequence and maximum binary tree
AU - Chandrasekaran, Karthekeyan
AU - Grigorescu, Elena
AU - Istrate, Gabriel
AU - Kulkarni, Shubhang
AU - Lin, Young San
AU - Zhu, Minshen
N1 - Funding Information:
Funding Karthekeyan Chandrasekaran: Supported by NSF CCF-1814613 and NSF CCF-1907937. Elena Grigorescu: Supported by NSF CCF-1910659 and NSF CCF-1910411. Gabriel Istrate: 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. Young-San Lin: Supported by NSF CCF-1910411. Minshen Zhu: Supported by NSF CCF-1910659.
Publisher Copyright:
© Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, and Minshen Zhu;
PY - 2020/12
Y1 - 2020/12
N2 - 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.
AB - 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.
KW - Heapability
KW - Maximum binary tree
KW - Permutation directed acyclic graphs
UR - http://www.scopus.com/inward/record.url?scp=85101467770&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85101467770&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.IPEC.2020.7
DO - 10.4230/LIPIcs.IPEC.2020.7
M3 - Conference contribution
AN - SCOPUS:85101467770
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 15th International Symposium on Parameterized and Exact Computation, IPEC 2020
A2 - Cao, Yixin
A2 - Pilipczuk, Marcin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 15th International Symposium on Parameterized and Exact Computation, IPEC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -