eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
77:1
77:15
10.4230/LIPIcs.MFCS.2023.77
article
A Polynomial-Time Algorithm for MCS Partial Search Order on Chordal Graphs
Rong, Guozhen
1
Yang, Yongjie
2
https://orcid.org/0000-0002-7731-6818
Li, Wenjun
1
Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, Changsha University of Science and Technology, China
Chair of Economic Theory, Saarland University, Saarbrücken, Germany
We study the partial search order problem (PSOP) proposed recently by Scheffler [WG 2022]. Given a graph G together with a partial order on the set of vertices of G, this problem determines if there is an 𝒮-ordering that is consistent with the given partial order, where 𝒮 is a graph search paradigm like BFS, DFS, etc. This problem naturally generalizes the end-vertex problem which has received much attention over the past few years. It also generalizes the so-called ℱ-tree recognition problem which has just been studied in the literature recently. Our main contribution is a polynomial-time dynamic programming algorithm for the PSOP of the maximum cardinality search (MCS) restricted to chordal graphs. This resolves one of the most intriguing open questions left in the work of Scheffler [WG 2022]. To obtain our result, we propose the notion of layer structure and study numerous related structural properties which might be of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.77/LIPIcs.MFCS.2023.77.pdf
partial search order
maximum cardinality search
chordal graphs
clique graphs
dynamic programming