eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
1:1
1:18
10.4230/LIPIcs.ISAAC.2019.1
article
Graph Searches and Their End Vertices
Cao, Yixin
1
https://orcid.org/0000-0002-6927-438X
Wang, Zhifeng
2
Rong, Guozhen
2
Wang, Jianxin
2
Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
School of Computer Science and Engineering, Central South University, Changsha, China
Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al. a decade ago, and only by then we started to realize how little we understand it. Even the apparently naïve question "which vertex can be the last visited by a graph search algorithm," known as the end vertex problem, turns out to be quite elusive. We give a full picture of all maximum cardinality searches on chordal graphs, which implies a polynomial-time algorithm for the end vertex problem of maximum cardinality search. It is complemented by a proof of NP-completeness of the same problem on weakly chordal graphs. We also show linear-time algorithms for deciding end vertices of breadth-first searches on interval graphs, and end vertices of lexicographic depth-first searches on chordal graphs. Finally, we present 2^n * n^O(1)-time algorithms for deciding the end vertices of breadth-first searches, depth-first searches, and maximum cardinality searches on general graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.1/LIPIcs.ISAAC.2019.1.pdf
maximum cardinality search
(lexicographic) breadth-first search
(lexicographic) depth-first search
chordal graph
weighted clique graph
end vertex