arXiv subjects

Guozhen Rong

Publications and source records attributed to Guozhen Rong.

5 recordsLinked to original sources

arXiv2026

When Graph Traversal Meets Structured Preferences: Unified Framework and Complexity Results

Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph and interpret the preference ordering of each voter as the outcome of traversing the graph according to a graph search. We focus on six fundamental paradigms: breadth-first search (BFS), depth-first search (DFS), breadth-first search (LexBFS), lexicographic depth-first (LexDFS), maximum cardinality search (MCS), and maximal neighborhood search (MNS). Within this framework, we study the problem of determining whether a given preference profile admits a graph support subject to structural restrictions, that is, whether there exists a graph such that each preference ordering can be generated by traversing the graph under the chosen paradigm. For all considered paradigms, we show that this problem is NP-hard when the graph support is required to have at most $k$ edges, where $k$ is a given integer. We further extend these hardness results to the case where the graph support is required to have maximum degree $k$. For DFS, we prove that recognizing whether a preference profile admits a tree support can be solved in polynomial time. Moreover, existing results imply polynomial-time solvability of the problem for all remaining graph traversals, except BFS and LexBFS, for which the complexity remains open.

cs.GT↗

arXiv2023

A Polynomial-Time Algorithm for MCS Partial Search Order on Chordal Graphs

We study the partial search order problem (PSOP) proposed recently by Scheffler [WG 2022]. Given a graph $G$ together with a partial order over the set of vertices of $G$, this problem determines if there is an $\mathcal{S}$-ordering that is consistent with the given partial order, where $\mathcal{S}$ 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 ${\mathcal{F}}$-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.

cs.DS↗

arXiv2021

Cycle Extendability of Hamiltonian Strongly Chordal Graphs

In 1990, Hendry conjectured that all Hamiltonian chordal graphs are cycle extendable. After a series of papers confirming the conjecture for a number of graph classes, the conjecture is yet refuted by Lafond and Seamone in 2015. Given that their counterexamples are not strongly chordal graphs and they are all only $2$-connected, Lafond and Seamone asked the following two questions: (1) Are Hamiltonian strongly chordal graphs cycle extendable? (2) Is there an integer $k$ such that all $k$-connected Hamiltonian chordal graphs are cycle extendable? Later, a conjecture stronger than Hendry's is proposed. In this paper, we resolve all these questions in the negative. On the positive side, we add to the list of cycle extendable graphs two more graph classes, namely, Hamiltonian $4$-\textsc{fan}-free chordal graphs where every induced $K_5 - e$ has true twins, and Hamiltonian $\{4\textsc{-fan}, \overline{A} \}$-free chordal graphs.

cs.DM↗

arXiv2019

Characterization and Linear-time Recognition of Paired Threshold Graphs

In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well studied. We present a vertex ordering characterization of this graph class, which enables us to prove that it is a subclass of interval graphs. Further study of clique paths of paired threshold graphs leads to a simple linear-time recognition algorithm for the class.

cs.DS↗

arXiv2019

Graph Searches and Their End Vertices

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 $2^n\cdot n^{O(1)}$-time algorithms for deciding the end vertices of breadth-first searches, depth-first searches, maximum cardinality searches, and maximum neighborhood searches on general graphs.

cs.DS↗