arXiv subjects

Rongxia Tang

Publications and source records attributed to Rongxia Tang.

4 recordsLinked to original sources

arXiv2025

List rainbow connection number of graphs

An edge-coloured path is rainbow if all of its edges have distinct colours. Let $G$ be a connected graph. The rainbow connection number of $G$, denoted by $rc(G)$, is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices are connected by a rainbow path. The strong rainbow connection number of $G$, denoted by $src(G)$, is the minimum number of colours in an edge-colouring of $G$ such that, any two vertices are connected by a rainbow geodesic (i.e., a path of shortest length). These two notions of connectivity of graphs were introduced by Chartrand, Johns, McKeon and Zhang in 2008. In this paper, we introduce the list rainbow connection number $rc^\ell(G)$, and the list strong rainbow connection number $src^\ell(G)$. These two parameters are the versions of $rc(G)$ and $src(G)$ that involve list edge-colourings. Among our results, we will determine the list rainbow connection number and list strong rainbow connection number of some specific graphs. We will also characterise all pairs of positive integers $a$ and $b$ such that, there exists a connected graph $G$ with $src(G)=a$ and $src^\ell(G)=b$, and similarly for the pair $rc^\ell$ and $src^\ell$. Finally, we propose the question of whether or not we have $rc(G)=rc^\ell(G)$, for all connected graphs $G$.

math.CO↗

arXiv2023

Two Parallel PageRank Algorithms via Improving Forward Push

Initially used to rank web pages, PageRank has now been applied in many fields. With the growing scale of graph, accelerating PageRank computing is urged and designing parallel algorithm is a feasible solution. In this paper, two parallel PageRank algorithms IFP1 and IFP2 are proposed via improving the state-of-the-art Personalized PageRank algorithm, i.e., Forward Push. Theoretical analysis indicates that, IFP1 can take advantage of the DAG structure of the graph, where the dangling vertices improves the convergence rate and the unreferenced vertices decreases the computation amount. As an improvement of IFP1, IFP2 pushes mass to the dangling vertices only once but rather many times, and thus decreases the computation amount further. Experiments on six data sets illustrate that both IFP1 and IFP2 outperform Power method, where IFP2 with 38 parallelism can be at most 50 times as fast as the Power method.

cs.DS↗

arXiv2022

Construction, Extension and Paths of Near-Homogeneous Tournaments

A homogeneous tournament is a tournament with $4t+3$ vertices such that every arc is contained in exactly $t+1$ cycles of length $3$. Homogeneous tournaments are the first class of tournaments that are proved to be path extendable, which means that every nonhamiltonian path $P$ in such a tournament $T$ can be extended to a path $P'$ with the same initial and terminal vertex and $V(P')=V(P)\cup \{u\}$ for a certain vertex $u\in V(T)\backslash V(P)$. In order to find more path extendable tournaments we study the generalization of homogeneous tournaments called near-homogeneous tournaments, in which every arc is contained in $t$ or $t+1$ cycles of length $3$. Near-homogeneity has been defined in tournaments with $4t+1$ vertices. In this paper, we raise a new method to construct near-homogeneous tournaments with $4t+1$ vertices. We then show that the definition of near-homogeneous tournament can be extended to tournaments with an even number of vertices. Finally we verify path extendability of near-homogeneous tournaments, thus expand the class of path extendable tournaments.

math.CO↗

arXiv2021

A Parallel PageRank Algorithm For Undirected Graph

As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph under investigation is directed or not. Thus, some important properties of undirected graph\textemdash symmetry on edges, for example\textemdash is ignored. In this paper, we propose a parallel PageRank algorithm specifically designed for undirected graphs that can fully leverage their symmetry. Formally, our algorithm extends the Chebyshev Polynomial approximation from the field of real function to the field of matrix function. Essentially, it reflects the symmetry on edges of undirected graph and the density of diagonalizable matrix. Theoretical analysis indicates that our algorithm has a higher convergence rate and requires less computation than the Power method, with the convergence rate being up to 50\% higher with a damping factor of $c=0.85$. Experiments on six datasets illustrate that our algorithm with 38 parallelism can be up to 39 times faster than the Power method.

cs.NI↗