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Xirong Xu

Publications and source records attributed to Xirong Xu.

15 recordsLinked to original sources
arXiv2024

Influence Maximization in Hypergraphs Using A Genetic Algorithm with New Initialization and Evaluation Methods

Influence maximization (IM) is a crucial optimization task related to analyzing complex networks in the real world, such as social networks, disease propagation networks, and marketing networks. Publications to date about the IM problem focus mainly on graphs, which fail to capture high-order interaction relationships from the real world. Therefore, the use of hypergraphs for addressing the IM problem has been receiving increasing attention. However, identifying the most influential nodes in hypergraphs remains challenging, mainly because nodes and hyperedges are often strongly coupled and correlated. In this paper, to effectively identify the most influential nodes, we first propose a novel hypergraph-independent cascade model that integrates the influences of both node and hyperedge failures. Afterward, we introduce genetic algorithms (GA) to identify the most influential nodes that leverage hypergraph collective influences. In the GA-based method, the hypergraph collective influence is effectively used to initialize the population, thereby enhancing the quality of initial candidate solutions. The designed fitness function considers the joint influences of both nodes and hyperedges. This ensures the optimal set of nodes with the best influence on both nodes and hyperedges to be evaluated accurately. Moreover, a new mutation operator is designed by introducing factors, i.e., the collective influence and overlapping effects of nodes in hypergraphs, to breed high-quality offspring. In the experiments, several simulations on both synthetic and real hypergraphs have been conducted, and the results demonstrate that the proposed method outperforms the compared methods.

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arXiv2023

Influence Maximization based on Threshold Model in Hypergraphs

Influence Maximization problem has received significant attention in recent years due to its application in various do?mains such as product recommendation, public opinion dissemination, and disease propagation. This paper proposes a theoretical analysis framework for collective influence in hypergraphs, focusing on identifying a set of seeds that maximize influence in threshold models. Firstly, we extend the Message Passing method from pairwise networks to hypergraphs to accurately describe the activation process in threshold models. Then we introduce the concept of hyper?graph collective influence (HCI) to measure the influence of nodes. Subsequently, We design an algorithm, HCI-TM, to select the Influence Maximization Set, taking into account both node and hyperedge activation. Numerical simu?lations demonstrate that HCI-TM outperforms several competing algorithms in synthetic and real-world hypergraphs. Furthermore, we find that HCI can be used as a tool to predict the occurrence of cascading phenomena. Notably, we find that HCI-TM algorithm works better for larger average hyperdegrees in Erdos-Rényi (ER) hypergraphs and smaller power-law exponents in scale-free (SF) hypergraphs.

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arXiv2019

Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks THLNs

The twisted hypercube-like networks($THLNs$) contain several important hypercube variants. This paper is concerned with the fault-tolerant path-embedding of $n$-dimensional($n$-$D$) $THLNs$. Let $G_n$ be an $n$-$D$ $THLN$ and $F$ be a subset of $V(G_n)\cup E(G_n)$ with $|F|\leq n-2$. We show that for arbitrary two different correct vertices $u$ and $v$, there is a faultless path $P_{uv}$ of every length $l$ with $2^{n-1}-1\leq l\leq 2^n-f_v-1-α$, where $α=0$ if vertices $u$ and $v$ form a normal vertex-pair and $α=1$ if vertices $u$ and $v$ form a weak vertex-pair in $G_n-F$($n\geq5$).

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arXiv2018

Decycling Number of Linear Graphs of Trees

The decycling number of a graph $G$ is the minimum number of vertices whose removal from $G$ results in an acyclic subgraph. It is known that determining the decycling number of a graph $G$ is equivalent to finding the maximum induced forests of $G$. The line graphs of trees are the claw-free block graphs. These graphs have been used by Erdős, Saks and Sós to construct graphs with a given number of edges and vertices whose maximum induced tree is very small. In this paper, we give bounds on the decycling number of line graphs of trees and construct extremal trees to show that these bounds are the best possible. We also give bounds on the decycling number of line graph of $k$-ary trees and determine the exact the decycling number of line graphs of perfect $k$-ary trees.

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arXiv2012

The crossing number of pancake graph $P_4$ is six

The {\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six.

cs.DM↗
arXiv2012

An upper bound for the crossing number of bubble-sort graph Bn

The crossing number of a graph G is the minimum number of pairwise intersections of edges in a drawing of G. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory 59, 145-161 (2008)], we give an upper bound of the crossing number of n-dimensional bubble-sort graph Bn.

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arXiv2012

Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

As the size of a multiprocessor system increases, processor failure is inevitable, and fault identification in such a system is crucial for reliable computing. The fault diagnosis is the process of identifying faulty processors in a multiprocessor system through testing. For the practical fault diagnosis systems, the probability that all neighboring processors of a processor are faulty simultaneously is very small, and the conditional diagnosability, which is a new metric for evaluating fault tolerance of such systems, assumes that every faulty set does not contain all neighbors of any processor in the systems. This paper shows that the conditional diagnosability of bubble sort graphs $B_n$ under the PMC model is $4n-11$ for $n \geq 4$, which is about four times its ordinary diagnosability under the PMC model.

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arXiv2011

The crossing number of locally twisted cubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erdős and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.

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arXiv2011

On the 3-$γ_t$-Critical Graphs of Order $Δ(G)+3$

Let $γ_t(G)$ be the total domination number of graph $G$, a graph $G$ is $k$-total domination vertex critical (or\ just\ $k$-$γ_t$-critical) if $γ_t(G)=k$, and for any vertex $v$ of $G$ that is not adjacent to a vertex of degree one, $γ_t(G-v)=k-1$. Mojdeh and Rad \cite{MR06} proposed an open problem: Does there exist a 3-$γ_t$-critical graph $G$ of order $Δ(G)+3$ with $Δ(G)$ odd? In this paper, we prove that there exists a 3-$γ_t$-critical graph $G$ of order $Δ(G)+3$ with odd $Δ(G)\geq 9$.

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arXiv2011

Roman domination number of Generalized Petersen Graphs P(n,2)

A $Roman\ domination\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\rightarrow\{0,1,2\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\sum_{u\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\ domination\ number$ of $G$, denoted by $γ_{R}(G)$. In this paper, we study the {\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $γ_R(P(n,2)) = \lceil {\frac{8n}{7}}\rceil (n \geq 5)$.

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arXiv2011

On the Domination Number of Generalized Petersen Graphs P(ck,k)

Let $G=(V(G),E(G))$ be a simple connected and undirected graph with vertex set $V(G)$ and edge set $E(G)$. A set $S \subseteq V(G)$ is a $dominating$ $set$ if for each $v \in V(G)$ either $v \in S$ or $v$ is adjacent to some $w \in S$. That is, $S$ is a dominating set if and only if $N[S]=V(G)$. The domination number $γ(G)$ is the minimum cardinalities of minimal dominating sets. In this paper, we give an improved upper bound on the domination number of generalized Petersen graphs $P(ck,k)$ for $c\geq 3$ and $k\geq 3$. We also prove that $γ(P(4k,k))=2k+1$ for even $k$, $γ(P(5k,k))=3k$ for all $k\geq 1$, and $γ(P(6k,k))=\lceil\frac{10k}{3}\rceil$ for $k\geq 1$ and $k\neq 2$.

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