arXiv subjects

Xichan Liu

Publications and source records attributed to Xichan Liu.

3 recordsLinked to original sources

arXiv2023

An Adaptive Hybrid Channel Reservation Medium Access Control Protocol for Differentiated QoS

In a densely deployed distributed wireless network, there may be various types of traffic with differentiated Quality of Service (QoS) requirements. However, when the network is heavily loaded, the collision increases significantly, making it difficult to guarantee the QoS of traffic. Designing an efficient Medium Access Control (MAC) protocol to guarantee the QoS of different types of traffic is an essential research direction. Channel reservation mechanism is a promising approach to improving QoS. However, few studies have focused on the channel reservation mechanism for differentiated traffic. It is difficult to take into account both the QoS of real-time traffic and the collision issue for ordinary traffic. To address this issue, this paper proposes the Differentiated Service Guarantee Adaptive Reservation Mechanism (DSGARM) protocol. A hybrid reservation mechanism is proposed by combining the absolute reservation mechanism and the relative reservation mechanism. The absolute reservation mechanism is adopted for real-time traffic. Meanwhile, the relative reservation mechanism is adopted for ordinary traffic. An adaptive algorithm is proposed to calculate the reservation parameters that meet the delay requirements based on the network conditions. The proposed work can be widely applied in the densely deployed distributed wireless network with differentiated QoS requirements. In addition, this paper establishes a mathematical model for the proposed mechanism and theoretically analyzes the performance. Simulations verify that the mathematical model provides a good approximation of the protocol performance and demonstrates the advantages of the proposed protocol.

cs.NI↗

arXiv2023

The $A_α$ spectral radius of $k$-connected graphs with given diameter

Let $G$ be a graph with adjacency matrix $A(G)$ and degree diagonal matrix $D (G)$. In 2017, Nikiforov defined the matrix $A_α(G) = αD(G) + (1-α)A(G)$ for any real $α\in[0,1]$. The largest eigenvalue of $A_α(G)$ is called the $A_α$ spectral radius or the $A_α$-index of $G$. Let $\mathcal{G}_{n,k}^d$ be the set of $k$-connected graphs of order $n$ with diameter $d$. In this paper, we determine the graphs with maximum $A_α$ spectral radius among all graphs in $\mathcal{G}_{n,k}^d$ for any $α\in[0,1)$, where $k\geq2$ and $d\geq2$. We generalizes the results about adjacency matrix of Theorem 3.6 in [P. Huang, W.C. Shiu, P.K. Sun, Linear Algebra Appl., 488 (2016) 350--362] and the results about signless Laplacian matrix of Theorem 3.4 in [P. Huang, J.X. Li, W.C. Shiu, Linear Algebra Appl., 617 (2021) 78--99]. Furthermore, we also obtain the upper and lower bounds of the extremal graph in $\mathcal{G}_{n,k}^d$.

math.CO↗

arXiv2022

The $A_α$ spectral radius with given independence number $n-4$

Let $G$ be a graph with adjacency matrix $A(G)$ and degree diagonal matrix $D (G)$. In 2017, Nikiforov [Appl. Anal. Discrete Math., 11 (2017) 81--107] defined the matrix $A_α(G) = αD(G) + (1-α)A(G)$ for any real $α\in[0,1]$. The largest eigenvalue of $A(G)$ is called the spectral radius of $G$, while the largest eigenvalue of $A_α(G)$ is called the $A_α$ spectral radius of $G$. Let $\mathcal{G}_{n,i}$ be the set of graphs of order $n$ with independence number $i$. Recently, for all graphs in $\mathcal{G}_{n,i}$ having the minimum or the maximum $A$, $Q$ and $A_α$ spectral radius where $i\in\{1,2,\lfloor\frac{n}{2}\rfloor\,\lceil\frac{n}{2}\rceil+1,n-3,n-2,n-1\}$, there are some results have been given by Xu, Li and Sun et al., respectively. In 2021, Luo and Guo [Discrete Math., 345 (2022) 112778] determined all graphs in $\mathcal{G}_{n,n-4}$ having the minimum spectral radius. In this paper, we characterize the graphs in $\mathcal{G}_{n,n-4}$ having the minimum and the maximum $A_α$ spectral radius for $α\in[\frac{1}{2},1)$, respectively.

math.CO↗