A novel modeling approach for vertical handover based on dynamic k-partite graph in heterogeneous networks

The future network world will be embedded with different generations of wireless technologies,such as 3G,4G and 5G.At the same time,the development of new devices equipped with multiple interfaces is growing rapidly in recent years.As a consequence,the vertical handover protocol is developed in order to provide ubiquitous connectivity in the heterogeneous wireless environment.Indeed,by using this protocol,the users have opportunities to be connected to the Internet through a variety of wireless technologies at any time and anywhere.The main challenge of this protocol is how to select the best access network in terms of Quality of Service(QoS)for users.For that,many algorithms have been proposed and developed to deal with the issue in recent studies.However,all existing algorithms permit only the selection of one access network from the available networks during the vertical handover process.To cope with this problem,in this paper we propose a new approach based on k-partite graph.Firstly,we introduce k-partite graph theory to model the vertical handover problem.Secondly,the selection of the best path is performed by a robust and lightweight mechanism based on cost function and Dijkstra’s algorithm.The experimental results show that the proposed approach can achieve better performance of QoS than the existing algorithms for FTP traffic and video streaming.

Perfect Matching in k-partite k-graphs and 3-uniform HM-bipartite Hypergraphs

Let H=(V,E)be an n-balanced k-partite k-graph with partition classes V1,...,Vk.Suppose for every legal(k-1)-tuple f contained in V\V1 and for every legal(k-1)-tuple g contained in V\Vk such that f∪g■E(H),we have d(f)+d(g)≥n+1.In this paper,we prove that under this condition H must have a perfect matching.Another result of this paper is about the perfect matching in 3-uniform hm-bipartite hypergraphs.Let G be a 3-uniform hm-bipartite hypergraph with one of whose sides V1 has the size n,the another side V2 has size 2 n.If for all the legal 2-tuple f with|f∩V1|=1 and for all the legal 2-tuple g with|g∩V1|=0,we have d(f)≥n-2 and d(g)>n/2,then G has a perfect matching.

An O(k^2n^2) Algorithm to Find a k-Partition in a k-Connected Graph

Although there are polynomial algorithms of finding a 2-partition or a 3-partition for a simple undirected 2-connected or 3-connected graph respectively, there is no general algorithm of finding a k-partition for a k-connected graph G = (V, E), where k is the vertex connectivity of G. In this paper, an O(k2n2) general algorithm of finding a k-partition for a k-connected graph is proposed, where n = |V|.

The Fractional Metric Dimension of Permutation Graphs

Let G =（V（G）, E（G）） be a graph with vertex set V（G） and edge set E（G）. For two distinct vertices x and y of a graph G, let RG{x, y} denote the set of vertices z such that the distance from x to z is not equa l to the distance from y to z in G. For a function g defined on V（G） and for U V（G）, let g（U） =∑s∈Ug（s）. A real-valued function g ： V（G） → [0, 1] is a resolving function of G if g（RG{x, y}） ≥ 1 for any two distinct vertices x, y ∈ V（G）. The fractional metric dimension dimf（G）of a graph G is min{g（V（G）） ： g is a resolving function of G}. Let G1 and G2 be disjoint copies of a graph G, and let σ ： V（G1） → V（G2） be a bijection. Then, a permutation graph Gσ =（V, E） has the vertex set V = V（G1） ∪ V（G2） and the edge set E = E（G1） ∪ E（G2） ∪ {uv ｜ v = σ（u）}. First,we determine dimf（T） for any tree T. We show that 1 〈 dimf（Gσ） ≤1/2（｜V（G）｜ ＋ ｜S（G）｜） for any connected graph G of order at least 3, where S（G） denotes the set of support vertices of G. We also show that, for any ε 〉 0, there exists a permutation graph Gσ such that dimf（Gσ）- 1 〈 ε. We give examples showing that neither is there a function h1 such that dimf（G） 〈 h1（dimf（Gσ）） for all pairs（G, σ）, nor is there a function h2 such that h2（dimf（G）） 〉 dimf（Gσ） for all pairs（G, σ）. Furthermore,we investigate dimf（Gσ） when G is a complete k-partite graph or a cycle.

Improvement on the Neural Algorithm for Communication Network Partitioning Design

In paoer ,an algorithn based on neural network was propsced for the communication metwork k-partitioning design.This paper simplifies the energy function,so that the optimal solution can be got nore easily,Computer simulation results demonstrate the effectiveness of the algorithm.