A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs
Abstract
:1. Introduction
- The MCOAP model is proposed from an approximate point of view. In the case that most important service performance of WMNs is guaranteed, the model can also consider multiple QoS metrics in WMNs;
- The problem of MCOAP is formulated, then an approximation algorithm called HMAA, which approximates QoS constraints with a specific constraint, is developed;
- The theoretical properties of the proposed algorithm are analyzed. The analysis results show that the proposed algorithm achieves lower complexity and approximate optimal solution for WMNs.
2. Problem Description and Related Works
3. An Anypath Routing Approximation Algorithm for QoS
3.1. Design of HMAA Algorithm
3.1.1. HMAA Algorithm Implementation Steps Are as Follows
3.1.2. Detailed Procedure of HMAA Algorithm
Algorithm 1. HMAA algorithm. |
Input:, the source node s, the destination node t |
Output: Anypath |
1. for each in do |
2. |
3. |
4. |
5. end for |
6. |
7. |
8. |
9. while & do |
10. |
11. |
12. |
13. for each incoming link in E do |
14. |
15. |
16. if then |
17. |
18. |
19. |
20. for do |
21. |
22. end for |
23. end if |
24. end for |
25. end while |
26. if |
27. ; OUTPUT ; |
28. else Output NO Feasible Anypath; |
29. end if |
30. END |
3.1.3. An Example of HMAA Algorithm
- (a)
- In system initialization, the first node t is cleared to zero, then added to the anypath P;
- (b)
- After the node t is added to the queue P, and of the neighbors of node t (cyan nodes u4, u3 and u5) are updated by the red dotted arrows, respectively, so that and . Thus, the values of the other two nodes (blue font marked next to the node) can be obtained in the same way;
- (c)
- Compare the values of nodes (u3, u4, u5), the smallest node is u4, which is added to queue P, then the determined edge link is updated as shown in bold arrows. Update and of neighbor nodes (u1, u3) of u4, it can obtain , , , ;
- (d)
- Compare the values of nodes (u1, u3), the smallest node is u3, which is added to queue P. Update and of neighbor node u1, it can obtain , , . Thus, the values of node u2 can also be obtained (blue font marked above the node);
- (e)
- Compare the values of nodes (u1, u2), the smallest node is u1, which is added to queue P. Update and of neighbor node s, it can obtain , , ;
- (f)
- Through the reverse order search, the source node s is finally added to the queue P, and the anypath routing is found. Thus, the first weight can be obtained by and . Check the first constraint that , then the HMAA algorithm ends and the anypath routing is found, where .
3.2. Analysis of HMAA Algorithm
4. Simulation Experiment and Performance Evaluation
4.1. Experiment and Analysis of HMAA Algorithm Operation Efficiency
4.2. Experiment on Real WMNs Network for HMAA Algorithm
4.3. Experiment and Analysis of HMAA Algorithm
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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s, t | the source node and the destination node, respectively |
m, n | the edge and the node number of graph G, respectively |
ith weight of node v | |
forwarding probability from node v to node u | |
F | forwarding sets of node v |
forwarding probability from node v to forwarding sets F | |
K | the number of QoS requirements |
the set of weights of the edges | |
the set of constraints | |
ith QoS requirement | |
the anypath routing from source node s to destination node t | |
the optimal anypath routing | |
the approximate optimal anypath routing | |
ith weight from node v to destination node t along | |
the maximum weight of node v | |
the maximum weight from node v to destination node t along | |
the maximum weight from forwarding sets F to destination node t along |
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Yang, W.; Zeng, X.; Lai, G. A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs. Mathematics 2022, 10, 4557. https://doi.org/10.3390/math10234557
Yang W, Zeng X, Lai G. A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs. Mathematics. 2022; 10(23):4557. https://doi.org/10.3390/math10234557
Chicago/Turabian StyleYang, Weijun, Xianxian Zeng, and Guanyu Lai. 2022. "A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs" Mathematics 10, no. 23: 4557. https://doi.org/10.3390/math10234557
APA StyleYang, W., Zeng, X., & Lai, G. (2022). A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs. Mathematics, 10(23), 4557. https://doi.org/10.3390/math10234557