1. 3-Approximation Algorithm for Joint Routing and Link Scheduling in Wireless Relay Networks Chi-Yao Hong ( 洪啟堯 ) and Ai-Chun Pang ( 逄愛君 ) Dept. of Electrical and Computer Engineering, National Taiwan University IEEE Transactions on Wireless Communications, Vol. 8, No 2, Feb. 2009

2. 2 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Agenda  Introduction  A joint and link-scheduling algorithm  Linear programming based routing  Makespan link scheduling  Time complexity analysis  Performance evaluation  Conclusion

3. 3 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Introduction  Resource control functions  Link scheduling algorithm  NP-complete problem [7]  Routing scheduling algorithm N-RS N-RSN-RS RS RS RS RS RSRS MR-BS MS

4. 4 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Introduction  Related work  Link scheduling algorithm  With QoS consideration [1]-[3]  Only Best-effort (BE) consideration  Without QoS consideration [4]-[7]  System throughput as an essential performance  Link scheduling algorithm+ routing algorithm  Higher time-complexity [9]

5. 5 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Introduction  Goals  Maximize the network throughput  Joint link scheduling and routing algorithms

6. 6 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Problem Definition RS MR-BS MS Network Topology  Given the network topology BSRSMS Directed Graph G=(V,E) BS RS MS (1) (2) (3) (4) (5) (6) (7)

7. 7 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Problem Definition  Given the network topology BSRSMS Directed Graph G=(V,E) BS RS MS (1) (2) (3) (4) (5) (6) (7) Conflict Graph G c =(V c,E c ) 3 1 24 57 6

8. 8 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Problem Definition  Three disjoint subsets of the vertex set V  V B : the set of BS  V R : the set of RSs  V S : the set of SSs  Traffic demands p s  Aggregate uplink traffic for n s, for all n s belong to V S BS RS MS

9. 9 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Linear Programming Based Routing  Objective function:  Minimize the scheduling length  Subject to  (1)  (2) Aggregation traffic from n i to n j The total time of n i for transmitting the data nrnr njnj Flow Conservation constraints for RS n j

10. 10 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Linear Programming Based Routing  Objective function:  Minimize the scheduling length  Subject to  (3)  (4)  (5) Each SS n s has no incoming traffic Each BS n b has no outgoing traffic The nonnegative flow constraint

11. 11 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Linear Programming Based Routing  Objective function:  Minimize the scheduling length  Subject to  (6) The traffic demand constraint p s for each SS n s

12. 12 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Makespan Link Scheduling  Input 56 1 Conflict Graph G c 32 4 7 l c (1)=1 l c (3)=3 l c (6)=6 l c (2)=2 l c (5)=5 l c (7)=7 l c (4)=4 ξ c (1)=1+2+3+4=10 ξ c (3)=3+1+4+6=14 ξ c (6)=6+3+4+7=20 ξ c (7)=7+4+5+6=22 ξ c (5)=5+2+4+7=18 ξ c (2)=2+1+4+5=12 ξ c (4)=4+1+2+3=10

13. 13 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Makespan Link Scheduling  Initialization 56 1 Conflict Graph G c 32 4 7 l c (1)=1 l c (3)=3 l c (6)=6 l c (2)=2 l c (5)=5 l c (7)=7 l c (4)=4 ξ c (1)=1+2+3+4=10 ξ c (3)=3+1+4+6=14 ξ c (6)=6+3+4+7=20 ξ c (7)=7+4+5+6=22 ξ c (5)=5+2+4+7=18 ξ c (2)=2+1+4+5=12 ξ c (4)=4+1+2+3=10

14. 14 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Makespan Link Scheduling 56 1 32 4 7 l c (1)=1 l c (3)=3 l c (6)=6 l c (2)=2 l c (5)=5 l c (7)=7 l c (4)=4 ξ c (1)=1+2+3+4=10 ξ c (3)=3+1+4+6=14 ξ c (6)=6+3+4+7=20 ξ c (7)=7+4+5+6=22 ξ c (5)=5+2+4+7=18 ξ c (2)=2+1+4+5=12 ξ c (4)=4+1+2+3=10  Slot τ=1 l c (1)=0 ξ c (1)=0+2+3+4=9 l c (5)=4 ξ c (5)=4+2+4+7=17 l c (6)=5 ξ c (6)=5+3+4+7=19

15. 15 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Makespan Link Scheduling 56 32 4 7 l c (3)=3 l c (2)=2 l c (7)=7 l c (4)=4 ξ c (3)=3+1+4+6=14 ξ c (7)=7+4+5+6=22 ξ c (2)=2+1+4+5=12 ξ c (4)=4+1+2+3=10  Slot τ=2 l c (5)=4 ξ c (5)=4+2+4+7=17 l c (6)=5 ξ c (6)=5+3+4+7=19 l c (2)=1 ξ c (2)=1+1+4+5=11

16. 16 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Time Complexity  Each time slot in Algorithm  : the maximal degree of vertices in G c  Time Complexity  k : Number of time slots

17. 17 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Performance evaluation  Simulator  For LP-routing problem: LINGO  For IMS: unknown  Data rate  Access link = 6 Mbps  Relay link = 18.36 Mbps  Comparisons  Dijkstra’s shortest path algorithm  Centralized scheduling [15] SS RS BS

18. 18 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Performance evaluation  Traffic demand p s for each SS s  Gamma distribution  P mean : mean traffic demand  P var : variance of p s

19. 19 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Performance evaluation

20. 20 Speaker : Chi-Tao Chiang ( 蔣季陶 ) Meeting 報告簡報 Conclusion  Joint routing and link-scheduling algorithm for TDMA-based relay networks  Simulation results  Better throughput than other protocols