Resilient Networks Missouri S&T University CPE 6510 Graph Robustness and Algorithms

Transcription

1 Resilient Networks Missouri S&T University CPE 6510 Graph Robustness and Algorithms Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and Technology 23 February 2017 rev Egemen K. Çetinkaya

2 Graph Robustness and Algorithms Outline Introduction Connectivity improvement Diversity improvement Analysis 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 2

3 Graph Robustness and Algorithms Introduction Introduction Connectivity improvement Diversity improvement Analysis 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 3

4 Network Design and Optimization Introduction and Motivation Communication networks faces several challenges random and targeted attacks large scale disasters links and node failures Need for a cost-efficient optimization method multiple objective functions cost minimization resilience (reliability, robustness, connectivity is also used) Optimizations possible links: add or rewire new links nodes additions: location of nodes 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 4

5 Network Design and Optimization Overview Many problems are NP-hard Cost and resilience are opposing objectives Backbone and access networks differ Two methods to improve graph connectivity rewiring and link additions Realistic criterion exists can you add a direct fiber link between LA and NY? Many graph metrics exist focus on algebraic connectivity and path diversity algebraic connectivity measure robust connectivity [ÇAP+2013] path diversity is crucial for measuring survivability [RJS2014] 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 5

6 Graph Robustness and Algorithms Connectivity Improvement Introduction Connectivity improvement Diversity improvement Analysis 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 6

7 Algebraic Connectivity Improvement Background and Related Work Algebraic connectivity Laplacian matrix: diagonal depends on degree a(g) is second 2 nd smallest eigenvalue of Laplacian matrix measures robust connectivity more links failures needed to be partitioned [WM2008] Rewiring edges [SSG2013] rewiring edges to increase algebraic connectivity a(g) Adding edges [WM2008] adding edges to increase algebraic connectivity a(g) lowest degree and random 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 7

8 Algebraic Connectivity Improvement Algorithm Objective identify the best links to be added to improve a(g) reduce the cost by selecting the least cost links Candidate links heuristic is to choose lowest degree nodes search space is reduced from O(n 2 ) to O(n) [AÇS2014a] iterations depend on number of links to be added Link selection based on: a(g), cost, and parameter rank function: rank[l]=(1 )a(g) + (1 cost(l)) Output an ordered list of the best selected links (highest ranked) 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 8

9 Algebraic Connectivity Improvement Example Optimization nodes and 9 links graph 28 max. links, 28 9=19 links to be searched heuristic reduces it to be 11 links connected to lowest degree nodes For = 0, link (7,1) highest a(g); for = 1, link (0,2) lowest cost 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 9

10 Graph Robustness and Algorithms Diversity Improvement Introduction Connectivity improvement Diversity improvement Analysis 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 10

11 Path Diversity Background 0 1 D(P 2 ) = 2 / 3 P 0 2 D(P 1 ) = Path diversity measure of links and nodes in common EPD: effective path diversity [0,1) normalized diversity with respect to a single shortest path measure of E2E flow resilience TGD: total graph diversity is average of EPD for all pairs: quantifies available diversity in graph D P k 1 P k P P 0 0 [RJS2014] 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 11

12 Objective Path Diversity Improvement Algorithm identify the best links to be added to improve TGD reduce the cost by selecting the least cost links Candidate links heuristic is to choose node pairs with the lowest EPD search space is reduced from O(n 2 ) to O(nm) where m is the lowest degree node pairs Link selection based on: EPD and cost if multiple EPD candidates, select with the least cost Output an ordered list of the best selected links [AÇS2014b] 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 12

13 Topology Optimization Algorithm PD Optimization Example 4 [AÇS2014b] : Los Angeles, LA 1: Houston, TX 2: Kansas City, MO 3: Chicago, IL 4: Boston, MA 5 nodes, 5 links, 5 candidate links, lowest EPD pair Best link (1,3): the most EPD increase, least costly 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 13

14 Graph Robustness and Algorithms Analysis Introduction Connectivity improvement Diversity improvement Analysis 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 14

15 Analysis Dataset and Parameters Three real world providers CORONET Internet2 Level 3 Dataset three physical graphs 20 links to be added Varying h (5, 10, 15) and k (4, 8, 12) while λ = 0.5 Flow robustness: betweenness, closeness, degree ratio of connected components to all pairs 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 15

16 Algorithm Comparison Cost of Optimized Physical-Level Topologies CORONET Internet2 Level 3 Add 20 links in each graph, parameters: PD: h = 15, k = 12, λ = 0.5; a(g): = 0 (no cost, max a(g)) a(g) optimised graphs incur more cost a(g): CORONET > Level 3 > Internet2 PD: Internet2 > CORONET > Level 3 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 16

17 Algorithm Comparison Flow Robustness of Optimized Topologies CORONET Internet2 Level 3 Attack 50 nodes adaptively based on: betweenness, closeness, degree centrality a(g) optimised graphs react better to attacks betweenness > closeness > degree FR 0: 35/99 Level 3; 30/75 CORONET; 25/57 Internet2 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 17

18 References and Further Reading [AÇS2014a] Mohammed J.F. Alenazi, Egemen K. Çetinkaya, and James P.G. Sterbenz, Cost-efficient algebraic connectivity optimisation of backbone networks, Optical Switching and Networking, Volume 14, Part 2, pp , August [AÇS2014b] Mohammed J.F. Alenazi, Egemen K. Çetinkaya, and James P.G. Sterbenz, Cost-Efficient Network Improvement to Achieve Maximum Path Diversity, in Proceedings of the 6th IEEE/IFIP International Workshop on Reliable Networks Design and Modeling (RNDM), Barcelona, November 2014, pp [ÇAP+2015] Egemen K. Çetinkaya, Mohammed J.F. Alenazi, Andrew M. Peck, Justin P. Rohrer, and James P.G. Sterbenz, Multilevel Resilience Analysis of Transportation and Communication Networks, Telecommunication Systems, Volume 60, no. 14, pp , December February 2017 MST CPE 6510 Graph Robustness and Algorithms 18

19 References and Further Reading [RJS2014] Justin P. Rohrer, Abdul Jabbar, and James P.G. Sterbenz, Path Diversification for Future Internet End-to-End Resilience and Survivability, Telecommunication Systems, Vol. 56, no. 1, pp , May [SSG2013] A. Sydney, C. Scoglio, and D. Gruenbacher, Optimizing algebraic connectivity by edge rewiring, Applied Mathematics and Computation, vol. 219, no. 10, pp , January [WM2008] H. Wang and P.V. Mieghem, Algebraic connectivity optimization via link addition, Proc. of IEEE/ACM Bionetics, February 2017 MST CPE 6510 Graph Robustness and Algorithms 19

20 End of Foils 23 February 2017 MST CPE 6510 Graph Robustness and Algorithms 20