An Efficient Algorithm for OSPF Subnet Aggregation ICNP 2003

1. An Efficient Algorithm for OSPF Subnet AggregationICNP 2003 Aman Shaikh Dongmei Wang, Guangzhi Li, Jennifer Yates, Charles Kalmanek University of California, Santa Cruz (UCSC) AT&T Labs - Research ICNP 2003

2. Motivation • As OSPF areas grow (number of routers, number of subnets), scalability problems arise • Number of updates, routing table size… • Aggregation of subnet addresses into less specific prefixes across OSPF areas reduces resource consumption • Price: sub-optimal forwarding! • Aggregates are configurable in router: how should these be selected? • Trade-off between amount of aggregation and sub-optimality in forwarding • Algorithm by Rastogi et al., Infocom 2002 • Requires complete topology of the entire OSPF domain ICNP 2003

3. Contribution • Theorem: errors caused by sub-optimal forwarding can be bounded using ONLY parameters local to an area • Aggregation algorithm: select minimum number of aggregates such that errors due to sub-optimal forwarding is minimized • Can be applied on a per-area basis • Big plus from operational point-of-view • Ability to trade-off number of aggregates versus sub-optimality in forwarding • Amenable to on-line implementation ICNP 2003

4. Overview of OSPF • OSPF is a link-state protocol • Every router learns entire network topology within same area • Routers are vertices, links are edges • Every link assigned weights through configuration • Every router uses Dijkstra’s single source shortest path algorithm to build its forwarding table • Router runs Dijkstra’s algorithm with itself as the root • Packets are forwarded along shortest paths defined by link weights ICNP 2003

5. Border routers Area 1 Area 2 Areas in OSPF • OSPF allows domain to be divided into areas for scalability • Areas are numbered 0, 1, 2 … • Hub-and-spoke with area 0 as hub • Every link assigned to exactly one area • Routers with links in multiple areas are called border routers Area 0 ICNP 2003

6. OSPF domain R1’s View R1 R1 Area 0 Area 0 200 100 200 100 R2 R3 R2 R3 400 500 400 500 300 200 300 200 B1 B2 B1 B2 20 10 C1 C2 50 60 70 20 10 10.10.5.0/24 10.10.4.0/24 10.10.5.0/24 10.10.4.0/24 Area 1 Area 1 Summarization with Areas • Each router learns • Entire topology of its attached areas • Information about subnets in remote areas and their distance from the border routers • Distance = sum of link costs from border router to subnet ICNP 2003

7. R1 R1’s View Area 0 200 100 R2 R3 400 500 300 200 B1 B2 70 = max(20, 70) 60 = max(10, 60) Area 1 10.10.4.0/23 Aggregation • Border routers can aggregate multiple subnets into a single less specific prefix • Distance assigned to aggregate = max(distance to subnets covered by the aggregate) • Advantage: reduction in resource consumption • Disadvantage: leads to sub-optimal forwarding as packets may not be forwarded along the shortest paths ICNP 2003

8. 70 60 Selected path to 10.10.4.0/24 due to aggregate 10.10.4.0/23 Shortest path to 10.10.4.0/24 10.10.4.0/23 Path Selection Error R1 Area 0 R1’s View 200 100 R2 R3 400 500 300 200 B1 B2 Area 1 20 60 10.10.4.0/24 • Path selection error for source-destination pair due to aggregates = • distance of the selected path - distance along the shortest path Optimization problem: find minimum number of aggregates such that maximum path selection error is minimized ICNP 2003

9. Path length from source s to subnet t Increase in path length from source s to subnet t due to aggr. X s B1 t X No path selection error s B2 t X Same increment via B1 and B2 No path selection error s B2 t X < Diff. in increment Diff. in path lengths Path selection error < s B2 t X Diff. in increment Path selection error  max |diff. in incr. by border rtrs i & j| Max is taken over all border router pairs Error bound Does not depend on source, hence can be determined by parameters local to area Bound on Path Selection Error ICNP 2003

10. Aggregation Algorithm • Optimization problem: select minimum number of aggregates such that path selection error bound is minimized • Error bound can be determined using parameters local to area • Algorithm • Step 1: Determine a set of candidate aggregates • Use of an Aggregate Tree [Rastogi:02] to identify candidate aggregates • Step 2: Select set of aggregates from candidate aggregates such that path selection error bound is minimized • Dynamic program based algorithm ICNP 2003

11. subnet aggregate 10.10.4.0/21 Set 1 of aggrs. 10.10.4.0/22 10.10.2.0/23 Set 2 of aggrs. 10.10.6.0/23 10.10.4.0/23 10.10.3.0/24 10.10.2.0/24 10.10.7.0/24 10.10.6.0/24 10.10.5.0/24 10.10.4.0/24 Step 1: Creating Aggregate Tree • Binary tree where each node = prefix A/M • A = IP address, M = mask • Leaves represent subnet prefixes • Edge represents “prefix-containment” relationship • Parent prefix contains prefixes of its two children • Each node covers all nodes in its sub-tree ICNP 2003

12. Step 2: Aggregate Selection • Find m aggregates (1 m no. subnets) satisfying error bound • Minimize m through binary search • To find m aggregates (recursive) • Option 1: Include root • Have to find (m – 1) aggregates from two sub-trees • Try to find n aggregates from left sub-tree and (m – 1 – n) aggregates from right sub-tree • Option 2: Do not include root • Have to find m aggregates from two sub-trees • Try to find n aggregates from left sub-tree and (m – n) aggregates from right sub-tree ICNP 2003

13. Performance Evaluation • Evaluation using simulated network topologies • Topology represented by • N subnets, B border routers • Compact address assignment to the subnets • B x N distance matrix • Individual elements chosen randomely between Dmin and Dmax • Investigated: • Effectiveness of algorithm as error bound increases • Number of subnets (N), number of border routers (B), distance of border routers to subnet (Dmax – Dmin) • Run-time and memory usage • Scaling with number of subnets (N) and error bound ICNP 2003

14. Effectiveness of Algorithm • Number of border routers (B) = 2, Dmax – Dmin = 100 • Observations: • Reduction in number of aggregates by 50% for 25 % error bound • Number of subnets has no impact on effectiveness ICNP 2003

15. Effectiveness of Algorithm (cont’d.) • Number of subnets (N) = 80, Dmax – Dmin = 100 • Observation: effectiveness of the algorithm decreases as number of border routers (B) increases • Random selection of distances exacerbates problem ICNP 2003

16. Run-time of Aggregate Selection Algorithm • Number of border routers (B) = 2, Dmax – Dmin = 100 • Observations: • Lower the error bound, higher the run-time • Run-time lies between O(N3) and O(N4) ICNP 2003

17. Algorithm Memory Usage • Number of border routers (B) = 2, Dmax – Dmin = 100 • Observation: space complexity is O(N3) • Majority consumed by array used for dynamic programming • Very little of this space is actually utilized ICNP 2003

18. Summary • Result: Path selection error due to aggregation in OSPF can be bounded by ONLY parameters local to an area • Aggregation Algorithm: Select minimum number of aggregates such that bound on path selection error is minimized • Can be applied on a per-area basis • Big plus from operational point-of-view • Ability to trade-off number of aggregates with path selection error • Amenable to on-line implementation • Performance: Effective in reducing the number of aggregates (50%) with a small error (25%) • Effectiveness decreases as number of border routers increases ICNP 2003

19. Future Work • Evaluate effectiveness of algorithm on real OSPF network topologies • Reduce overall algorithm space and time complexities • Improve effectiveness of algorithm as number of border routers increases • Related subject: algorithm for assigning addresses to subnets to maximize algorithm effectiveness ICNP 2003