1. AHOP Problem and QoS Route Pre-computation Adam Sachitano IAL

2. Citations 1.Computing shortest paths for any number of hops, Orda and Guerin, IEEE/ACM Transactions on Networking (TON) Volume 10, Issue 5 (October 2002) p. 613 - 620 2.Precomputation schemes for QoS routing, Orda and Sprintson, IEEE/ACM Transactions on Networking (TON) Volume 11, Issue 4 (August 2003) p. 578 – 591

3. Computing shortest paths for any number of hops Known as the AHOP problem (all hops optimal path) Involves identifying the minimum weight path or paths for all hop counts Fundamental issue in QoS routing –Guarantees may include: cost, delay, bandwidth, etc. –“Determining the cheapest path available that meets a desired level of service”

4. AHOP focus Computational complexity of solving AHOP for prevalent cost functions Two solutions are presented with best known complexity Speculation on future work leading to precomputation schemes

5. AHOP Generalization from several routing algorithms used to guarantee a certain SLA on connectivity or performance Traffic must be routed along paths which can meet such guarantees at a minimal cost to the network The most general case of this problem is known to be NP-complete

6. AHOP special cases The general case is not the most interesting in routing More interesting (specific) cases related to QoS routing are solvable with tractable solutions –Minimum number of hops is a realistic and practical measure of network cost –Min-hop paths easily computed using well- known algorithms (i.e., Bellman-Ford)

7. Specific AHOP complexity Bottleneck metrics –Weight of a bottlenecked path is the maximum (or minimum) value of its link weights Additive metrics –Weight is the sum of the weights of the links that comprise the path

8. Bottleneck Metrics Common example: Bandwidth –The maximum bandwidth of a particular path between points A and B cannot be greater than the minimum bandwidth of the links composing the path

9. Additive Metrics Common example: End-to-end delay –The total delay of a particular path between points A and B is not less than the sum of the delays of the links composing that path

10. AHOP vs. shortest-path For the shortest-path problem, the same solution can be used for additive and bottleneck metrics. For the AHOP problem, the solutions and complexities of those solutions for additive and bottleneck metrics differ

11. AHOP short story Lower-bound for additive metrics is Ω(N 3 ) –AHOP for additive metrics is a problem which contains the Restricted Shortest Path problem, which is known to be NP-hard Average case for bottleneck metrics is O(N 3 /log(N)) Pseudocode and analyses of algorithms corresponding to these results is presented in [1]

12. Conclusions Authors establish worst-case complexities for AHOP in general Authors show that special cases of AHOP are more pertinent to QoS and show better worst-case complexities for these Authors presented algorithms which solve the special cases in the presented run times

13. Benefits and Caveats Important in QoS: Solving AHOP computes, for each hop count n, the best service guarantees feasible between a source node and all other destinations on the network However, even if the solutions are tractable, performing them repeatedly (i.e., for repeated requests) will be computationally expensive

14. Future work Segue into Precomputation Computing AHOP for all possible sources as well Formulate the possibility for a “route server” which would be a network element that performs these AHOP computations for all sources/destinations (offloading this burden from core routers) Such a network element would require an efficient scheme of precomputation

15. Justification of Precomputation Providing for the growth in data traffic and network capabilities requires new ways of managing networks This is currently infeasible due to constraints on computing power of existing core network elements

16. Precomputation Precomputation-based methods have been proposed as a means to: –facilitate scalability –improve response time –reduce computation load on network elements

17. Precomputation on core elements Computing AHOP on-line and on-demand during periods of high load will only increase the burden on core network elements Solution: Use periods of low processor load to perform QoS routing-related computations (such as solving AHOP) in advance as background processes Subsequent requests which have a solution due to this advanced preparation could be served and routed instantly

18. Precomputation on core elements On networks of typical hierarchical topology, precomputation can lead to improvements in network overhead by reducing amortized computation costs at core network elements

19. Precomputation Mechanics Precomputation is achieved by a two-step precomputation scheme: –Advanced preparation: precomputation of paths for varying event parameters (scope determined by feasibility) –Event arrival: events are dispatched according to a precomputed route meeting the event’s QoS needs

20. A priori preparation A core router could compute AHOP for all known destinations for a variety of possible event parameters –Complete routes could be stored if time and space are available –Partial computations which would support faster route resolution could be stored Core routers would have to be pre-configured as to which route metrics to consider in this step

21. Event Arrival Assuming that some method of storing complete routes resulting from the a priori phase is available, event arrivals will be handled by ‘looking up’ an acceptable route OR Assuming that only partial computations are carried out in the a priori phase, additional computations would have to be carried out here

22. Delay example Suppose a router is configured to consider delay- based SLAs on a network Router spends periods of low load precomputing AHOP routes from itself to known destinations for a certain (controllable) range of possible delay constraints Incoming events are reconciled with precomputed delay ranges, an acceptable route is selected, and the event is dispatched

23. Scalability Benefits: Traditional vehicles for facilitating scalability: –Reducing network element load –Limiting the amount of link state information Precomputation provides for both of these, resulting in lower total overhead across the network

24. Fault Tolerance Benefits: Failures of network elements must be handled by rerouting traffic around the failure This can be handled more quickly if alternative routes have been precomputed

25. Benefits to bursty traffic / load balancing: Periods of bursty traffic can be handled with lower amortized overhead A packet’s time in a router’s queue would be reduced due to lower overhead in dispatching previous requests If a number of routes for a given SLA have been computed, then events requesting that SLA can be evenly dispatched among the different acceptable precomputed paths

26. Current uses of precomputation comparison IP static routing tables QoS has higher overhead than standard IP routing QoS complexity and demanding SLAs make QoS computation more desirable

27. Problem: Precomputation in hierarchical networks In networks composed of subdomains, knowledge about the internal structure of a subdomain may be restricted A scheme for topology aggregation is briefly presented

28. Topology aggregation A network composed of subnetworks is analyzed according to links in and out of the subnetworks. Unrestricted information about the subnetwork is “published” by border routers on these links This information is used by outside routers in precomputation schemes Such a scheme provides for more scalable QoS routing

29. Complexity For bottleneck metrics, the IBF method presented in the AHOP paper is used Though a lower-bound was shown in the AHOP paper for additive metrics, the problem in general is NP-hard (it contains RSP) Instead of the method presented in AHOP, a polynomial-time method which gives an eta- approximation of an optimal solution is presented and analyzed Given the methods presented in the paper, overall load is reduced by precomputation [2]

30. Future work A more in-depth investigation into when precomputation should be applied Methods to perform precomputation sporadically and recompute only when the network changes drastically. “Route server” network elements –For each routing subdomain, install a network element tasked solely with precomputation and handling of route requests from core routers in its peer group