1. Flattened Butterfly: A Cost-Efficient Topology for High-Radix Networks ______________________________ John Kim, William J. Dally &Dennis Abts Presented by: Evan Su

2. Basic metrics Basic topologies Why high-radix Router microarchitecture High-radix topologies

3. Interconnection networks used to connect processors and memories in multiprocessors, as switching fabrics for high-end routers and switches, and for connecting I/O devices. Definition: determines arrangement of channels and nodes in the network (road map) Often first step in network design

4. Performance Metrics Average Hop Count Average Latency throughput Bisection Bandwidth

5. Hop Count The number of links traversed between source and destination

6. Latency Defined as the time it takes for a packet to traverse the network Latency= Header latency + serialization latency – Header latency: head arrives at input port – Serialization: time for rest of the packet to catch up

7. Throughput Data rate (bits/sec) that the network accepts per input port Offered load - % of capacity network accepts

8. Bisection Bandwidth Split N nodes into two groups of N/2 nodes such that the bandwidth between these two groups is minimum Why is it relevant: if traffic is completely random, the probability of a message going across the two halves is ½- tells how much traffic a network can support ( ½ of total traffic bandwidth)

9. 9 Grid Hypercube Torus Criteria 64 nodes BusRing2Dtorus6-cubeFully connected Performance Bisection bandwidth 1216321024 Topology Examples

10. Why High Radix? Definition: number of inputs/outputs for each router For past 20 years, used low-radix k-ary n-cubes (torus) – Routers didn’t have enough bandwidth to support high radix Network routers have growth curve that obeys Moore’s law – Bandwidth increased – Packet length stayed the same – Latency gone down

11. Why High Radix? Approximately an order of magnitude increase in bandwidth every 5 years Bandwidth growth result of: – Increase in signaling rate – Increase in number of signals

12. High-Radix Routers

13. High-Radix vs. Low-Radix Cost Power dissipation latency

14. Cost Increasing radix of routers monotonically reduces overall cost Network cost proportional to total router bandwidth – Router pins – Connectors For fixed bisection bandwidth, cost proportional to hop count – High-radix => lower hop count

15. Cost

16. Power Power dissipated decreases with increasing radix Power proportional to number of router nodes As radix increases, hop count decreases and router nodes decrease as well – Independent of individual router node Router power due to I/O circuits, switch bandwidth. arbitration logic more complex with higher radix but negligible fraction of total power

17. Latency Bandwidth (B) is divided among 2k input and output channels so b = B/2k H = # hops t r = delay in router L = length of packets b = channel bandwidth B = total Bandwidth k = radix

18. Aspect Ratio Differentiate by dT/dk and set equal to zero Expression on right side determines router radix that minimizes network latency

19. Optimal Latency

22. Router Microarchitecture (VC) Route computation (RC) – based on info stored in header, select output port Virtual-channel allocation (VA)- packet must gain exclusive access to virtual channel of output port Switch allocation (SA)- if there is a free buffer in channel, flit can vie for access to crossbar Switch traversal (ST) – transfers flit from input to output buffers

23. Router Microarchitecture (VC)

24. Microarchitecture for High-radix Routing computation – linear function of bandwidth VC Allocator – quadratic function of input/ output ports because take bids from all ports Switch Allocator- quadratic function of ports

25. Baseline Performance Due to head of line blocking Before, overprovision switch because low cost

26. Fully buffered crossbar Separate the queuing up Had to compete for input and output of switch With crosspoint, decouples two allocations, always make forward progress

27. Fully buffered crossbar Trade performance for cost Crosspoint buffering dominates chip area (quadratic)

28. Hierarchical crossbar Using subswitches, area grows O(vk 2 / p) Decouples allocation, reduces HoL blocking V = inputs K = radix P = number of subswitches

29. Hierarchical crossbar Worst case performance Uniform random traffic

30. Okay! Back to Topologies Butterfly Clos Flattened Butterfly

31. Butterfly Network K-ary n-fly: k n network nodes Example: 2-ary 3-fly Routing from 000 to 010 – Dest address used to directly route packet – Bit n used to select output port at stage n 0 0 00 1 1 2 2 3 3 4 4 5 5 6 6 7 7 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 01 02 03 10 11 12 13 20 21 22 23 010

32. Butterfly Network Pros – Low hop count: H = log k N Cons – Deterministic routing/ no path diversity – Doesn’t exploit traffic locality

33. Clos Network nxm input switch rxr input switch mxn output switch

34. Clos Network Butterfly folded back on itself Pros – Path diversity (good performance on both benign and adversarial) Cons – Double cost of butterfly – H = 2 log k (N)

35. Folded Clos Network (Fat Tree) Similar to Clos Exploits locality

36. Flattened Butterfly Network Routers in each row are combined 4-ary 2-fly2-ary 4 -fly

37. Flattened Butterfly Network Routers in each row are combined

38. Flattened Butterfly Network On benign traffic – Approaches performance/cost of Butterfly – ½ cost of Clos network Eliminates redundant hops when no need for load balancing On adversarial traffic – Matches cost/performance of folded Clos – Order of magnitude better performance than Butterfly Use non-minimal global-adaptive routing

39. Routing In Figure, there are two minimal routes between node 0 (0000 2 ) and node 10 (1010 2 ). In general, if two nodes a and b have addresses that differ in j digits, then there are j! minimal routes between a and b. This path diversity derives from the fact that a packet routing in a flattened butterfly is able to traverse the dimensions in any order.

40. Routing Algorithms uniform random traffic worst case traffic pattern VAL = Valiant’s non-minimal oblivious algorithm MIN = minimal adaptive, UGAL = non-minimal adaptive algorithm UGAL-S = UGAL using sequential allocation CLOS AD = non-minimal adaptive routing in a flattened Clos

41. Routing Algorithms Valiant – picks random middle node b, and routes minimally from s to b and ten b to d. achieves only ½ network capacity, regardless of traffic Minimal Adaptive- chooses minimal route Adaptive Clos – minimum routing in benign traffic, folded- Clos routing in adversarial

42. Performance Comparison To compare the performance, a network of node size 1024 is taken and is constructed using the following topology by maintaining a constant bisection bandwidth.

43. Performance Comparison Uniform random trafficWorst-case traffic

44. Cost Comparison

45. Conclusion Use high-radix routers to take advantage of increased router bandwidth Flattened Butterfly exploits high-radix routers and global adaptive routing to give cost-effective network Flattened butterfly has lower hop count than folded Clos and better path diversity than conventional Butterfly On adversarial traffic, exploits global adaptive routing to match performance of folded Clos with ½ the cost