Network Algorithms, Lecture 1: Intro and Principles

1. Network Algorithms, Lecture 1: Intro and Principles George Varghese, UCSD

3. Course Goal • Network Algorithms: Algorithms for key bottlenecks in a router (lookups, switching, QoS) • How to attack new bottlenecks: Changing world -> measurement, security • Algorithmics: Models and Principles. System thinking + Hardware + Algorithms

4. Different Backgrounds • Balaji: Stochastic Processes, randomized algorithms, QCN, DCTCP, 2 yr at Cisco (Nuova) • Tom: Former Cisco VP and Fellow. Architect of Cisco Catalyst and Nexus • Me: Algorithmic background. DRR, IP lookups. 1 year at Cisco (NetSift) • All worked on router bottlenecks. Want to reconcile our viewpoints. Fun for you

5. Course Grading • 4 Homeworks: 20% • Posted Weds, due Thus by 2pm • Course Project: 80% • Teams of 2 students • Ideally, original idea related to course leading to a paper; or, a detailed review of paper(s) on a topic. • 1 page abstract due by Mon, Apr 18th • Final project presentation + 5 page report • Office hours: • Balaji: Tuesday 10-11 -- George Wednesday 10-11 • TA: Mohammed, introduction

6. Course Outline • Lectures 1 to 2: Principles and Models • Lectures 3 to 5: Lookups • Lectures 6 to 9: Switching • Lectures 10 to 11: QoS • Later lectures: measurement, security, data center switching fabrics, congestion control, etc

7. Plan for Rest of Lecture • Part 1: Warm up example of algorithmic thinking • Part 2: Ten Principles for Network Algorithms

8. Warm Up: Scenting an Attack • Observation: Large frequency of uncommon characters within code buried in say URL. • Goal: Flag such packets for further observation.

9. Strawman Solution • Strawman: Increment character count and flag if any over threshold. • Problem: Second pass over array after packet

10. Oliver Asks for Less • Idea:Relax specification to alarm if count over threshold wrt current and not total length • Problem: Corner cases for small lengths

11. Oliver uses Algorithmic Thinking • Idea: Keep track of max relativized count and compare to length L at end. • Problem: Still 2 Reads, 1 Write to Memory. 1 Read is free (parallelism, wide memories)

12. Relax Specification: Approximate! • Idea: Round up thresholds to powers of 2 to use shifts. Have false positives anyway. • Problem: Initialize counts per packet

13. Lazy initialization • Idea: Use generation number and lazy count initialization. • Problem: Generation number wrap (Scrub)

14. Part 2, Ten Principles for Network Algorithms

15. Summary • P1: Relax Specification for efficiency • P2: Utilize degrees of freedom • P3: Shift Computation in Time • P4: Avoid Waste seen in a holistic view • P5: Add State for efficiency • P6: Exploit hardware parallelism and memories. • P7: Pass information (e.g., hints) in interfaces • P8: Use finite universe methods (bucket-sort etc) • P9: Use algorithmic thinking • P10: Optimize the Expected Case

16. P1: Relax Specifications IntServ Spec: Serve smallest, requires sorting DRR: Throughput fair, modify round robin, O(1) Router Output Queue Scheduling 1500 800 50

17. Forms of relaxing specification • Probabilistic: use randomization • Ethernet, RED • Approximate: • RED,TCP Round trip weights • Shift computation in space: Path MTU Calculate Min segment Size R1 E R2 4000 1500 Fragment?

18. P2: Utilize degrees of Freedom • Have you used all information (Polya)? • TCP: Reduce rate on drop; later, on ECN set • DCTCP: Use number of ECN bits set in window Calculate Send rate R1 E R2 10 G 1 G Pass ECN Bit

19. P2 in IP Lookups • Have you used all knobs under your control? Multiibit Trie: Many bits, 2 Reads Unibit Trie: One bit at a time P7 = 1000000*  5 Reads

20. P2 in Algorithms (keyword search) We hold these truths Last character first Boyer Moore truths

21. P3:Shift Computation in Time • Precompution: slow update, fast lookup • Lazy Evaluation: counter initialization • Expense Sharing (batching): timing wheels P7 = 100000* P6 = 10000* Precomputed Prefix of 100010

22. P4: Avoid Waste • When viewing system holistically • e.g: packet copies 3 bits 2 bits Avoid waste

23. P5: Add State • Those who do not learn from history . . . • BIC, QCN: Remember past high rate Past high Start here?

24. P6: Leverage Hardware • Exploit Parallelism (memory and processing) • Leverage diff memories: SRAM, DRAM, EDRAM 00000001 Touched rarely Keep in Slow memory Touched often Keep in Fast memory 00000101 00000011 Large set of Counters

25. P7: Pass information across layers • Do not hide information • Pass “hints” Add index to list Bypassing the Kernel in VIA

26. P8: Finite Universe Techniques • Bit Maps: Saves space & time by HW parallelism • Bucket sorting: skipping over empty elements? 11 14 12 13 TimerQueue

27. P8: Finite Universe Techniques • Cost of skipping empty buckets shared with incrementing current time. (P2) Current time = 10 11 12 13 Timerwheel 14

28. P9: Use Algorithmic Ideas • Not blindly reusing algorithms but using ideas • Binary Search on Hash Tables: 1 2 3 4 8 01 * 101* 11100000* 10000000* Or here? Start here

29. P10: Optimize Expected Case • Mostly worst case, sometimes expected case • Optimization should not be caught by testing! D, M E D D D->M Cache Router Instead of maintaining separate HW threads for cached and uncached, drop uncached!

30. Summary • P1: Relax Specification for efficiency • P2: Utilize degrees of freedom • P3: Shift Computation in Time • P4: Avoid Waste seen in a holistic view • P5: Add State for efficiency • P6: Exploit hardware parallelism and memories. • P7: Pass information (e.g., hints) in interfaces • P8: Use finite universe methods (bucket-sort etc) • P9: Use algorithmic thinking • P10: Optimize the Expected Case

31. Summing up • Course: router bottlenecks/network algorithms • Not just a recipe book but a way of thinking • Will see principles in action in later lectures • Next lecture: hardware models by Tom