Large-scale adaptive systems

1. Large-scale adaptive systems Lecture 3: Gossip-based algorithms Dr. Stefan Dulman s.o.dulman@tudelft.nl

2. Review previous lecture • Adaptation Mechanisms • Introduction • Feedback mechanisms • Example: Schools of fish, flocks of birds • Stigmergy • Example: Economic based mechanisms • Autopoiesis • Reinforcement learning • Example: trust-based system Large-scale adaptive systems, 2010

3. Related work • This lecture is based on the following material: • Maarten van Steen: Gossiping in Large-Scale Distributed Systems http://pds.twi.tudelft.nl/~epema/asci-a9-2010.html • OzalpBabaoglu: Complex Systemshttp://www.cs.unibo.it/~babaoglu/courses/cas/ • Giovanna diMarzoSerugendo: Adaptive Systemshttp://www.dcs.bbk.ac.uk/~dimarzo/courses/as.html Large-scale adaptive systems, 2010

4. Gossiping - Introduction • Large-scale systems around us: • Computer networks of all sorts • Supply chains (supply networks) • Peer-2-Peer data sharing systems • Sensor-actuation systems • Mobile ad-hoc networks • Size of systems increases fast • Scalability of algorithms becomes an issue • Distributed system – centralized control? • Even apparently static networks show mobility • Possible solution: IBM’s “autonomic computing” Large-scale adaptive systems, 2010

5. Autonomic computing • Large-scale systems requirements • Self configuring, self optimizing, self healing, self protecting… • Umbrella concept: “Self-*” • System characteristics: • Large number of entities interacting anyhow in simple ways • Decentralized – all “peers” are equal • Shows emergent behavior • Even if central control is applied! • Power grids, telephone systems, supply chains • Parasitic emergence is usually unforeseen (“cascade failures”) • Difficult to control (if feasible at all) Large-scale adaptive systems, 2010

6. Basic idea • Make interactions work for you rather than against you • Make use of the “parasitic behavior” – learn how to build on top of it • Simple actions based on local information • Simple interactions with neighbors • Use the power of randomization and large numbers Large-scale adaptive systems, 2010

7. Gossip-based interaction • Gossip: basic mechanism for spreading and aggregating information • Communication takes place locally • Nodes exchange information with neighbors • Robust, fast, scales well • Exchanged data can be anything • Exchanged data, references to nodes, actual programs, etc. • There is no centralized control or management Large-scale adaptive systems, 2010

8. Gossiping as a mechanism Large-scale adaptive systems, 2010

9. Gossip-based applications • Examples • Raw information dissemination • Data aggregation • Topology construction for overlay networks • Semantic clustering of nodes • Realizing storage facilities in ad hoc networks • Distributed signal processing • Not everything can be accomplished via gossiping! Large-scale adaptive systems, 2010

10. But… • Some observations • Emergent phenomena often encountered • Global properties emerging unexpectedly from local interactions • Theory is still lacking: models are difficult to validate • Adaptive random geometric graph theory • Many practical issues still to resolve • Adaptiveness (too many design-time parameters) • Security (attacking a gossip-based system is easy) • Competitive alternative single-point solutions Large-scale adaptive systems, 2010

11. Example – gossiping (multicasting) P. Eugster: Epidemic Information Dissemination in Distributed Systems (IEEE Computer, 2004)

12. Gossip (push) – fully connected network Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8 200x200 nodes Large-scale adaptive systems, 2010

13. Gossip (push-pull) – mesh network Round 1 Round 10 Round 20 Round 30 Round 40 Round 50 Round 60 Round 70 100x100 nodes, transmission range = 10 units Large-scale adaptive systems, 2010

14. Lecture 3: Overview • Introduction • Basics of gossiping algorithms • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010

15. Gossiping mechanism • Terminology • Anti-entropy: each node chooses another node and exchanges information about difference in states • Both nodes have access to identical information -> identical states • Gossiping: a node informs other nodes about its own state (infects the other nodes) and may stop • Notations • Object O has on node S the value val(O,S) and timestamp T(O,S) !!! We will use “gossiping” terminology for both mechanisms !!! Large-scale adaptive systems, 2010

16. Anti-entropy • Node S exchanges information with node S’ • Push: T(O,S’)<T(O,S) -> val(O,S’) <- val(O,S) • Pull: T(O,S’)>T(O,S) -> val(O,S) <- val(O,S’) • Push-pull: S and S’ exchange their updates • Convergence speed: • O(logn) cycles update speed for fully connected network, random unicast model • 40000 nodes – 8 cycles to computethe average value Round 1 Round 8 Large-scale adaptive systems, 2010

17. Anti-entropy analysis • Setup: a source propagates updates in a fully connected network • Pi = probability that a node has not received update after i-th cycle • Two cases: • Pull: • the node was not updated during the i-th cycle and should contact another node during next cycle • Push: • the node did not update during i-thround and no node chooses it for the next round Large-scale adaptive systems, 2010

18. Gossiping mechanism • Basic mechanism • Node S (containing the update) contacts node S’ • If node S’ knows the update • Node S stops with probability p=1/k (S is effectively removed) • Otherwise • Node S contacts another random node S’’ Large-scale adaptive systems, 2010

19. Gossiping – mathematical model S – nodes not updated I – active nodes (updated) R – passive nodes (updated) Large-scale adaptive systems, 2010

20. Gossiping – mathematical model !!! Gossiping is not perfect !!! Large-scale adaptive systems, 2010

21. Convergence speed • Demonstration sketch: • Consider at each step in time values xi • Compute the standard deviation of xi at each time round (si) • Show that si decreases exponentially with time Fully connected networks, anti-entropy Large-scale adaptive systems, 2010

22. PushSum algorithm • Simple algorithm of computing average values • Each node starts with a (random) value & a weight • Nodes exchange pieces of the value with neighbors • In time, all values converge to a common mean value • PushSum is not strictly an “anti-entropy” algorithm! Node i: 1: {(mr,t-1,ωr,t-1)} – received pairs in round t-1 2: mi,t = Σr(mr,t-1) ωi,t = Σr (ωr,t-1) 3: choose random neighbor j 4: send to i and j: ( ½ mi,t, ½ ωi,t) 5: estimate in round t is: mi,t/ωi,t D. Kempe et al.: Gossip-Based Computation of Aggregate Information (FOCS 2003)

23. PushSum example Initial values mi+ mj ⅔(mi+ mj) ⅓(mi+ mj) mj mi = = ⅔ (ωi+ωj) ⅓ (ωi+ωj) 2 ωi ωj Final values: mi+ mj = = 2 i j 3 -> ⅓(mi+ mj) 6 -> ⅔ (mi+ mj) 0.67 → ⅓ (ωi+ωj) 1.33 → ⅔ (ωi+ωj)

24. Alternative approach – PushSum alg. • Introduce notion of diffusion speed • Speed with which the initial value diffuses through the network • Introduce the protocol PushVector • Identical to PushSum only that it uses binary weights for links • Prove diffusion speed obeys O(logn) law • Prove constant mass property • Prove geometric convergence in values D. Kempe et al.: Gossip-Based Computation of Aggregate Information (FOCS 2003)

25. PushSum & network dynamics • Convergence speed is influenced by: • Network diameter – reduced the convergence speed • Node mobility – mobility increases convergence speed • Number of random neighbors selected • Unicast – Multicast – Broadcast Anand D. Sarwate: The Impact of Mobility on Gossip Algorithms, IEEE Transactions on Information Theory

26. Influence of failures • Under ideal conditions (no failures): Σimi,t-1 = Σimi,t – mass conservation Σiωi,t-1 = Σiωi,t – weight conservation • In real environment: • Node failures: mass loss • Communication failures: mass loss • Churn: severe mass loss • Conclusion: • Average value decreases with time in real world conditions MárkJelasity: Gossip-based aggregation in large dynamic networks. ACM Trans. Computer Systems, 2005

27. Extension of PushSum • Computing averages: • mi,0 = “random”, ωi,0 = 1 • mi,∞ = sumi(mi,0)/n • Computing sums: • mi,0 = “random”, ωi,0 = 0, ω0,0 = 1 • mi,∞ = sumi(mi,0) • Counting the nodes in the network: • mi,0 = 1, ωi,0 = 0 • mi,∞ = sumi(mi,0) = n • Main properties hold for all variations: • The algorithms are guaranteed to converge • The convergence speed is the same in all cases Large-scale adaptive systems, 2010

28. Lecture 3: Overview • Introduction • Basics of gossiping algorithms • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010

29. Firefly synchronization • Several astonishing synchronization mechanisms in nature • Heart pacemaker cells • Chirping crickets • Clapping of an audience at a concert • Flashing of fireflies • A common phenomena underlying everything: coupled oscillators • Each actor is an independent “oscillator” • Oscillators couple through environment • Mechanical vibrations, air pressure, visual clues, olfactory signals • They influence each other, causing continuous minor adjustments, leading to synchrony “SYNC: The Emerging Science of Spontaneous Order” – Steven Strogatz

30. Fireflies • Certain species of male fireflies are known to synchronize their flashes despite: • Small connectivity (each firefly sees a limited number of neighbors) • Communication is not instantaneous • Independent local “oscillators” with random initial periods • Engineering approach • Style of interaction: anti-entropy, push mechanism • Local state S: current phase of the local oscillator and period • Small set of random neighbors • Update function: reset local oscillator based on phase of arriving flash Large-scale adaptive systems, 2010

31. The Ermentrout model • Modify the local oscillator period based on when the flash arrives: • If “too late” (φ<1/2) then “slow down” (increase period delta) • If “too early” (φ>1/2) then “speed up” (decrease period delta) Node i Node j Δφ Time !!!NetLogo animation !!! Large-scale adaptive systems, 2010

32. Lecture 3: Overview • Introduction • Basic gossip algorithm • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010

33. Cooperation in selfish environments • Example: P2P systems are usually open systems • Possible free riders • High level of free riding can degrade performance • Gossip-based algorithms can be used to sustain high levels of cooperation despite selfish nodes • Based on “copy” and “rewire” operations • Engineering the system • Pull interaction, local state: current utility, strategy and neighborhood within an interaction network • Select single random sample • Update function: copy strategy and neighborhood if the peer is achieving better utility Large-scale adaptive systems, 2010

34. Prisoner’s dilemma • Prisoner’s dilemma in SLAC • Nodes play PD with neighbors chosen randomly in the interaction network • Only pure strategies (always C or always D) • Strategy mutation: flip current strategy • Utility: average payoff achieved D. Hales: SLACER: Randomness to Cooperation in Peer-to-Peer Networks. StoDiS 2005

35. Lecture 3: Overview • Introduction • Basic gossip algorithm • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010

36. Random sampling • Problem: extract random samples from a set • Example: • The set: {1,2,3,1,2,3,2,1,2,3,2,1,2,3,2,1,2,3,3,3} • Solutions: • Pick randomly i in the range 1-20 and pick the ith element • Etc… • Solution needs to generate random samples according to the distribution of the set: • Element frequencies {1,2,3}→ {0.25,0.4,0.35} Large-scale adaptive systems, 2010

37. Distributed random sampling • Set is distributed over n nodes • Problem: pick random samples from the set without gathering all the data at a central point {2,3,2,1} {2,3} {3,2,1} {1} {1,2} {1,2,3} {3,3} Original set: { 1,2,3, 1, 2,3,2, 1,2, 3,2,1, 2,3,2,1, 2,3, 3,3 } {2,3,2} Large-scale adaptive systems, 2010

38. Push-Random algorithm • Protocol uses short messages • Each node holds only one element • Messages contain one element + one weight Node i: 1: {(qr,t-1,ωr,t-1)} – received pairs in round t-1 2: ωi,t = Σr (ωr,t-1) qi,t = picked at random from {qr,t-1} with prob. wr,t-1/ωi,t 3: choose shares αi,j,t for each neighbor j 4: send to each neighbor j: (qi,t, αi,j,t·ωi,t) 5: random sample in round t is: qi,t Large-scale adaptive systems, 2010

39. Lecture 3: Overview • Introduction • Basic gossip algorithm • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010

40. Formation creation • Ubiquitous computing • Large number of mobile “smart” physical objects with identification, sensing and computing power • Rescue teams with mobile devices • Automobiles in vehicular networks • Swarms of robots • Satellites in earth orbit • Adhoc wireless communication networks based on physical proximity and contact • Broadcast and multicast model rather than unicast Large-scale adaptive systems, 2010

41. Formation creation • Dynamic collection of agents that can move in any direction • Each agent has an unique ID and can determine the relative position of any other agent • Agents have access to a peer sampling service • Devise a protocol such that mobile agents self organize intro pre-specified global formations without central control Large-scale adaptive systems, 2010

42. Gossip framework instantiation • Engineering a solution: • Pull interaction, local state S: current physical position and motion vector • Select k random samples from populations • Update function: compute motion vector based on positions of most and least preferred neighbor Mark Jelasity: T-Man: Gossip-based Overlay Topology Management. Engineering Self Organizing Systems

43. Summary • Introduction • Basic gossip algorithm • Applications • Firefly synchronization • Cooperation in selfish environments • Random sampling • Formation creation • Summary Large-scale adaptive systems, 2010