Gossip Gossip pping in pp pp pping in p g g Bolo Bolo ogna ogna Ozalp Ba Ozalp Ba abaoglu abaoglu ALMA MATER STUDIORUM – U ALMA MATER STUDIORUM – U UNIVERSITA’ DI BOLOGNA UNIVERSITA’ DI BOLOGNA
Background Background • 2003: Márk Jelasity brings t he gossipping gospel to Bologna from Amsterdam • 2003-2006: We get good mi ilage from gossipping in the context of Project BISON • 2005-present: Continue to g get milage in the context of Project DELIS Babaoglu Leiden M Meeting 2
What have we done? What have we done? • We have used gossipping to o obtain fast, robust, decentralized solutions for • Aggregation • Overlay topology managemen nt • Heartbeat synchronization • Cooperation in selfish environ ments Babaoglu Leiden M Meeting 3
Collaborators Collaborators • Márk Jelasity • Alberto Montresor • Alberto Montresor • Gianpaolo Jesi • Toni Binci T i Bi i • David Hales • Stefano Arteconi Babaoglu Leiden M Meeting 4
Proac Proac ctive gossip framework ctive gossip framework // active thr // read do forever wait(T ti ime units) q = Selec q = Selec ctPeer() ctPeer() push S to o q pull S q f rom q q S = Updat te(S,S q ) // passive thr // i h read d do forever (p, (p,S p ) = pu p ) p ull * from * push S to p S = Update e(S,S p ) Babaoglu Leiden M Meeting
Proac Proac ctive gossip framework ctive gossip framework • To instantiate the framework To instantiate the framework k, need to define k need to define • Local state S • Method SelectPeer() Method SelectPeer() • Style of interaction ▴ push-pull ▴ push ▴ pull • Method Update() M th d U d t () Babaoglu Leiden M Meeting 6
# 1 Aggreg Aggreg gg gg g g gation gation g ALMA MATER STUDIORUM – U ALMA MATER STUDIORUM – U UNIVERSITA’ DI BOLOGNA UNIVERSITA’ DI BOLOGNA
Gossip fr Gossip fr ramework instantiation ramework instantiation • Style of interaction: push-pu ull • Local state S : Current estim mate of global aggregate • Method SelectPeer() : Single e random neighbor • Method Update() : Numerica Method Update() : Numerica al function defined according to al function defined according to desired global aggregate (ar ithmetic/geometric mean, min, max, etc.) , ) Babaoglu Leiden M Meeting 8
Exponential conv Exponential conv vergence of averaging vergence of averaging Babaoglu Leiden M Meeting 9
Properties of goss Properties of goss sip-based aggregation sip-based aggregation • In gossip-based averaging, g p g g, if the selected peer is a p globally random sample, the en the variance of the set of estimates decreases expone entially • Convergence factor: 2 ) ρ = E ( σ i + 1 1 E ( σ 2 ) ≈ ≈ 0.303 E ( σ i ) 2 e 2 e Babaoglu Leiden M Meeting 10
Robustness of ne Robustness of ne etwork size estimation etwork size estimation 1000 nodes crash at 1000 nodes crash at the beginning of each cycle the beginning of each cycle Babaoglu Leiden M Meeting 11
Robustness of ne Robustness of ne etwork size estimation etwork size estimation 20% of messages are lost 20% of messages are lost Babaoglu Leiden M Meeting 12
# 2 Topology M Topology M gy gy Management Management g ALMA MATER STUDIORUM – U ALMA MATER STUDIORUM – U UNIVERSITA’ DI BOLOGNA UNIVERSITA’ DI BOLOGNA
Gossip fr Gossip fr ramework instantiation ramework instantiation • Style of interaction: push-pu ull • Local state S : Current neigh • Local state S : Current neigh hbor set hbor set • Method SelectPeer() : Single e random neighbor • Method Update() : Ranking f function defined according to desired topology (ring, mesh h, torus, DHT, etc.) Babaoglu Leiden M Meeting 14
Mesh Example Mesh Example Mes h.mov Babaoglu Leiden M Meeting 15
Sorting example Sorting example Line.m mov Babaoglu Leiden M Meeting 16
Exponent Exponent tial convergence - time tial convergence - time Babaoglu Leiden M Meeting 17
Exponential conve Exponential conve ergence - network size ergence - network size Babaoglu Leiden M Meeting
# 3 Heartbeat Syn Heartbeat Syn y nchronization nchronization ALMA MATER STUDIORUM – U ALMA MATER STUDIORUM – U UNIVERSITA’ DI BOLOGNA UNIVERSITA’ DI BOLOGNA
Synchrony in nature Synchrony in nature • Nature displays astonishing p y g cases of synchrony among y y g independent actors • Heart pacemaker cells • Chirping crickets • Menstrual cycle of women livin ng together • Flashing of fireflies • Actors may belong to the sa ame organism or they may be parts of different organisms Babaoglu Leiden M Meeting 20
Coupled oscillators Coupled oscillators • The “Coupled oscillator” mo odel can be used to explain the phenomenon of “self-synchr ronization” • Each actor is an independen nt “oscillator”, like a pendulum • Oscillators coupled through p g their environment • Mechanical vibrations • Air pressure p • Visual clues • Olfactory signals • They influence each other, c causing minor local adjustments that result in gl obal synchrony Babaoglu Leiden M Meeting 21
Fireflies Fireflies • Certain species of (male) fir reflies (e.g., luciola pupilla ) are known to synchronize their f y flashes despite: p • Small connectivity (each firefly y has a small number of “neighbors”) • Communication not instantane eous • Independent local “clocks” wit h random initial periods Babaoglu Leiden M Meeting 22
Gossip fr Gossip fr ramework instantiation ramework instantiation • Style of interaction: push • Local state S : Current phase • Local state S : Current phase e of local oscillator e of local oscillator • Method SelectPeer() : (smal ll) set of random neighbors • Method Update() : Function to reset the local oscillator based on the phase of arrivin ng flash Babaoglu Leiden M Meeting 23
Experimental results Experimental results fireflie es.mov Babaoglu Leiden M Meeting 24
Exp Exp ponential convergence ponential convergence Babaoglu Leiden M Meeting 25
# 4 Cooperatio Cooperatio p p n in Selfish n in Selfish Environ Environ nments nments ALMA MATER STUDIORUM – U ALMA MATER STUDIORUM – U UNIVERSITA’ DI BOLOGNA UNIVERSITA’ DI BOLOGNA
Outline Outline • P2P networks are usually op P2P networks are usually op pen systems pen systems • Possibility to free-ride • High levels of free-riding can s High levels of free riding can s seriously degrade global seriously degrade global performance • A gossip-based algorithm ca • A gossip-based algorithm ca an be used to sustain high an be used to sustain high levels of cooperation despite e selfish nodes • Based on simple “copy” and • Based on simple copy and d “rewire” operations d rewire operations Babaoglu Leiden M Meeting 27
Gossip fr Gossip fr ramework instantiation ramework instantiation • Style of interaction: pull • Local state S : Current utility y , strategy and neighborhood within an interaction network k • Method SelectPeer() : Single g e random sample p () • Method Update() : Copy stra ategy and neighborhood if the peer is achieving better utility p g y y Babaoglu Leiden M Meeting 28
SLAC Algorith SLAC Algorith m: “Copy and Rewire” m: “Copy and Rewire” E F D G C C A A H “Copy” strategy py gy B “Rewire” K J Babaoglu Leiden M Meeting 29
SLA SLA AC Algorithm: “Mutate” AC Algorithm: “Mutate” E F D G C C A A H “Mutate” strategy B Drop current links K J Link to random node Link to random node Babaoglu Leiden M Meeting 30
Prisoner’s Dilemma Prisoner’s Dilemma • Prisoner’s Dilemma in SLAC C • Nodes play PD with neighbors p y g s chosen randomly in the interaction y network • Only pure strategies (always C C or always D ) • Strategy mutation: flip current strategy • Utility: average payoff achieve ed Babaoglu Leiden M Meeting 31
Cycle 180: Sm Cycle 180: Sm mall defective clusters mall defective clusters Babaoglu Leiden M Meeting 32
Cycle 220: Cycle 220: Cooperation emerges Cooperation emerges Babaoglu Leiden M Meeting 33
Cycle 230: Cycle 230: Cooperating cluste Cooperating cluste Cooperating cluste Cooperating cluste er starts to break apart er starts to break apart er starts to break apart er starts to break apart Babaoglu Leiden M Meeting 34
Cycle 300: Defective Cycle 300: Defective e nodes isolated, small e nodes isolated, small coope coope coope coope erative clusters formed erative clusters formed erative clusters formed erative clusters formed Babaoglu Leiden M Meeting 35
Phase tra Phase tra ansition of cooperation ansition of cooperation nodes ating n coopera % of c Babaoglu Leiden M Meeting 36
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