Gossip algorithms : “infect forever” dynamics Low-level objectives: – One-to-all: Disseminate rumor from source node to all nodes of network – All-to-all: Each node initially holds specific rumor, to be spread to all nodes Applications – One-to-all: announce change in topology (new node arrival) in ad hoc network; spread content (data chunk) of interest to all nodes in P2P network – All-to-all: monitoring global state of network (eg sensors spreading warnings about abnormal temperature…)

Types of gossip algorithms Synchronization modes: – Synchronous (slotted time, simultaneous operations by each node) – Asynchronous (continuous time, single node wakes up & performs operation) Type of operation: contact neighbor node to – Push all known rumors – Pull rumors known by contacted node – Push-Pull: do both Neighbor selection: – Uniform at random among neighbors, i.i.d. over node wake-up events – Round-robin – …

Non-complete, possibly sparse graphs: conductance, isoperimetric constant and expanders

Extension (2) Competing epidemic disseminations  Context: P2P system for live streaming dissemination (such as PPLive)  Users want to obtain sequence of rumors (=data packets) injected by source node, with low delay  Upload bandwidth constraint: only 1 rumor can be pushed by any node in one time  Local scheduling decision: which packet to push? ? Sender’s packets Receiver’s packets ???

9 Favors overall system performance: creates potential for new transmissions from receiver An example strategy: uniform random peer, latest « chunk » push ?? Sender’s chunks Receiver’s chunks Last chunk ?????? Fraction of reached nodes Time

10  Allows streaming at 63% of optimal rate with optimal delay, (by performing source coding at source node, creating redundancy in disseminated chunks) [Bonald-Massoulie-Mathieu et al, 2008] uniform random peer, latest « chunk » push Performance with complete graph