Download slides - Network and Systems Laboratory

On Heterogeneous Overlay
Construction and Random Node
Selection in Unstructured P2P Networks
Presenter: 游創文
Outline
•
•
•
•
•
•
Motivation
Relate work
Algorithm for graph construction
Selection walks on the built graph
Experiments
Conclusion
Motivation
• Unstructed P2P and overlay networks
– Use random walks to build unstructured graphs and do node
selection
• Requirements to build a good graph and do random
selection
–
–
–
–
Load balance
Heterogeneity
Simplicity
Scalability
• Design heterogeneous graph building and random node
selection algorithms
– Practical to deploy and functional over a wide range of
requirements
Unstructured P2P overlay network
• Organize peers in a random graph in flat
or hierarchical manners (e.g. super-peers
layer)
– Random graph construction
• Two steps involved in function of P2P
Systems
– Query Phase
• random node selection on top of the graph
– Delivery Phase
Related work
• Gia
– Unstructured file sharing system that uses random
walk
– Give high capacity nodes higher degrees and more
information to store
– Not give control over degree or load
• SCAMP
– Build graphs where the average node degree is
proportional to the log of the number of nodes
– Not give enough control over node degree or load
Related work
• Araneola
– Build regular graphs that could potentially be used for random
selection
– Doesn’t discuss the case of heterogeneity
– Assumption: the existing nodes contacted by newly joining
nodes are uniformly picked
– Run constant background protocol
• Law and Siu
– A distributed mechanism to construct a regular random graphs
– Not handle heterogeneity and is vulnerable to unexpected node
departures.
• SelfLoops & Iterative scaling
– Random walk methods not suitable to use for graph construction
or to accommodate heterogeneity
– Extend by this paper
Initial node discovery
• For any node that wants to join the graph
– know at least one already existing member in
the graph
• Light-weight approach
– A small set (of about 10) of the most recently
joined nodes
Algorithms for graph construction
(requirements)
• Truly random walk
– Selected uniformly randomly
– High degree nodes  high probability to be selected
– More severe for build walks (Compound itself as the
network grows)
• Add bias to ensure high degree nodes don’t
keep collecting more links
• Heterogeneous requirement
– Higher capacity nodes have proportionally higher
nodes degrees than lower capacity nodes
Algorithms for graph construction
• Node i in the graph to establish a fixed number of links
Ki, called outlinks, with randomly select nodes in the
graph
– Lead to nodes obtaining roughly as many inlinks as outlinks
• A node never has the option of refusing a request to
create an inlink
– For simplicity
– The bias tends to prevent the need for this
• Counteract the effects of early joiners obtaining more
inlinks
– Stronger bias
– Actively manage each node’s indegrees
• Nodes with high indegrees to move an inlink to nodes with low
indegrees
Taxonomy of Biased walks
• Biased-halting
– Next hop at a node is picked uniformly from all links at
the node.
– Ended at each node with a random probability
• Inversely to the degree of the node
– Average length could be fixed
– Ex: SelfLoops, SCAMP
• Biased-forwarding
– Selection of next hop in the walk
• Weighted against high degree nodes
– # of hops is set at a fixed constant H
– InlinkInvProb, TotalInvProb, Iterative Scaling
Taxonomy of Biased walks
• Tradeoff
– Biased-forwarding  state exchange with
their neighbors (their degree..)
– biased-halting tend to unfairly load highdegree nodes (tends to be forwarded to highdegree nodes)
SelfLoops (SL)
• Emulate a graph with perfectly uniform node degrees
– adding virtual links to oneself (self loops).
• Original work
– not support heterogeneity or provide the needed bias for build
walks
• Modification
– For selection walks
• the virtual degree of each node α its outdegree
– For build walks
• The virtual degree α (outdegree2/indegree)
Refresh of SelfLoops (SL)
• A node discards one of its links and chooses another
• Steady state
– Net change in the expected indegree of i due to the refresh is
zero
loses an inlink = gains an inlink
c*indeg(i)
= c’ * (outdeg(i)2 /indeg(i) )
indeg(i)
= c’’ * outdeg(i)
c’’
=1
• Much harder to estimate the virtual hop length to achieve
a desired average real hop-length
– Conservative option is to use a large enough value  results a
larger average hop-length
Problems of biased-halting
• Any given walk can be quite short
• Hybrid approach
– If the expected walk length was h hops
– First h/2 hops, use on of the biasedforwarding
– Later half, use selfloops
– Call this as hybrid TotalInvProb-SelfLoops
Inverse-Probability walks
• Probability of forwarding a walk to a node
– InlinkInvProb, IP
• α (outdegree/ indegree), used for build walks
– TotalInvProb, or TIP
• α (outdegree/ total degree), used for selection
walks
Iterative Scaling (IS)
• Biased-forwarding walk
– Each node assigns outgoing and incoming
weights to each of its links
– Iterative computation across all links
• Derive the elements of a matrix when the row and
column sums are known
– The outgoing (incoming) weight of a link
• the node’s probability (perception of the probability)
that it’s picked during a random walk from the
other (the other end of the link)
Iterative Scaling (IS)
• Incoming weight assigned by a to link l = the outgoing
weight assigned by b to link l
– set WtAIN(l) = WtBout(l)
• Bring the system to a state where at every node both the
incoming and outgoing weights add to 1 each.
• A sufficiently long random walk is equally likely to end at
any node.
• Heterogeneity
– Select
• Ideal probability that a node is selected α its outdegree
– Build
• Ideal probability is α (outdegree2/indegree)
• Update at A
– The incoming weight for each link A  B is scaled by the
estimated probability of a walk reaching B before the
normalization is performed.
A
N
WNA
Some issues
• Exchanging neighbor information (IP or IS)
– Each node send a message to all of its neighbors
every time it experiences a link change
– Piggyback the neighbor information on other
message
– Not good for high-degree graphs
• Graph refreshes
– Periodically remove a outlink and replace it with
another randomly
– Overhead , graph changes, more complex
SwapLinks (SW)
• Inspire from Law and Siu
• Modify It to handle heterogeneity and robust to
unexpected node departures
• Two kinds of walks
– OnlyInLinks – each node chooses uniformly randomly
among its inlinks only
– OnlyOutLinks – each node chooses uniformly
randomly among its outlinks only
SwapLinks (SW)
• Lost a outlink
– Relace the outlink with a new neighbor O discovered
with an OnlyInLinks build walk
• Lost an inlink
– Check if its indegree < its outdegree
• If so, use OnlyOutLinks to discover a node I
B
I
Neighbor of I
B
I
Neighbor of I
• No need to exchange state with neighbors
Selection walks
• How a graph is walked
• Four ways
– TotalInverseProb (TIP), Iterative Scaling (IS),
SelfLoop (SL), hybrid TIP-SL (Hyb-TIP-SL)
Experiments setup
• Static simulation
– Fully added or deleted before the next node is added or deleted
– No packet loss
• Two scenarios
– Shrink (build then shrink to 25% of its original)
– Churn (build then churn, 2N churn events, expected network size
is N)
• Setup
– N = 5000, build walk length of 10 hops
– Except In the case of heterogeneity, a constant outdegree of 5 at
every node
• 10M selection walks, the graph has M nodes at the time
of selection
– Look the distribution of the selected nodes and the selection load
balance
Four graph-construction techniques
(Homogeneous case)
• Graph with or without refreshes (exception SwapLink)
• Status update (IS and IP)
– 1-hop updates of any link change
– piggybacking
• SCAMP, TrueRandom (each node forms 5 (expected)
outlinks with distinct uniformly chosen nodes)
• Load balance under node addition
– 10 nodes are added and the load placed on previously existing
nodes (Repeat 100 times)
– Average load per node (AvgBLoad-Add ), Standard deviation of
the load ( Dev(BLoad-Add) )
– focus on the load placed on already existing nodes
– The same load on the network irrespective of the size of the
graph
Four graph-construction techniques
(Homogeneous case)
• Node departure
– M/5 nodes randomly
– Average load per node AvgBLoad-Kill and
Dev(BLoad-Kill)
Result of four graph-construction
techniques
(Homogeneous case)
Graph Construction under
heterogeneity
• Heterogeneous
– Expected outdegree is also 5
• Each of the N nodes is a default-degree node with
probability 0.5 (outdegree of 5)
• A heterogeneous node with probability 0.5
(outdegree uniformly randomly from [2, 50])
– Churn or shrink is performed after all nodes
have joined and formed all their outlinks.
• The modifications made
– The walk prob indeed work as intened
Graph Construction under
heterogeneity
• Average indegree and the build load grow
linearly with the outdegree
Quality of random selection on
homogeneous graphs
• Distribution of the selected nodes, distribution of load
imposed by the select walks
– Use Standard deviation of hits rate to represent
• Not employ piggybacking on the selection walks
– # of selection walks is comparatively large
– Start from a single node, log the number of hits each node receives
1. All nodes  same outdegree of 5
2. # of walks = 10 *current number
of nodes in the graph
Quality of random selection on
homogeneous graphs
• Selection load seen by a node
– # of selection walks that pass through or end at the node
• The origins of the walks is distributed across the graph
– Load distribution should be uniform
Selection with heterogeneity
• Quality of selection when nodes have different
outdegrees
• Same setup as graph building under heterogeneity
• Running 12500 random selection walks
• All selection methos are function satisfactorily well
Distribution of selection hits as
a function of the outdegree
Scaling to larger sizes
• Measure # of hops it takes to obtain a random selection
distribution whose standard diviation is within 5% of that
of true random distribution
• Graphs are churned before the selections
• # of selection = 10 * the network size
Scaling to larger sizes
• Swaplink
– builds good graphs even at large scale
Conclusion
• A mechanism for building random graphs and doing
random selection (SwapLinks)
–
–
–
–
Simple
Scalable
Good control over heterogeneity
Enable the desired random selection by setting of only a single
parameter (desired node degree) of each node
• Future work
–
–
–
–
Implement and test in a real setting
Compare with a random selection strategy that uses DHTs.
Consider misbehaving nodes
Establishing proximal neighbors (low latency or high BW)