LDEPTH - A New Lightweight P2P Architecture

LDEPTH: A Low Diameter Hierarchical P2P Network Architecture

KOUSHIK SINHA

SOUTHERN ILLINOIS UNIVERSITY, CARBONDALE

Contents

Introduction

Background

LDEPTH P2P Architecture

Resource Look-up

Resource Join

Fault Tolerance

Conclusion

Introduction

Peer-to-Peer (P2P) overlay networks provide computational and data resource sharing capability

Scalable

Fault tolerant

Self-organizing

Distributed solution

2 broad classes of P2P networks

Unstructured

Structured

Introduction

Unstructured P2P networks

Peers are organized into arbitrary topologies

Flooding commonly used mechanism for resource look up

Resource look-up time complexity typically O(n), n = number of nodes in the P2P network

Example: Gnutella, Yappers

Structured P2P networks

Peers organized into specific topologies

Typically more efficient resource look-up time compared to Unstructured P2P networks [O(log n)]

Handling frequent peer joining and leaving (known as churn) more complex than in Unstructured P2P

Example: Chord, Pastry, Tapestry, HP2P

Structured P2P Networks

Typically use Distributed Hash Tables (DHTs)

Provides efficient data insertion, lookup, deletion operations

But, maintaining DHTs is complex task - needs significant effort to handle problem of churn

How to reduce the amount of effort in maintaining the structure while still providing an efficient resource query service?

Hybrid systems attempt to incorporate advantages of both structured and unstructured architectures

Efficient data look up vis-à-vis handling churn and providing fault tolerance still open problem

Basic Idea

Linear Diophantine Equation (LDE)

We consider solutions for LDE of the form

𝒂𝒏 ≡ 𝒃 𝒎𝒐𝒅 𝒄 𝑎, 𝑏, 𝑐 ∈ 𝐼

The above LDE has 𝒅 mutually incongruent solutions, where 𝑑 = gcd(𝑎, 𝑐)|𝑏

Alternative form of the above equation:

𝒂𝒏 + −𝒄 𝒌 = 𝒃, 𝑘 ∈ 𝐼

Solutions are of the form:

𝑛 = 𝑛0 + 𝑐𝑡

𝑑

𝑘 = 𝑘0 + 𝑎𝑡

𝑑

For a given 𝑡, all solutions of the form 𝒏𝟎 + 𝒕𝒄

𝒅+𝒎𝒄 are mutually congruent

𝑛0, 𝑛0 +𝑐

𝑑, 𝑛0 + 2

𝑐

𝑑, … , 𝑛0 + (𝑑 − 1)

𝑐

𝑑

Each of the 𝑑 solutions are mutually incongruent modulo 𝐜

LDEPTH Architecture

Solutions of LDE can be used as logical addresses of peers in P2P Network

Create overlay ring network consisting of maximum 𝒅 logical address points for each of 𝒅 equivalence classes

Each address point 𝑛0 + 𝑡𝑐

𝑑corresponds to a distinct resource/group identifier

Two resource-types/groups in the ring network are neighbors if their assigned addresses differ by 𝑐

𝑑

The last and first addresses on the ring differ by (r − 1)𝑐

𝑑

Diameter of the ring network can be at most 𝒅

𝟐

With each logical address 𝑛0 + 𝑡𝑐

𝑑on the ring:

Infinite number of mutually congruent logical addresses can be associated 𝒏𝟎 + 𝒕𝒄

𝒅+𝒎𝒄

Logically equivalent to peers one-hop away from each other clique

All peers in clique must contain resource-type of logical address 𝑛0 + 𝑡𝑐

𝑑

LDEPTH Architecture

We define resource as tuple < 𝑅𝑖 , 𝑉 >

𝑅𝑖 : resource type

𝑉: resource value

Each resource type can have many values

For example: 𝑅𝑖 denote resource type songs, 𝑉1, 𝑉2 particular artists

< 𝑅𝑖 , 𝑉1 > will denote songs by artist 𝑉1 ; < 𝑅𝑖 , 𝑉2 > will denote songs by artist 𝑉2

Peer 𝑝 can have multiple resource types

For resource types 𝑅𝑖 and 𝑅𝑗 , peer 𝑝 will be members of groups 𝐺𝑖 and 𝐺𝑗 with different logical addresses

LDEPTH Architecture

At level-1: Transit ring network consisting of max. 𝑑 peers, 𝑃𝑖 , 0 ≤ 𝑖 < 𝑑

Equal to number of distinct resource types

Transit ring network used for efficient data lookup

At level-2: Each 𝑃𝑖 head of group of peers with same resource type 𝑅𝑖

Level-2 peers form complete graph (𝐺𝑖)

Each 𝑃𝑖 in transit network maintains global resource table (GRT)

<Resource Type, Resource Code, Group Head Logical Address>

All communication between node 𝒑𝒊 ∈ 𝑮𝒊 and 𝒑𝒋 ∈ 𝑮𝒋 happens only via nodes in transit ring

G0

G1

Gr-1

Gi

Level 1

P0

P1

Pi

Pr-1

Gi = Group i

Pi = Group Head of G i

Transit Ring Network

Level 2 Networks

Data Lookup

Intra-Group Data Lookup

Data lookup in group 𝐺𝑖 : peer 𝑝𝑎 possessing < 𝑅𝑖 , 𝑉𝑎 > requests resource < 𝑅𝑖 , 𝑉𝑏 >

Peer 𝑝𝑎 sends requests to group head 𝑃𝑖

Group head 𝑃𝑖 broadcasts request for < 𝑅𝑖 , 𝑉𝑏 > in group 𝐺𝑖

Note: 𝐺𝑖 is a complete graph

If ∃𝑝𝑏 with < 𝑅𝑖 , 𝑉𝑏 > , 𝑝𝑏 unicasts < 𝑅𝑖 , 𝑉𝑏 > to requesting node 𝑝𝑎

Data Lookup

Inter-Group Data Lookup: 𝑝𝑖 ∈ 𝐺𝑖 requests resource < 𝑅𝑗 , 𝑉∗ > ∈ 𝐺𝑗

Assume there are currently 𝑟 distinct resource types in network 𝑟 groups on transit ring network

𝑝𝑖 unicasts resource lookup request to its group-head 𝑃𝑖

From GRT: 𝑃𝑖 determines Group Head Logical Address 𝑃𝑗 for group 𝐺𝑗 with resource type 𝑅𝑗

𝑃𝑖 computes ℎ = | 𝑛0 + 𝑖𝑐

𝑑− 𝑛0 + 𝑗

𝑐

𝑑|

If ℎ >𝑟

2, then forward message to predecessor: message moves anti-clockwise on transit ring to reach 𝑃𝑗

Otherwise, forward message to successor: message moves clockwise on transit ring to reach 𝑃𝑗

𝑃𝑗 broadcasts within its group 𝐺𝑗 for resource < 𝑅𝑗 , 𝑉∗ >

If found in some 𝑝𝑗 ∈ 𝐺𝑗, 𝑝𝑗 unicasts < 𝑅𝑗, 𝑉∗ > to 𝑝𝑖

Data Lookup

Complexity

Intra-Group Lookup

O(1) message complexity since each group is a complete graph

Inter-Group Lookup

Bounded by 2 +𝑟

2messages

Independent of number of peers in the P2P network (𝑛)

In existing structured P2P networks like Chord, message complexity is a function of 𝑛

New Resource/Peer Joining

New Peer 𝒑 with existing Resource Type 𝑹𝒊

Node 𝑝 contacts Group-head 𝑃0 of first group 𝐺0

𝑃0 determines address of 𝑃𝑖 (group head for resource type 𝑅𝑖)

𝑃0 unicasts address of 𝑝 to 𝑃𝑖

𝑃𝑖 allocates to 𝑝 next available logical address in 𝐺𝑖 𝑛0 + 𝑖𝑐

𝑑+ 𝑞𝑐

𝑃𝑖 asks all peers 𝑝𝑘 𝜖 𝐺𝑖 to update their routing tables with new peer 𝑝

𝑃𝑖 unicasts to 𝑝 its allotted logical address and list of neighbors in 𝐺𝑖

New Resource/Peer Joining

New Peer 𝒑 with new Resource Type 𝑹𝒕

Assume there are currently 𝑟 distinct resource types in LDEPTH transit ring

last group-head is 𝑃𝑟 with successor 𝑃0 and predecessor 𝑃𝑟−1

Node 𝑝 contacts Group-head 𝑃0 of first group 𝐺0 on transit ring

𝑃0 allocates next available logical address on transit ring to 𝑝 for new resource type 𝑅𝑡 𝑛0 + (𝑟 + 1)𝑐

𝑑 Logical address 𝑃𝑡 = 𝑃𝑟+1

𝑃0 unicasts newly allotted logical address of 𝑝 to 𝑃𝑟

𝑃0 updates its predecessor from 𝑃𝑟 to 𝑃𝑡

𝑃𝑟 updates its successor from 𝑃0 to 𝑃𝑡

𝑃0 broadcasts message to all other group heads to update their GRTs with information of new group 𝐺𝑡

𝑃0 unicasts logical address 𝑃𝑡 to 𝑝

𝑝 becomes group-head 𝑃𝑡 for new group 𝐺𝑡 containing resources of type 𝑅𝑡

New resource type always added after the last group-head 𝑷𝒓

Fault Tolerance

Case 1: Group member (but not group head) crashes or leaves

Group members periodically exchange HELLO packets

If a group member 𝑝 crashes or leaves, neighbors will eventually come to know of it

Other peers in group delete entry for 𝑝 from list of neighbors

Case 2: Group Head crashes or leaves

Each group 𝐺𝑖 maintains a candidate/back-up group head 𝑝𝑖∗

𝑝𝑖∗ chosen as second lowest logical address of 𝐺𝑖 𝑛0 + 𝑖

𝑐

𝑑+ 𝑐

𝑃𝑖 periodically copies its GRT to 𝑝𝑖∗

Group heads on the transit ring network periodically exchange HELLO packets with successor and predecessor peers

Group member exit news doesn’t propagate beyond group

Fault Tolerance

Case 2.1: Group head 𝑃𝑖 leaves

First broadcasts in 𝐺𝑖 that 𝑝𝑖∗ will henceforth be new group head

Informs predecessor 𝑃𝑖−1 and successor 𝑃𝑖+1 of 𝑝𝑖∗’s IP address

Logical address of 𝑝𝑖∗ changed to 𝑛0 + 𝑖

𝑐

𝑑 designated logical address of 𝐺𝑖 ’s group-head

𝑝𝑖∗ chooses a new back-up group head 𝑝𝑖

∗∗ node with logical address 𝑛0 + 𝑖

𝑐

𝑑+ 2𝑐

Case 2.2: Group head 𝑃𝑖 fails

Peers 𝑃𝑖−1, 𝑃𝑖+1 on transit ring, and back-up group-head 𝑝𝑖∗ learns about failure eventually

𝑝𝑖∗ broadcasts in 𝐺𝑖 that 𝑝𝑖

∗ will henceforth be new group head

𝑝𝑖∗ informs predecessor transit ring predecessor 𝑃𝑖−1 and successor 𝑃𝑖+1 of 𝑝𝑖

∗’s new status & IP address

𝑝𝑖∗ chooses a new back-up group head 𝑝𝑖

∗∗ 𝑛0 + 𝑖

𝑐

𝑑+ 2𝑐

Group Head exit updates restricted to group peers, and transit ring predecessor & successor nodes

Conclusion

Proposed new 2-level hierarchical structured P2P network architecture

LDE computationally lightweight as compared to existing DHT based P2P networks

Efficient intra and inter group data/resource look-up algorithms

Message complexity independent of number of nodes in P2P network

Efficient algorithms proposed for new resources/nodes joining network

Efficient handling of peers leaving/failing

Updates restricted only to group members and transit ring successor & predecessor nodes

Thank You