A TOKEN-BASED BROADCAST ALGORITHM OVER DHT FOR

LARGE-SCALE COMPUTING INFRASTRUCTURES

Kun Huang

and Dafang Zhang

School of Computer and Communication,

School of Software, Hunan University

Changsha, Hunan Province 410082, P. R. China

Keywords: Computing infrastructure, Peer-to-Peer network, Distributed hash table, Broadcast, Load balancing.

Abstract: Scalable and efficient broadcast is essential to the large-scale computing infrastructures such as PlanetLab

and Grids. By exploiting the greedy routing mechanisms of Distributed Hash Table (DHT), existing DHT-

based broadcast algorithms suffer from the limitations of scalability and load balancing, incurring high

construction and maintenance overhead for a distributed broadcast tree (DBT). This paper presents a token-

based broadcast algorithm over DHT for the large-scale computing infrastructures, where each node selects

the finger nodes as its children by a token value in a top-down approach. Theoretical analysis and

experimental results show that the token-based broadcast algorithm can construct and maintain a balanced

DBT with low overhead, where the branching factors of each node are at most two, and the tree height is

(log )Onin a Chord of

nodes, without any extra storage space and explicit maintenance overhead.

1 INTRODUCTION

The large-scale computing infrastructures such as

PlanetLab (Bavier, et al., 2004) and Grids (Foster, et

al., 2001) have become increasingly important for

developing and evaluating many emerging

distributed applications. Typically, these computing

infrastructures consist of large numbers of personal

workstations and dedicated servers scattered around

the world. For example, PlanetLab (2008) currently

consists of 870 nodes at 460 sites. As the size of the

computing infrastructures continues to grow, it is

very challenging to efficiently manage such large-

scale dynamic distributed systems.

Distributed broadcast is one of the fundamental

primitive operations of distributed information

management systems (Renesse, et al. 2003;

Yalagandula and Dahlin, 2004; Oppenheimer, et al.

2008; Jain, et al., 2007) to disseminate information

on a global scale. For example, in PlanetLab,

researchers replicate their programs, along with the

corresponding execution environment, on tens of

thousands of nodes before launching a distributed

application. In recent years, the Peer-to-Peer (P2P)

based broadcast algorithms have been proposed to

perform scalable content distribution across the

large-scale computing infrastructures. There are two

design principles for a P2P-based broadcast

algorithm according to overlay structures: tree-based

and mesh-based approaches. The tree-based

approach constructs a tree overlay rooted at the

source node as the content delivering structure, such

as ESM (Chu, et al., 2002), NICE (Baerjee, et al.,

2002), Scribe (Castro, et al., 2002), and Bayeux

(Zhuang, et al., 2001). Since the single tree structure

is vulnerable to the failure of an interior node, the

multiple-tree approaches such as SplitStream (Castro,

et al., 2003) and CoopNet (Padmanbhan, 2002) are

proposed to improve the resilience, where each sub-

stream of content is delivered along one of multiple

disjoint trees. The mesh-based approach such as

Bullet (Kostic, et al., 2003), FastReplica

(Cherkasova and Lee, 2003), Bullet’ (Kostic, et al.,

2005), BitTorrent (Cohen, 2003), and CoBlitz (Park,

et al., 2006) constructs a data-driven mesh overlay

as a swarm system, where each node has a small set

of neighbours to exchange data. Despite of these

arguments (Venkataraman, et al, 2006; Wang, et al,

2007) against the two approaches, the tree-based

approach is more suitable for the large-scale

computing infrastructures with a large fraction of

relatively stable dedicated nodes due to its simplicity

and controlled overhead.

It is crucial for a DHT-based broadcast algorithm

to meet scalability, robustness and load balancing.

First, the algorithm should scale well to a large

123

Huang K. and Zhang D. (2009).

A TOKEN-BASED BROADCAST ALGORITHM OVER DHT FOR LARGE-SCALE COMPUTING INFRASTRUCTURES.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 123-130

DOI: 10.5220/0002200101230130

 SciTePress

number of participating nodes with only a limited

number of messages passing with respect to the size

of these computing infrastructures. Also it should

have low construction and maintenance overhead for

a distributed broadcast tree (DBT). Second, the

algorithm should be robust to the dynamics of node

arrivals and departures. Finally, the algorithm should

ensure good load balancing in the sense that the

broadcast workload is evenly distributed among all

the participating nodes in the DBT, without any

performance bottleneck or hotspot of content

delivery. Therefore, load balancing is essential for

scalability and robustness of a P2P-based broadcast

algorithm.

Recently, most DHT-based broadcast algorithms

(Yalagandula, et al., 2004; Oppenheimer, et al., 2008;

Jain, et al., 2007; Cai and Hwang, 2007; Castro, et

al., 2002; Castro, et al., 2003; Padmanbhan, et al.,

2002; Park and Pai, 2006; Zhuang, et al., 2001;

Zhang, et al., 2003; Renesse and Bozdog, 2004; El-

Ansary, et al., 2003; Ratnasamy, et al., 2001) have

been proposed. These broadcast algorithms utilize

the routing mechanisms of DHT to build up an

overlay routing path between a source node and each

destination node, and then construct a DBT rooted at

the source node by merging all the routing paths in a

top-down approach (El-Ansary, et al., 2003) or in a

bottom-up approach (Castro, et al., 2002). However,

such broadcast algorithms suffer from the limitations

of scalability and load balancing. First, DHT is a

greedy routing algorithm, where each node always

forwards a searched key to the closest preceding

node in its finger table, whose identifier is closer to

the key in the identifier space. The greedy essence of

DHT results in existing DHT-based broadcast

algorithms construct a flat and unbalanced DBT

either in a top-down approach (El-Ansary, et al.,

2003) or in a bottom-up approach (Castro, et al.,

2002). Second, existing DHT-based broadcast

algorithms have high construction and maintenance

overhead for a DBT with respect to a large number

of participating nodes. For example, the reverse-path

forwarding based broadcast algorithm (Castro, et al.,

2002) requires interior nodes to contain its children

for reverse forwarding using extra storage space,

which leads to high overhead of maintaining these

children. Moreover, although existing DHT-based

broadcast algorithms adopt the pushdown and

anycast methods (Castro, et al., 2002; Castro, et al.,

2003) to tackle the overloading of nodes by

adjusting the branching factors between nodes,

Bharambe et al. (2005) indicate that these

adjustment methods result in a significant number of

non-DHT links that are present in the DBT but are

not part of the routing links of DHT, which not only

restricts the scalability of DBT but also incurs higher

maintenance overhead of these non-DHT links due

to the dynamic nodes.

To address the above issues, this paper presents a

token-based broadcast algorithm over DHT for

scalability and load balancing in the large-scale

computing infrastructures. The key idea of the

token-based broadcast algorithm is that by

leveraging the topology and routing mechanisms of

Chord, each node selects the finger nodes as its

children by a token value in a top-down approach.

Theoretical analysis and experimental results show

that the token-based broadcast algorithm can

construct and maintain a scalable and balanced DBT,

where the branching factors of each node are at most

two, and the tree height is

(log )Onin a Chord

n nodes, without any extra storage space for each

node and explicit maintenance overhead for the

parent-child membership in the DBT.

The rest of the paper is organized as follows.

Section 2 overviews the Chord network. In Section 3,

we present in details the token-based algorithm.

Section 4 presents our experimental results. Related

work is introduced in Section 5 and Section 6

concludes the paper.

2 CHORD OVERVIEW

The Chord network is modelled as an undirected

graph

(,)GVE

, where the vertex set V

contains

n nodes and E is the set of overlay links

between nodes. According to the identifiers of nodes,

Chord organizes nodes as a ring topology in the

circular space. An object’s identifier

k is assigned to

the first node whose identifier is equal to or

follows

k in the identifier space of Chord. This node

is called the successor node of the identifier

k ,

denoted by

()Succ k . In Chord, ()Pred u refers to the

immediate predecessor of a node

u , while ()Succ u

refers to the immediate successor of a node

u .

Besides its immediate predecessor and successor,

each node

u also maintains a set of m finger nodes

that are spaced exponentially in the identifier space

of Chord. The

finger node of a node

, denoted

(,)Finger u i , is the first node that succeeds

by at

least

in the identifier space, that

(,) (( 2)mod2)

Finger u i Succ u=+ ,

where

01im

≤

≤−.

Chord adopts a greedy finger routing algorithm

(Stoica, et al., 2001) to recursively (or iteratively)

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124

forward a query message with an object’s

identifier

k to its successor node

()Succ k

that

maintains a pair

(,)kv , where

is the object’s value.

When a node

u want to lookup an object’s

identifier

k , it forwards a query message with the

identifier

k to its finger node

(,)Finger u j

, which is

closest to the successor node

()Succ k in the circular

identifier space, satisfying

(,) (, ()]Finger u j u Succ k∈

and

{ ( ( , ), ),0 1}Min Dist Finger u j k j m≤≤ − , where

(, )Dist u u is the numeric distance between two

identifiers

and

, that is

12 1 2

(, ) ( 2)mod2

Dist u u u u=−+ . And then the finger

node

(,)Finger u j continues to forward the query

message to the next node using the similar routing

algorithm, until to the successor node

()Succ k

Therefore, the finger routing algorithm of Chord is a

scalable and efficient lookup algorithm, with

average routing path length of

(log )On

and average

node state space of

(log )Onin a Chord of

nodes.

3 TOKEN-BASED BROADCAST

3.1 Token-based Broadcast Algorithm

This section presents a token-based broadcast

algorithm over DHT to achieve the scalability and

load balancing. In the token broadcast algorithm,

each node adaptively selects the finger nodes as its

children by a token value, and then a balanced DBT

is constructed in a top-down approach.

The DBT construction process of the token-

based broadcast algorithm is as follows. First, on

receiving a broadcast message with a token value

t ,

each node

selects the

finger node

(,)

Finger N t as its left child and the (1)

t + finger

node

(, 1)

Finger N t + as its right child. Second,

forwards the broadcast message with the

incremental token value

to its children, until no

any child is selected. Note that when receiving a

broadcast message with the token value

t , each node

selects its left child

and right child

, and

then checks to see whether its children’s identifiers

are not beyond the identifier of the source node,

satisfying

(,) (,)

dl ds

Dist N N Dist N N< and

(,) (,)

dr ds

Dist N N Dist N N< . If not,

does not

forward the broadcast message to

. When

initiating a broadcast message with a token

value

0t = , a source node

must adjust the token

value

t to skip its duplicated finger nodes, by

checking whether the condition

(,) (,1)

Finger N t Finger N t

≠

+ is satisfied. If not, then

the token value is incremented as

1t+= and

continues to check the above condition. Figure 1

illustrates the pseudo-codes of the token-based

broadcast algorithm.

Figure 1: Pseudo-codes of token-based broadcast

algorithm.

Figure 2 depicts a balanced DBT construction

example using the token-based broadcast algorithm

in a 16-node Chord, where there is the uniform

identifier space. In Figure 2(a), the source node

initiates a broadcast message with a token

value

, and selects

(,0)N Finger N= and

(,1)N Finger N

as its left and right children

respectively, and then forwards the broadcast

message with the incremental token value

and

;

and

continues to select their

children and increment the token value, and then

further forward the broadcast message, until no any

child is selected. When receiving the broadcast

message with the token value

3k = ,

have

no any child and don’t forward any broadcast

message, since the identifiers of their children are

more than the identifier of the source node

Figure 2(b) illustrates that the corresponding

balanced DBT is constructed from the finger routing

paths in Figure 2(a). Therefore, Figure 2 shows that

A TOKEN-BASED BROADCAST ALGORITHM OVER DHT FOR LARGE-SCALE COMPUTING

INFRASTRUCTURES

125

the token-based broadcast algorithm constructs a

balanced DBT, where the branching factors of each

node are at most two, and the tree height

log 4n =

⎡⎤

⎢⎥

, in which 16n = is the number of

nodes in Chord.

N15

N14

N7N9

N12

N13

N11

N10

Figure 2: Balanced DBT construction using token-based

broadcast algorithm in a 16-node Chord. (a) Finger routing

paths rooted at N

. (b) Constructed balanced DBT rooted

at N

3.2 Algorithm Analysis

In essence, the token-based broadcast algorithm is to

select the appropriate children for each node using a

token value to alternately cover all destination nodes.

Unlike the k-ary search based broadcast algorithm,

the token-based broadcast algorithm adopts the

exponential growth of the interval distance to

forward a broadcast message. So it is guaranteed by

the novel children selection strategy that the token-

based algorithm can construct a balanced DBT and

eliminate the duplicated broadcast messages

between nodes.

Figure 3 illustrates the properties of token-based

broadcast algorithm in a 16-node Chord. Figure 3(a)

depicts the case that a source node

forwards a

broadcast message to a destination node

. The



Figure 3: Properties of token-based broadcast algorithm in

a 16-node Chord. (a) Finger routing paths rooted at N

with different exponential interval distance. (b)

Alternately covering all the destination nodes to construct

balanced DBT rooted at N

token-based algorithm selects the children with the

exponential growth of the interval distance such

2 ,

2 , and

2 , whereas the k-ary search based

algorithm selects the children with the exponential

decay of the interval distance such as

2 ,

and

2 . As seen in Figure 3(b), when a source

node

forwards a broadcast message to all

destination nodes, each node

i selects

Token and

(1)

Token + finger nodes as its left and right children

respectively. The interval distance between parent

and children in such circular space is exponentially

growing and all destination nodes

12 15

NNL are

alternately covered to construct a balanced DBT root

Also, the DBT constructed by the token-based

broadcast algorithm is scalable, where the tree

height is

(log )Onin which

is the number of nodes

in Chord. We assume that a source node is

u and a

destination node is

v , satisfyinguv≠ . Since there is

the uniform identifier space of Chord,

u adjusts the

token value

Token t

to skip the duplicated finger

nodes in its finger table, and then forwards the

incremental token value until it is

Token m= . Thus,

(a)

(b)

(a)

(b)

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126

the finger routing path from

u to v

222

ttt

uu v

+→++ →→L , which

has

hmt=− hops, and we compute

((,))22

Max Dist u v =−in which 2

is the average

range between two immediately adjacent nodes in

Chord. Due to

22/

n= , we deduce

loghmt n=−=

Hence, it is proved that the tree height is

(log )Onand

the DBT is scalable.

Moreover, the token-based broadcast algorithm

needs no explicit construction and maintenance

overhead for such balanced DBT. First, since the

token-based algorithm selects the children only by a

token value in a top-down approach, each parent

does not need extra storage space for its children. So

the balanced DBT is implicitly constructed from the

finger routing paths of Chord. Second, on node

arrivals and departures, Chord adopts a finger

stabilization algorithm (Stoica et al., 2001) to

periodically update the finger tables of nodes. But

the token-based algorithm does not need extra cost

to repair the parent-child membership, which

significantly reduces the maintenance overhead of

the balanced DBT. Therefore, the DBT constructed

by the token-based broadcast algorithm has no any

extra storage cost and explicit maintenance overhead

of each node.

4 EVALUATION

This section presents the simulation experiments to

validate the token-based broadcast algorithm. We

implement three DHT-based broadcast algorithms

including the k-ary search based broadcast algorithm,

the reverse-path forwarding based broadcast

algorithm, and the token-based broadcast algorithm.

The performance metrics of a DHT-based

broadcast algorithm include branching factor, path

length, message overhead, and message imbalance

factor. Branching factor refers to the number of a

node’s children in a DBT. Path length refers to hops

of a finger routing path from a source node to a

destination node. Message overhead refers to the

number of messages for constructing and

maintaining a DBT. Message imbalance factor refers

to the ratio between the maximal number of

messages and average number of messages on each

node in a DBT. In the experiments, we simulate

from 16 to 2048 Chord nodes to examine the

performance metrics of above three algorithms.

Figure 4 depicts the comparison of branching

factor. Figure 4(a) shows that there is the same

maximal branching factor of

log n for both the k-ary

Network size

16 32 64 128 256 512 1024 2048

Maximal branching factor

k-ary

reverse

token

Branching factor

01234567891011

CDF

1.0

k-ary

reverse

token

Figure 4: Branching factor. (a) Maximal branching factor.

(b) Cumulative distribution functions in a 2048-node

Chord.

search based and reverse-path forwarding based

algorithms, whereas there is the constant maximal

branching factor of 2 for the token-based algorithm.

For example, in a 2048-node Chord, both the k-ary

search based and reverse-path forwarding based

algorithms have the same maximal branching factor

of 11, while the token-based algorithm has the

maximal branching factor of 2. As seen in Figure

4(b), both the k-ary search based and reverse-path

forwarding based algorithms construct a skewed

DBT, while the token-based algorithm constructs a

balanced DBT. For example, about 88% of nodes in

the DBT constructed by both the k-ary search based

and reverse-path forwarding based algorithms has

the branching factors of equal to or less than 2 and

the remaining 12% have the branching factors from

3 to 11. In the token-based algorithm, about 50% of

nodes in the DBT have the branching factors of 2,

and the remaining 50% are almost leaf nodes

without any branching factor. Therefore, the token-

based broadcast algorithm constructs a balanced

DBT, where the branching factors of each node are

at most two.

Figure 5 depicts the comparison of path length.

Figure 5(a) shows that the token-based algorithm has

the same maximal path length of

log n with both

the k-ary search based and reverse-path forwarding

based algorithms. As seen in Figure 5(b), compared

to both the k-ary search based and reverse-path

(a)

(b)

A TOKEN-BASED BROADCAST ALGORITHM OVER DHT FOR LARGE-SCALE COMPUTING

INFRASTRUCTURES

127

forwarding based algorithms, the token-based

algorithm increases 20%~40% of average path

length. The root cause lies in the fact that both the k-

ary search based and reverse-path forwarding based

algorithms construct a skewed and fat DBT from the

shortest finger routing paths, whereas the token-

based algorithm constructs a balanced and narrow

DBT from the novel finger routing paths. Despite

that, a DBT constructed by the token-based

algorithm guarantees the same max broadcast

latency of

log n

with both the k-ary search based and

reverse-path forwarding based algorithms. Therefore,

the token-based broadcast algorithm construct a

scalable DBT, where the tree height is

(log )On

which

is the number of nodes in Chord.

Network size

16 32 64 128 256 512 1024 204

Maximal path length

k-ary

reverse

token



Network size

16 32 64 128 256 512 1024 204

Average path length

k-ary

reverse

token

Figure 5: Path length. (a) Maximal path length. (b)

Average path length.

Figure 6 depicts the comparison of message

overhead in the uniform identifier space of Chord. As

seen in Figure 6, both the k-ary search based and

token-based algorithms have the same messages

1n − , while the reverse-path forwarding based

algorithm has

2( 1)n − messages. The root cause lies in

the fact that the reverse-path forwarding based

algorithm constructs a DBT in a bottom-up approach

and a broadcast message is forwarded along the

reverse finger routing paths of Chord, while both the

k-ary search based and our token-based algorithms

construct a DBT in a top-down approach and a

broadcast message is forwarded along the finger

routing paths. When a node arrives and departs, the

finger stabilization algorithm (Stoica et al., 2001) of

Chord produces the average messages of

(log )On for

maintaining the finger tables of relative nodes. Thus

the reverse-path forwarding based algorithm needs

extra average messages of

(log )Onto maintain the

parent-child membership of each node in the DBT.

Therefore, the token-based broadcast algorithm

constructs and maintains a balanced DBT without

any extra storage cost for the children of each node

and explicit maintenance overhead for the parent-

child membership in the DBT.

Network size

16 32 64 128 256 512 1024 2048

Number of messages

k-ary

reverse

token

31 31

62 63

126

127

254

127

255

510

255

511

1022

511

1023

2046

1023

2047

4094

2047

Figure 6: Message overhead.

Network size

16 32 64 128 256 512 1024 2048

Message imbalance factor

k-ary

reverse

token

2.1

1.1

2.6

1.0

1.0 1.0

1.0

1.0 1.0

3.0

3.5

4.0

4.5

5.0

5.5

Figure 7: Message imbalance factor.

Figure 7 depicts the comparison of message

imbalance factor. As seen in Figure 7, both the k-ary

search based and reverse-path forwarding based

algorithms have the same message imbalance factor

as a function of network sizes, while the token-based

algorithm has the constant message imbalance factor

independent of network sizes. For example, in a

2048-node Chord, the message imbalance factor is

about 5.5 for both the k-ary search based and reverse-

path forwarding based algorithms, while the message

imbalance factor is kept about 1.0 for our token-

based algorithm. Compared to both the k-ary search

based and reverse-path forwarding based algorithms,

the token-based broadcast algorithm reduces

50%~82% of the message imbalance factor, which

further validates that a DBT constructed by the

token-based algorithm is balanced.

(a)

(b)

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5 RELATED WORK

There have been many research efforts on multicast

and broadcast in past decades. In general, broadcast

is a special case of multicast. In recent years,

application-level multicast and broadcast algorithms

are categorized into tree-based and mesh-based

approaches as follows.

In the tree-based approach, a tree overlay rooted

at a source node is constructed as the content

delivering structure. For example, ESM (Chu, et al.,

2002) is a classic application-layer multicast system

towards small-sized groups. NICE (Baerjee, et al.,

2002) is proposed to support a larger number of

participating nodes using a hierarchical clustering

approach. Bayeux (Zhuang, et al., 2001) is proposed

to construct a scalable and fault-tolerant application-

layer multicast system by replicating root nodes and

clustering receivers via identifier on top of Tapestry

(Zhao, et al., 2002). Since the single tree structure is

vulnerable to node dynamics, the multiple-tree

approach has been proposed, where a forest with

multiple disjoint sub-trees is constructed and each

sub-stream of the content is delivered along each

sub-tree. For example, SplitStream (Castro, et al.,

2003) is proposed to construct an interior-node

disjoint forest of multiple Scribe (Castro, et al., 2002)

trees on top of Pastry (Rowstron and Druschel,

2001). CoopNet (Padmanbhan, et al., 2002) is

proposed to compute locally random or node-

disjoint forests of trees, primarily designed for

resilience to node departures.

In the mesh-based approach, a data-driven mesh

overlay is constructed as a swarm system, where

each node has a small of neighbours to exchange

data. For example, Bullet (Kostic, et al., 2003) and

Bullet’ (Kostic, et al., 2005) are proposed for large-

file distribution in the wide area, where a overlay

mesh is constructed over any overlay tree and each

node transmits a disjoint set of data to its children in

order to maintain uniform distribution of each data

and achieve high throughput. BitTorrent (Cohen,

2003; Huang, et al., 2008) is one of the most popular

P2P content distribution systems, where all

participating nodes upload and download equal-

sized blocks in parallel. These mesh-based swarm

systems can mitigate link stresses and the

performance bottleneck of the origin, but can incur

enormous traffic stresses on the Internet Service

Providers (ISP).

Moreover, distributed aggregation is also one of

the fundamental primitive operations. Aggregation is

to recursively compute the global information by

applying an aggregate function such as min, max,

count, and sum on a set of local status in the large-

scale computing infrastructures. DHT-based

aggregation algorithms for global resource monitor

and discovery related to our work have been recently

proposed. For example, Astrolabe (Renesse, et al.,

2003) is a DNS-like distributed management service

by organizing the resources into a hierarchy of

domains, specifying an aggregation tree between

domains, and exchanging information across

domains using an unstructured gossip protocol.

SDIMS (Yalagandula and Dahlin, 2004) is a

scalable distribution information system, where each

attribute is hashed to a key and the aggregation tree

rooted at the key is built upon the routing

mechanisms of Plaxton. Other algorithms also

include SOMO (Zhang, et al., 2003), Willow

(Renesse and Bozdog, 2004), and DAT (Cai and

Hwang, 2007). The token-based broadcast

algorithms combined with these DHT-based

aggregation algorithms can provide a scalable and

load-balanced distributed information management

in the large-scale computing infrastructures.

6 CONCLUSIONS

It is critical for the large-scale computing

infrastructures to support for scalable and efficient

broadcast. Existing DHT-based broadcast algorithms

suffer from the limitations of scalability and load

balancing. This paper presents a token-based

broadcast algorithm over DHT for the large-scale

computing infrastructures, where by leveraging the

topology and routing mechanisms of Chord, each

node selects the finger nodes as its children by a

token value in a top-down approach. Experimental

results show that compared to existing broadcast

algorithms, the token-based broadcast algorithm

reduces 50%~82% of the message imbalance factor.

Therefore, the token-based broadcast algorithm

constructs a scalable and balanced DBT, without any

extra storage cost and explicit maintenance overhead,

which is suitable for the large-scale computing

infrastructures.

ACKNOWLEDGEMENTS

This work is supported by the National Science

Foundation of China under grant No.60673155 and

No.90718008.

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129

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