Compact Tree Plus Algorithms for
Application-Level Multicast Communications in
Nobuo Funabiki* Megumi Isogai* Toru Nakanishi* Teruo Higashinot
*Department of Communication Network Engineering, Okayama University,
3-1-1 Tsushimanaka, Okayama 700-8530, Japan
tGraduate School of Information Science and Technology, Osaka University,
1-5 Yamadaoka, Suita, Osaka 565-0871, Japan
Abstract- Application-level multicast (ALM) communications
replicate packets on host level to deliver them from a single
source to multiple clients, so that it can efficiently realize a
variety of network applications using moving pictures such as
video conferences, distance learning, and video-on-demands. In
this paper, we propose the CT+ (Compact Tree Plus) algorithm for
finding a better ALM routing tree in terms of delay minimization
between hosts. CT+ consists of a tree construction stage from
the existing CT algorithm, and a newly added iterative tree
improvement stage. Then, we define the extended ALM routing
problem and its heuristic algorithm ExCT+, to optimize the
effectiveness of the multihome network in ALM communications
by selecting multihomed hosts and connections in the ALM
routing tree simultaneously. For their evaluations, we construct a
network simulation model named MINET (Multiple-ISPNETwork
simulator), where the topology is composed of multiple ISP
backbone networks with IX connections, and the network traffic
is generated by following the M/M/1 queuing process. The
simulation results using MINET verify the effectiveness of our
Recently, a variety of network applications with delivering
moving pictures such as video conferences, distance learning,
and video-on-demands have been demanded due to the spread
of broadband networks in every place. In these applications,
the multicast communication plays a key technology of de-
livering high bandwidth packets from a single source to
multiple destinations while reducing server loads and saving
network transmission bands. In multicast communications,
intermediate nodes on a routing path replicate packets to
deliver them to multiple clients. Currently, the application-
level multicast (ALM) communication has been noticed as a
practical multicast, where packets are replicated on host level,
instead of router level as in the IP multicast (IPM) [I]-.
ALM has several advantages over IPM, that it does not require
sophisticated routers to handle IPM functions and multicast
IP addresses, and it allows the flow control and the packet
retransmission scheme at the transport layer, because each pair
of hosts is connected through the unicast connection. Further-
more, ALM provides the flexibility of selecting connections
between hosts by users.
In ALM, the routing path between hosts usually becomes
a tree, where each vertex represents a host and each edge
represents a unicast connection between two hosts. Therefore,
the routing path is called an ALM routing tree in this paper.
The proper selection of an ALM routing tree is very important
for the delay minimiization that is essential in various ALM
applications involving motion picture streaming and large
data sharing among distributed hosts while concering the
resource limitation at hosts. This ALM routing problem has
been formulated as an NP-hard combinatorial optimization
problem, and several algorithms have been reported -.
The compact tree (CT) algorithm  has been known as a
typical algorithm for this problem. CT greedily constructs a
tree by selecting connections one-by-one such that resulting
partial trees minimize the maximum delay between any pair
of hosts while satisfying the constraint. However, the solution
quality of CTmay be insufficient, because it does not adopt the
improvement stage that has usually been adopted in heuristic
algorithms for NP-hard problems . Based on a local search
method, the improvement stage sometimes drastically refines
an initial solution of the construction stage.
ALM has several drawbacks in the increase of delay due
to longer paths than IPM, the increase of host loads due to
packet replications and plural connections at hosts, and the
increase of consumed network bands due to transmissions of
duplicated packets on network links. These drawbacks are
particularly undesirable for streaming applications including
video conferences where the data synchronization between
hosts is inevitable. For this solution, we have proposed the
introduction of the multihome network to ALM. In the mul-
tihome network, each host may have connections with one
or more internet service providers (ISPs). By selecting the
best ISP under the current network condition after measuring
RTT and the available bandwidth , the multihome network
can alleviate these drawbacks in ALM. To be more precise,
the multihome network can reduce communication loads on
1-4244-0000-7/05/$20.00 ©2005 IEEE.
the access links between hosts and ISP nodes (host access
points) by using different ISP links, and on the links in
internet exchangers (IXs) by exchanging ISPs at hosts instead
of exchanging them at IXs. In addition, the multihome network
provides the possibility of drastically shortening the routing
path by using single-ISP connections where both end hosts
are connected with the same ISP.
In this paper, we define the ALM routing problem in
the multihome network, and propose its compact tree plus
algorithm (CT+) by adding the improvement stage to CT. This
improvement stage repeats the replacement of a randomly se-
lected connection by another one that does not only satisfy the
constraint but also minimizes the delay among candidates. This
replacement is always processed regardless of the increase of
the delay, as long as such a connection exists. This mandatory
replacement avoids the convergence to a poor local minimum.
In reality, the current network environment does not allow
every host to have connections with multiple ISPs. Besides, the
multihome network usually costs more than the conventional
singlehome network. In practical, only a part of hosts partic-
ipating ALM applications should be multihomed. Therefore,
in this paper, we define the extendedALM routing problem in
the multihome network to select multihomed hosts and connec-
tions simultaneously under the limitation of the multihomed
cost, and present its extended CT+ algorithm (ExCT+). We
also study the effect of the increase of multihomed hosts in
the delay minimization in ALM.
For evaluations ofour algorithms and schemes forALM, we
construct a network simulation model named MINET (Multi-
ISP NETwork simulator). The network topology consists of
multiple ISP backbone networks and one IX for ISP connec-
tions. The IX directly connects one node in each ISP with a
node in any other ISP. The ISP backbone network exists on the
same square area. The topology is generated by following the
Waxman method , and the node nearest to the center of
the square is connected to a node in IX. The delay of each link
is given by the sum of the transmission delay, the switching
delay, and the buffering delay . The background traffic
is provided through random generations and terminations of
unicast connections by following the M/M/1 queuing model
. Each connection is routed along the shortest path when
any buffering delay is zero. When a new connection arrives,
its requested bandwidth is consumed on every link along the
path. When the total consumed bandwidth exceeds the link
capacity, the buffering delay occurs there.
The rest of this paper is organized as follows: Section
II formulates the ALM routing problem in the multihome
network and presents CT+. Section III defines the extended
ALM routing problem and presents ExCT+. Section IV out-
lines MINET. Section V evaluates the performance of our
algorithms using MINET with the increase of multihomed
hosts. Section VII concludes this paper with some discussions
on further studies.
II. CT+ FOR ALM ROUTING PROBLEM
A. ALM Routing Problem in Multihome Network
In the ALM routing problem in the multihome network, con-
nections between hosts are described by a directed weighted
ALM application. A directed edge e E E is assigned a weight
d(e) E W to represent the delay of the packet transmission
through the corresponding connection. When one end host of a
connection has connections with a ISPs and another one does
with b ISPs in the multihome network, the number of directed
edges corresponding to this connection is given by 2 x a x b.
In ALM, a host may replicate packets to send them to mul-
tiple hosts individually. If the number of packet replications
is too large, both the loads of the host and the access link
connecting the host and the access point of an ISP become
too high. Thus, the limit of the number of replications or host
connections for host v in the ALM routing tree T is given
as the degree constraintA'degree
between any pair of hosts should be minimized for motion
picture streaming applications.
From the above discussion, the ALM routing problem in
the multihome network is summarized as follows:
(V, E, W). A vertex v E V represents a host in the
In T, the both-way delay
< ALM routing problem in multihome network >
* Input: a connection graph G = (V, E, W) with multiple
edges, a degree limit A'egree.
* Output: an ALM routing tree T = (V?ET) with ETCE.
. Constraint: the number of packet replications at host v
is less than or equal to its limit:
degreeT(v) . Adegree
where degreeT(V) is the number of children of host v in
Objective: to minimize the maximum delay between any
pair of hosts E:
wherePij represents the routing path between host i and
host j in T.
B. Delay Observation
The delay of a connection is observed by sending a probe
packet from the source host to the destination and calculating
the difference between the sending time and the receiving
one, before the algorithm is applied. The synchronization of
clocks in every host is necessary in this scheme where it
can be realized by using GPS (global positioning system)
or NTP (network time protocol). Here, we note that if we
always observe the delay for every connection, the load of
this delay observation becomes very high, because n hosts
require 0(n2) observations even for a singlehome network.
Thus, we need to confine connections for delay observations in
the implementation of CT+ by pruning the connections whose
delays have been very large in past observations.
111. ExCT+ FOR EXTENDED ALM ROUTING PROBLEM
The proposed CT+ is a two stage heuristic algorithm for
the ALM routing problem. The tree construction stage adopts
the procedure of CT, and the tree improvement stage adopts
the state transition method that is a variant of a local search
1) Tree Construction Stage by CT: CT greedily constructs
an ALM routing tree T by initially including only one host
in V into T and then, sequentially expanding T by adding a
connection one-by-one that satisfies the degree constraint and
minimizes the maximum delay between any pair of hosts in
the resulting tree. In our implementation, every host is tried as
the initial host in T, and the best result in terms of the delay
among all the trials is selected as the final solution from CT,
to improve the solution quality.
< CT >
1) Initialize T= (VT, ET) by VT =v E V and ET = $
2) Terminate the procedure if VT = V.
3) Add one connection to T such that (1) it connects a host
in VT and another one inVIVT, (2) it satisfies the degree
constraint in T, and (3) it minimizes the maximum delay
between two hosts in T among candidates.
4) Return to step 2).
2) Tree Improvement Stage: The tree improvement stage
repeats modifications of T by replacing a randomly selected
connection in T by a different one that satisfies the degree
constraint if it exists. This compulsory replacement aims the
avoidance of a poor local minimum convergence that can often
occur in heuristic algorithms.
< CT+ >
1) Adopt T from CT as an initial tree, set the best found
tree Tbest = T, and initialize the number of iterations t
2) Terminate the procedure if t = K x IVI, and output
3) Randomly select a connection in ET and remove it from
T. This operation separates T into two partitions.
4) Add a different connection to T such that (1) it connects
the two partitions, (2) it satisfies the degree constraint,
and (3) it minimizes the maximum delay among can-
didates. If such a connection does not exist, return the
removed connection to T.
5) Memorize T as Tbest if the maximum delay between
two hosts in T is smaller than that in Tbest.
6) Increment t by 1, and return to step 2).
3) Time Complexity ofCT+: In the construction stage, step
3) requires O(1V12) time. In the improvement stage, step 4)
requires O(1V13) time where each of O(1V12) connections in
E is evaluated with O(IVI) delay calculations. As a result, the
time complexity of CT+ is O(KIVI4).
A. Extended ALM Routing Problem in Multihome Network
As mentioned in Section 1, every host in an ALM ap-
plication may not be multihomed due to the cost and ISP
infrastructures. If the total cost for multihomed hosts is limited,
multihomed hosts should be selected with appropriate ISP
connections simultaneously when the ALM routing tree is
constructed. Therefore, we define the extended ALM routing
problem in the multihome network to cope with this issue. As
the input to this problem, we assume the following conditions:
1) Every host has already been connected with one ISP.
2) The list of available ISPs is given at each host, and
the delay of any connection between hosts using an
additional ISP in the list can be observed without an
3) The total cost for multihomed hosts is limited by a
Then, for this problem, the following multihome cost con-
straint is imposed additionally to the ALM routing problem:
E c(v, k)<Acost
where c(v, k) is the cost for using the k-th ISP connection at
host v, and M is the set of additionally used ISP connections
B. Proposal ofExCT+
In the proposed ExC'T+, any additional ISP connection
is used only if it satisfies the multihome cost constraint.
Specifically, in step 3) of the construction stage and step 3) of
the improvement stage in CT+, an additional ISP connection
is selected there when either of the following two conditions
is satisfied in addition to satisfying the conditions for CT+:
. the additional ISP connection has already been used at
the total cost does not exceed Acost when the ISP
connection is newly used at the host.
Besides in the implementation, in step 2) of the improve-
ment stage, if the removed connection from T uses an addi-
tional ISP connection and no other in T uses it at the host,
the multihome cost is decreased by its cost.
IV. MULTI-ISP NETWORK SIMULATOR MINET
The topology of MINET consists of multiple ISP backbone
networks (10 ISPs in simulations) and one IX as illustrated
in Figure 1. The topology of an ISP backbone network is
generated by the Waxman method , where nodes (100
nodes in simulations) are randomly located on a square called
the network field (3, OOOkm on each side in simulations). In
each ISP network, the node nearest to the center in the network
field is selected as a node in IX. IX connects any pair of nodes
C Proposal ofCT+
B. Link Delay
The delay of a link is given by the sum of the transmission
delay, the switching delay, and the buffering delay. The
transmission delay is the time required to propagate packets
physically through the signal transmission line, and is given by
dividing the line length with the light speed (300, OOOkm/s).
The switching delay is the time to switch received packets
to their destination ports at the router, and can be constant
(lOms in simulations). The buffering delay is the time for
packets to stay in buffers to wait for their delivery from
output ports, and is given by dividing the queued packet size
with the transmission bandwidth of the link. The buffering
delay appears when the amount ofpacketflows through a link
exceeds the link capacity. In simulations, the link capacity is
set 5Gbps for IX and lGbps for ISP.
C. Background Traffic
The goal of the algorithms in this paper is to find an
ALM routing tree with the minimum delay between any
pair of hosts under conventional network conditions. As the
network background traffic in MINET, unicast connections are
randomly generated and terminated between any pair of nodes
by following the M/M/1 queuing model at each node. That is,
a connection arrives at a node by the Poisson probability with
a randomly selected destination node, and it continues by the
exponential probability. The connection is routed through the
shortest path from the source node to the destination when
any buffering delay is zero. The amount of packet flows of
the links along the path is increased by the given traffic of
the connection, which is randomized between 100Kbps and
1OMbps in simulations.
In order to generate heterogeneous network loads, we intro-
duce the dispersion of connection arrival rates and burst con-
nections. In the former scheme, all the nodes are categorized
into a high-load group and a low-load group by a constant
ratio (1: 4 in simulations). Then, the connection arrival rate
is randomly selected between the highest value and the lowest
one for each node. In simulations, these values are set 0.8s-1
/ 0.2s-1 for the high-load group, and 0.4s-1 / 0.1s-1 for
the low-load group. The termination rate is randomly selected
between ls-1 and 0.1s-1 at any node. For the latter scheme,
a constant fraction of connections (10% in simulations) is
selected as burst connections, where the link capacity (lGps)
becomes fully occupied for ls.
V. EVALUATIONS BY SIMULATIONS
A. Simulation Steps
The performance of the proposed CT+ and ExCT+
evaluated through simulations using MINET. Actually, each
MINET simulation is performed through the following steps:
1) The host configuration is set up.
2) The network state transits from the initial one to a
stationary one by calculating background traffics for
3) The delay of a connection between each pair of hosts
through every available ISP connection is observed for
4) The algorithm finds an ALM routing tree.
5) The delay of a connection between each pair of hosts
through the ALM routing tree is observed for lOOs, and
the maximum delay between two hosts is calculated,
while an ALM application (1.5Mbps) is executed.
B. Host Configuration
The number of hosts n for an ALM application is set 10
and 50 in our simulations. The host locations are random-
ized within the network field. The number of additional ISP
connections at each host is fixed to one. Thus, two ISPs are
selected randomly for each host, where the first one becomes
the established connection, and the second is the additional
one. The nearest node in the corresponding ISP backbone
network from the host location is selected as the access node
to the host. The same tree degree limit A'gree is set 3 or 4
for every host. The multihome cost c(V, k) is set 1 for any ISP
connection at any host. Thus, the cost limit Acost is equivalent
to the upper bound on the number of multihomed hosts.
C. Delay Observation
The delay of a connection is calculated by the sum of delays
associated with the links along the path from its source host to
the destination. For accuracy, the delay observation is applied
100 times at every 1 second for any connection, and their
average value is used for evaluations.
D. Simulation Results
Figures 2-5 show changes of the maximum delay between
two hosts by using ALM routing trees found by CT (dashed
line), CT+ (double dashed line), and ExCT+ (solid line),
when the percentage of multihomed hosts among all the hosts
increases from 0% to 100%.
multihomed hostpercentage (%)
Maximum delay at ALM application (n = 10,Aldegree=3).
1) Comparison between Three Algorithms: In any figure,
the delay by CT+
CT, whereas the delay by ExCT+ is much smaller than the
delays by others when a part of hosts are multihomed. The
combination of the improvement stage and the multihomed
host selection in ExCT+ is very effective in reducing the
delay of the ALM routing tree. Thus, the repetition of the
simultaneous selection of connections and multihomed hosts
is critical for providing a high-quality ALM routing tree.
2) Effect of Multihome Network: In any figure, the delay
decreases as the percentage of multihomed hosts increases.
Thus, the results confirm the effectiveness of the multihome
network in reducing the delay in ALM by increasing the
number of single-ISP connections in the tree. However, this
effect becomes small for the case of n = 50, because many
connections even in the singlehome network can be single-ISP
ones, as the number of ISPs is fixed 10. We note that when
20% of hosts can be multihomed, ExCT+ achieves almost the
same delay for 100%. Thus, a small number of multihomed
hosts can reduce the delay in ALM. The detailed investigation
on the relationships between the number of multihomed hosts,
the number of ISPs, and the delay reduction by our algorithms
will be in our future studies.
is slightly smaller than the delay by
VI. RELATED WORK
In , Sheu et al. first introduced the peer-to-peer technique
for video streaming applications. In , Aharoni et al. first
proposed the concept of ALM communications. In , Cohen
et al. defined a family of minimum path set problems for
ALM communications, and proposed the maximum bottle-
neck tree algorithm for its maximum bottleneck version. In
, Pendarakis et al. presented a centralized middleware of
generating the minimum spanning tree for ALM communi-
cations called ALMI. In [61, Chu et al. proposed an ALM
protocol of generating the shortest widest path tree for ALM
communications on a mesh-type overlay network. In [l0],
Shi et al. proposed CT for ALM communications using MSNs
(multicast service nodes) that have been deployed around net-
multihomed host percentage (%)
Maximum delay at ALM application (n = 10, Qderee = 4)
mulihomed host percentage (%a)
Maximum delay at ALM application (n = 50, A'
works as multicast routers performed at host level. They also
proposed several modifications of CT so that as many ALM
requests as possible can be afforded in the MSN network. In
[II], Banerjee et al. formulated the minimum average-latency
degree-bounded directed spanning tree problem for the MSN
network, and proposed its distributed iterative approach where
the performance is compared with optimum solutions and CT
solutions. In , Yun et al. proposed a genetic algorithm for
an ALM routing problem with two objectives. In , Tran et
al. proposed an ALM solution called ZIGZAG organizing an
efficient routing tree with height logarithmic by the number of
clients and a node degree bound by a constant. In , Zhang
et al. proposed a hybrid multicast framework called Host
Multicast of automating the interconnection of IP-multicast
enabled islands and providing the multicast delivery to end
hosts where IP multicast is not available. In , Cheuk et al.
also proposed the similar scheme called Island Multicast using
overlay connections between IP-multicast enabled islands and
supporting IP-multicast for intra-islands. In , Bawa et al.
argued that masking peer transience is the primary challenge
ofALM communications for short lifetime hosts participating
0 Download full-text
.t- ...... -*
multihomed host percentage(%)
Maximum delay at ALM application (n = 51
in long-durationed multicast sessions, and outl]
layer to separate policy decisions in handling
from end-applications. Based on their concept
an ALM solution called PeerCast [171. In [18
presented a middleware with the multipath rou
ALM communications. In , Yamashita
a middleware for multiparty video communi(
Li et al. proposed a QoS-aware routing pro
communications on overlay networks called
Zhu et al. proposed schemes of applying the
with a two-redundant multicast graph to imp:
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of ALM solutions, and classified them accor
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QRON. In ,
rveyed a variety
rding to charac-
This paper has presented the CT+ (Comr
algorithm for the ALM (Application-Level Mi
problem, and the ExCT+ (Extended CT+) a
timize the effectiveness of the multihome ne
communications. Using the MINET (Multipl,
simulator), the effectiveness of these algoritl
Our future studies will include discussions on t]
tree modification to deal with joins and/or
during ALM applications, the use of availab]
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