HPF

Hybrid Periodical Flooding in Unstructured Peer-to-Peer Networks*
*
This work was partially supported by Michigan State University IRGP Grant 41114 and by Hong Kong RGC Grant HKUST6161/03E.
Zhenyun Zhuang1
, Yunhao Liu1
, Li Xiao1
and Lionel M. Ni2
1
Department of Computer Science and Engineering, Michigan State University, U.S.A.
2
Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong
{zhuangz1, liuyunha, lxiao}@cse.msu.edu, ni@cs.ust.hk
Abstract
Blind flooding is a popular search mechanism used
in current commercial P2P systems because of its sim-
plicity. However, blind flooding among peers or super-
peers causes large volume of unnecessary traffic al-
though the response time is short. Some improved sta-
tistics-based search mechanisms can reduce the traffic
volume but also significantly shrink the query coverage
range. In some search mechanisms, not all peers may
be reachable creating the so-called partial coverage
problem. Aiming at alleviating the partial coverage
problem and reducing the unnecessary traffic, we pro-
pose an efficient and adaptive search mechanism, Hy-
brid Periodical Flooding (HPF). HPF retains the ad-
vantages of statistics-based search mechanisms, allevi-
ates the partial coverage problem, and provides the
flexibility to adaptively adjust different parameters to
meet different performance requirements. The effective-
ness of HPF is demonstrated through simulation studies.
1 Introduction
In an unstructured P2P system, such as Gnutella [7]
and KaZaA [8], file placement is random, which has no
correlation with the network topology [17]. Unstruc-
tured P2P systems are most commonly used in today's
Internet. In an unstructured P2P system, when a source
peer needs to query an object, it sends a query to its
neighbors. If a peer receiving the query cannot provide
the requested object, it may relay the query to its own
neighbors. If the peer receiving the query can provide
the requested object, a response message will be sent
back to the source peer along the inverse of the query
path. The most popular query operation in use, such as
Gnutella and KaZaA (among supernodes), is to blindly
“flood" a query to the network. A query is broadcast
and rebroadcast until a certain criterion is satisfied. This
mechanism ensures that the query will be “flooded” to
as many peers as possible within a short period of time
in a P2P overlay network. However, flooding also
causes a lot of network traffic and most of which is un-
necessary. Study in [13] shows that P2P traffic contrib-
utes the largest portion of the Internet traffic based on
their measurements on three popular P2P systems,
FastTrack (including KaZaA and Grokster) [5],
Gnutella, and DirectConnect. The inefficient blind
flooding search technique causes the unstructured P2P
systems being far from scalable [11].
To avoid the large volume of unnecessary traffic in-
curred by flooding-based search, many efforts have
been made to improve search algorithms for unstruc-
tured P2P systems. One typical approach is statistics-
based, in which instead of flooding to all immediate
overlay neighbors, a peer selects only a subset of its
neighbors to query based on some statistics information
of some metrics and heuristic algorithms. When han-
dling a query message (either relayed from its neighbor
or originated from itself) in a statistics-based search al-
gorithm, the peer determines the subset of its logical
neighbors to relay the query message. Statistics-based
search mechanisms may significantly reduce the traffic
volume but may also reduce the query coverage range
so that a query may traverse a longer path to be satisfied
or cannot be satisfied. In some search mechanisms, not
all peers may be reachable creating the so-called partial
coverage problem. Our objective is trying to alleviate
the partial coverage problem and reduce unnecessary
traffic.
In this paper, Section 2 will give an overview and
classification of known search mechanisms. The con-
cept of our proposed periodical flooding method will be
introduced in Section 3. Based on periodical flooding
and weighted metrics in selecting relay neighbors, the
hybrid periodical flooding (HPF) method is detailed in
Section 3. The proposed HPF can improve the effi-
ciency of blind flooding by retaining the advantages of
statistics-based search mechanisms and by alleviating

the partial coverage problem. Section 4 describes our
simulation method and the performance metrics. Per-
formance evaluation of our proposed HPF method
against other search methods is described in Section 5.
Section 6 concludes the paper.
2 Search Mechanisms
In unstructured P2P systems, the placement of ob-
jects is loosely controlled and each peer has no hint
where the intended objects are stored. Without having
the global knowledge of the dynamic overlay network
and the locations of target peers, a source peer has to
send a query message to explore as many peers as pos-
sible in the overlay network. A well-designed search
mechanism should seek to optimize both efficiency and
Quality of Service (QoS). Efficiency focuses on better
utilizing resources, such as bandwidth and processing
power, while QoS focuses on user-perceived qualities,
such as number of returned results and response time.
In unstructured P2P systems, the QoS of a search
mechanism generally depends on the number of peers
being explored (queried), response time, and traffic
overhead. If more peers can be queried by a certain
query, it is more likely that the requested object can be
found. In order to avoid having query messages flowing
around the network forever, each query message has a
TTL (time-to-live: the number of times a query will be
forwarded) field. A TTL value is set to limit the search
depth of a query. Each time a peer receives a query, the
TTL value is decremented by one. The peer will stop
relaying the query if TTL becomes zero. A query mes-
sage will also be dropped if the query message has vis-
ited the peer before. Note that the query messages are
application-level messages in an overlay network.
In statistics-based search mechanisms, a peer selects
a subset of its neighbors to relay the query based on
some statistics information of some metrics and heuris-
tic algorithms. Based on the number of selected logical
query neighbors and the criteria in selecting logical
query neighbors, the statistics-based search algorithms
in unstructured P2P systems can be roughly classified
into two types: uniformed selection of relay neighbors
and weighted selection of relay neighbors.
2.1 Uniformed Selection of Relay Neighbors
In this approach, all logical neighbors are equally
treated when selected to relay the query message.
Blind flooding. Blind flooding mechanism relays the
query message to all its logical neighbors, except the
incoming peer. This mechanism is also referred as
breadth-first search (BFS) and is used among peers in
Gnutella or among supernodes in KaZaA. For each
query, each node records the neighbors which relay the
query to it. Thereby on each link, at most two query
messages can be sent across it. For an overlay network
with m peers and average n neighbors per peer, the total
traffic caused by a query is mn if the value of TTL is no
less than the diameter of the overlay network. Note that
in a typical P2P system, the value of m (more than mil-
lions) is much greater than n (less than tens) [13]. In
this approach, the source peer can reach its target peer
(object) through a shortest path. However, the overhead
of blind flooding is very large since flooding generates
large amount of unnecessary traffic, wasting bandwidth
and processing resource. The simplicity of blind flood-
ing makes it very popular in practice.
Depth-first search (DFS). Instead of sending que-
ries to all the neighbors, a peer just randomly selects a
single neighbor to relay the query message when the
TTL value is not zero and waits for the response. This
search mechanism is referred to as depth-first search
(DFS) and is used in Freenet [6]. DFS can terminate
timely when the required object has been found, thus
avoiding sending out too many unnecessary queries. In
DFS, the value of TTL should be set sufficiently large
to increase the probability of locating the object. The
maximum number of peers that a query message will
visit is TTL. Thus, setting a proper TTL value is a key
issue to determine the search quality. The response
time could be unbearably large due to the nature of its
sequential search process. Because of the random selec-
tion of relay neighbors, it is possible that an object can
hardly be found.
K-walker. In k-walker query algorithm proposed in
[10], a query is sent to k different walkers (relay
neighbors) from the source peer. For a peer in each
walker, it just randomly selects one neighbor to relay
the query. For each walker, the query processing is
done sequentially. For k walkers with up to TTL steps,
each query can reach up to k�TTL peers in the P2P
network. We can view k-walker search mechanism as a
multiple of DFS. It has been shown that k-walker
mechanism creates less traffic than that of BFS and
provides shorter response time than that of DFS. How-
ever, k-walker suffers limited query coverage range due
to the randomness nature in selecting query neighbors.
2.2 Weighted Selection of Relay Neighbors
Instead of randomly selecting relay neighbors, some
mechanisms have been proposed to select relay
neighbors more objectively so that neighbors who are
most likely to return the requested results are selected.
Some statistics information is collected based on some
metrics when selecting relay neighbors. Possible met-
rics include delay of the link to the corresponding
neighbor, the processing time of the neighbor, the com-
puting power, the cost (if possible), the amount of shar-
ing data, and the number of neighbors, etc.

Directed BFS (DBFS). Each peer maintains statistic
information based on some metrics, such as the number
of results received from neighbors from previous que-
ries or the latency of the connection with that neighbor.
A peer selects a subset of the neighbors to send its
query based on some heuristics, such as selecting the
neighbors that have returned the largest number of re-
sults from previous queries or selecting the neighbors
that have the smaller latency.
Routing indices (RI). The concept of routing indices
(RI) was proposed in [3]. Each peer keeps a local RI
that is a detailed summary of indices, such as the num-
ber of files on different topics of interests along each
path. When a peer receives a query, it forwards the
query to the neighbor that has the largest number of
files under a particular topic, rather than selecting relay
neighbors at random or flooding to all neighbors.
Some weighted-selection search mechanisms have
demonstrated performance improvement compared with
uniformed-selection search mechanisms. However,
weighted-selection search mechanisms have the partial
coverage problem to be illustrated in Section 2.4.
2.3 Other Approaches
In addition to the aforementioned search policies,
there are other techniques that may be used to improve
search performance. For example, a peer can cache
query responses in hoping that subsequent queries can
be satisfied quickly by the cached indices or responses
[14, 16, 17]. Peers can also be clustered based on dif-
ferent criteria, such as similar interests [14], location in-
formation [9], and associative rules [4]. Our proposed
statistics-based technique can be used to complement
these techniques.
2.4 Partial Coverage Problem
Statistics-based search algorithms indeed can reduce
network traffic. For example, compared with blind
flooding, DBFS can reduce the aggregate processing
and bandwidth cost to about 28% and 38%, respectively
with 40% increase in the response time [17]. However,
our study will show that statistics-based search mecha-
nisms may leave a large percentage of the peers un-
reachable no matter how large the TTL value is set. We
call this phenomena partial coverage problem. This
problem is illustrated in Fig.1(a). The number by an
edge is the latency between two logical nodes and the
number in each node is the number of shared files on
that peer. Suppose the size of selected neighbor subset
is one and the metric used to select the neighbor is
based on the number of shared files. We consider the
scenario when the query source is A who has four
neighbors (B, C, D, E). It will only send its query to C
since C has the largest number of shared files (170).
Similarly, C selects D who has the largest number of
shared files in all C’s neighbors (B, D, F, G) to relay
A’s query. Then D selects A in the same way, which
leads to a loop query path: A�C�D�A. Thus, only
three nodes are queried in the whole query process
while all other nodes are invisible from the query
source A. If we change the metric to be the smallest la-
tency, the problem still exists because another loop is
formed from source A, A�C�B�A. It is very possible
that the query cannot be satisfied in the loop. This prob-
lem can be less serious when the size of the query sub-
set increases, which will be discussed in Section 3.
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(a) Query path loops (b) Non-optimal query path
Figure 1. The partial coverage problem
Many statistics-based search approaches use only
one metric to collect statistics information to select re-
lay neighbors, which does not always lead to an optimal
search path. Figure 1(b) shows an example in which A
is still the source node. When the search metric is the
volume of shared data, the query path would be
A�D�E along which the query will check 250 files in
200 unit of time. But obviously if the query path is
A�C�G�F�H, the query can check 500 files in 20
units of time. The first path selected using one search
metric is not as good as the second one.
3 Hybrid Periodical Flooding
In order to effectively reduce the traffic incurred by
flooding-based search and alleviate the partial coverage
problem, we propose Hybrid Periodical Flooding (HPF).
Before discuss HPF, we first define Periodical Flooding.
3.1 Periodical flooding (PF)
We notice that in all the existing statistics-based
search techniques, the number of relay neighbors, h,
does not change at all peers along the query path. In the
case of blind flooding, the phenomenon exhibits traffic
explosion. The concept of periodical flooding tries to
control the number of relay neighbors based on the TTL
value along the query path. More specifically, given a
peer with n logical neighbors and the current value of
TTL, the number of relay neighbors, h, is defined by the
following function h=f(n,TTL). Thus, in blind flooding
(BFS), we have h=fBFS(n,TTL)=n.. In DFS, we have
h=fDFS(n,TTL)=1.
The function h=f(n,TTL) can be viewed as a periodi-
cal function that changes as TTL changes. We call a

search mechanism using a periodical function as peri-
odic flooding (PF), in which the query mechanism is
divided into several phases that are periodically re-
peated. We call the number of different repeated phases
as a cycle, C. In all existing statistics-based search tech-
niques, they all have a cycle of C=1, which are special
cases of PF. We can ask the following questions in or-
der to design an efficient search mechanism. In what
conditions does a search mechanism with C=1 behave
better than a search mechanism with C>1? What is the
optimal value of C in terms of a desired performance
metric under different underlying physical network to-
pologies? For a given C, what is the optimal number of
relay neighbors? One example of PF functions with
C=2 is shown below:
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(a) BFS (b) PF
Figure 2. Comparison between BFS and a PF
We compare BFS and the example PF in Fig. 2. Sup-
pose peer O initiates a query. Blind flooding (BFS) is
employed in Fig. 2(a) where the query is sent or for-
warded 36 times to reach all the nodes. We use thin
connections to represent the links on which the query
traverses once and thick connections to represent the
links on which the query traverses twice. We have ex-
plained that for each query, each peer records the
neighbors, which forward the query to it. Thereby on
each link, at most two query messages can be sent
across it. When a link is traversed twice, the unneces-
sary traffic is incurred. For example, one of the mes-
sages from A to B and from B to A is unnecessary.
These redundant messages are shown in Fig. 2(a) using
dotted arrows.
Figure 2(b) illustrates the query process of the ex-
ample PF. Peer O has 4 neighbors and has TTL=7. We
randomly select relay neighbors. Peer O will select 2
nodes (that is n/2=2 since TTL=7 that is odd), peers A
and C, as relay neighbors. Peer A has 5 neighbors. It
will select 2 neighbors (G and I) to relay the query initi-
ated from peer O since TTL=6 and h=�n/3�=2. Simi-
larly, peer C relays the query to peer B and N (TTL=6
and h=�n/3�=2). Although the redundancy problem
still exists in PF (such as the traffics from B to J and
from I to J), it is significantly reduced compared with
that of BFS.
Table 1. PF and Blind Flooding
TTL Query Msg New Peers Msg Per Peer
7 4 4 1.00
6 17 8 2.12
BFS
5 15 2 7.50
7 2 2 1.00
6 4 4 1.00
PF
5 9 8 1.12
Table 1 compares the redundancy degree of both PF
and BFS. It presents the query messages relayed to new
peers. For example, in BFS, peers with TTL=5 relay the
query to 15 peers, but only 2 of the 15 peers receive the
query first time. In PF, peers with TTL=5 relay the
query to 9 peer of which 8 are first time receivers. That
means for peers with TTL=5, BFS sends 7.5 queries to
one new queried peer in average, while PF only sends
1.12 queries to one new queried peer in average. An ef-
ficient mechanism should query more peers using less
messages. Thus PF is much more efficient than BFS in
terms of traffic volume.
3.2 Hybrid Periodical Flooding
HPF Overview
After determining the number of relay neighbors (h),
a peer decides which h nodes should be selected. A
simple approach called Random Periodical Flooding
(RPF) selects h relay neighbors at random. Selecting re-
lay neighbors more objectively may result in better per-
formance. For example, we may use the shared data
volume as a metric to select query neighbors if we find
that peers with more shared data are more likely to sat-
isfy queries. By selecting the neighbors with larger
number of shard data, a query is more likely to succeed
in less number of hops than that of random selection.
We may also use the latency between the peer and its
neighbors as a metric to select neighbors. In this case,
for a given TTL value, a query will experience a shorter
delay. If we consider multiple metrics in relay neighbor
selection, the search mechanism is expected to have
better performance. This motivates us to propose Hy-
brid Periodical Flooding (HPF) in which the number of
relay neighbors can be changed periodically based on a
periodical function and the relay neighbors are selected
based on multiple metrics in a hybrid way.
HPF differentiates with RPF in that RPF selects re-
lay neighbors randomly, and differentiates with DBFS
in that DBFS only uses one metric to select relay
neighbors. HPF selects neighbors based on multiple
metrics and provides flexibility to justify different pa-
rameters to improve overall performance. Let h denote
the expected number of relay neighbors, which is given

by h = h1 + h2 + … + ht, where t is the number of met-
rics used in relay neighbor selection and hi is the num-
ber of relay neighbors selected by metric i.
Metrics
There are many metrics that may be used to select re-
lay neighbors, such as communication cost, bandwidth,
number of returned results from the neighbor, average
number of hops from the neighbor to peers who re-
sponded the previous queries, and so on. These metrics
may have different weights for a system with different
query access patterns or different performance require-
ments. For example, we may give higher weights to
some metrics that are more sensitive to the performance
in a specific system. We have ��
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t
i
iw
1
1 , where iw is
the weight assigned to metric i ( ti ��1 ). To alleviate
the partial coverage problem, we select relay neighbors
in a hybrid way. We select hi neighbors using metric i,
where hi is determined by � �ii whh �� . Let Si denote
the set of neighbors selected based on the metric i. The
complete set of relay neighbors is i
t
i
SS
1�
� � , where
|S| iih � . Note that a neighbor may be selected by
more than one metric. Thus, the actual number of relay
neighbors selected may be less than h.
Termination of Search Queries
A query process is terminated when a pre-set TTL
value has been decreased to zero. Choosing an appro-
priate TTL value is very difficult. A large TTL may
cause higher traffic volume, while a small TTL may not
respond with enough number of query results. Further-
more there are no mutual feedbacks between the source
peer and the peers who forward or respond the query.
Thus it is hard for peers to know when to stop forward-
ing the query before the TTL value is reduced to zero.
Iterative Deepening [17] made an effort to address
this problem in some degree. In Iterative Deepening, a
policy P is used to control the search mechanism, which
provides a sequence of TTLs so that a query is flooded
from a very small TTL, and if necessary, to a gradually
enlarged scope. For example, one policy can be P={a, b,
c}, where P has three iterations. A query starts to be
flooded with TTL=a. If the query cannot be satisfied, it
will be flooded with TTL=b-a from all peers that are a
hops away from the source peer. Similarly if the query
still cannot be satisfied, it will be flooded with TTL=c-b
from all peers that are b hops away from the source peer.
In this policy, c is the maximal length of a query path.
Iterative Deepening is a good mechanism in the sense
that it alleviates the process time of middle nodes be-
tween iterations.
In HPF, we use this policy to terminate the success-
ful queries without incurring too much unnecessary
traffic. Since the combination is quite straightforward
and the performance of Iterative Deepening policy has
been evaluated in [17], this policy will not be re-
evaluated in this paper.
4 Simulation Methodology
We use simulation to evaluate the performance of
RPF and HPF and analyze the effects of the parameters.
4.1 Topology Generation
Two types of topologies, physical topology and logi-
cal topology, have to be generated in our simulation.
The physical topology should represent the real topol-
ogy with Internet characteristics. The logical topology
represents the overlay P2P topology built on top of the
physical topology. All P2P nodes are in the node subset
of the physical topology. The communication cost be-
tween two logical neighbors is calculated based on the
physical shortest path between this pair of nodes. To
simulate the performance of different search mecha-
nisms in a more realistic environment, the two topolo-
gies must accurately reflect the topological properties of
real networks in each layer.
Previous studies have shown that both large scale
Internet physical topologies [15] and P2P overlay to-
pologies follow small world and power law properties.
Power law describes the node degree while small world
describes characteristics of path length and clustering
coefficient [2]. Studies in [12] found that the topologies
generated using the AS Model have the properties of
small world and power law. BRITE [1] is a topology
generation tool that provides the option to generate to-
pologies based on the AS Model. Using BRITE, we
generate 10 physical topologies each with 10,000 nodes.
The logical topologies are generated with the number of
peers ranging from 1,000 to 5,000. The average number
of edges of each node is ranging from 6 to 20.
4.2 Simulation Setup
The total network traffic incurred by queries and av-
erage response time of all queries are two major metrics
that we use to evaluate the efficiency of a search
mechanism. High traffic volume will limit system scal-
ability and long response time is intolerable for users.
Network administrators care more about how much
network bandwidth consumed by a P2P system, while
users care more about the response time of queries,
which is viewed as a part of service quality of the sys-
tem.

0 5 10 15 20 25 30 35 40 45 50
0
1%
2%
3%
4%
5%
6%
7%
8%
Coverage Size
NodesDistribution(%)
1,000-node overlay network
10,000-node physical network
400 410 420 430 440 450 460 470 480 490 500
0
1%
2%
3%
4%
5%
6%
7%
8%
9%
Coverage Size
0 10 20 30 40 50 60 70 80 90 100
0
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
Coverage Size
Figure 3. Node distribution vs. cover-
age size. (h=1, metric 2)
In our simulation, we consider two metrics with the
same weight to select relay neighbors in HPF. In prac-
tice, more metrics could be used for neighbor selection.
The two metrics are the communication cost (metric 1)
that is the distance between a peer and its neighbor and
the shared number of files (metric 2) on each node.
Based on the first metric, a peer will select the
neighbors with the less communication costs. Based on
the second metric, a peer will select the neighbors with
the larger amount of shared data.
For each given search criterion, we distribute 100
files satisfying the search on the peers in a generated
P2P topology. That means there are totally 100 possible
results for a specific query in the whole P2P network.
The distribution of the 100 files on the network is ran-
dom. For each peer, we generate a number within 1 to
1000 as the number of shared files in this peer. Based
on the second metric in selecting relay neighbors, a
neighbor with more shared files is more likely to return
a response than a neighbor with less shared files.
5 Performance Evaluation
In this section, we present the simulation results to
show the effectiveness of HPF compared with DBFS
and BFS.
5.1 Partial Coverage Problem
Based on [3, 17], statistics-based search mechanisms
are more efficient and incur less traffic to the Internet
compared with blind flooding. However, statistics-
based search mechanisms have partial coverage prob-
lem as we discussed in Section 2.4. We quantitatively
illustrate the partial coverage problem in this section.
We first illustrate the case in which only one relay
neighbor is selected to send/forward a query (h=1)
based on the number of shared files in neighbors. We
set TTL as infinity. Figure 3 shows the node distribution
versus the number of peers being queried, which is de-
fined as coverage size. For example, queries initiated
from 8% of peers can only reach 10 other peers. Most
of peers can only push their queries to 10 to 30 other
peers. This means that loops are formed and only a very
small number of peers can be reached for any queries.
Note that the overlay network has 1000 nodes and the
physical network has 10,000 nodes. Figure 4 illustrates
the node distribution versus the coverage size, where
h=2 and TTL=infinity. The coverage size is about 400
peers in average, which is still a small number in a P2P
network.
Figure 5 shows node distribution versus coverage
size when we use network latency as the metric to se-
lect relay neighbors. Again, we see the partial coverage
problem. The partial coverage problem will disappear
when h=n, which is the case of blind flooding. We did
the same group of simulations on different topologies
using different metrics. The results are quite consistent.
Figure 6 shows the percentage of covered peers to total
peers versus the number of relay neighbors (h=1, 2, n/5,
n/4, n/3, n/2, and Sqrt(n)). The percentage of coverage
is larger for a larger h. A larger h means a smaller
chance for all reached peers to form a loop.
One Two 1/5 1/4 1/3 Half Sqrt
0
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Number of Relay Neighbors
PercentageofCoveredNodes
1.65%
42.4%
56.3%
63.0%
77.5%
87.5%
77.6%
Figure 6. Percentage of coverage vs. the number of
relay neighbors
5.2 Performance of Random PF
We have evaluated network traffic and average re-
sponse time of RPF that selects relay neighbors at ran-
dom. We can use many different periodical flooding
functions to determine the number of relay neighbors.
These functions should not be over complicated. We
have tried tens of periodical flooding functions with dif-
ferent C.

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Requested Number of Response Results
NormalizedQueryCost
BFS
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RPF (3)
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NormalizedQueryCost
BFS
RPF
DBFS
HPF
Figure 7. Normalized traffic of RPF Figure 8. Normalized response
time of RPF
Figure 9. Normalized traffic com-
parison
Figures 7 and 8 show the normalized network traffic
cost and normalized average response time versus the
required number of response results. The traffic and av-
erage response time always perform in opposite way. If
a search mechanism causes low traffic, it will suffer
from high response time and vice versa. RPF is de-
signed to provide an opportunity to have a tradeoff be-
tween total traffic and average response time, thus ob-
taining a better overall search performance. We may
expect a search mechanism to reduce a large amount of
traffic by increasing a little more response time or vice
versa. How to quantitatively measure the overall per-
formance based on the tradeoff is an issue.
It’s hard to find the best search mechanism. We de-
fine p to measure the overall performance, where
timetrafficp RC �� , traffic and time are nor-
malized value of total network traffic and average re-
sponse time, �C and �R are the weight parameters for
network traffic and response time, and �C + �R = 1. We
seek an asymptotically periodical flooding function
fa(n,TTL) such that p can be minimal or close to mini-
mal. If a system emphasizes more on low network traf-
fic, we can set �C > �R; otherwise, we can set �C < �R
for a system emphasizing more on quick response time.
Based on different topologies with different number
of average connections, and different values of �C and
�R, the functions of fa(n,TTL) may be derived differently.
In our simulation of HPF, the average number of edge
connections is 10. We choose �C = 0.6 and �R = 0.4.
Thus, the corresponding period function is derived as:
�
�
�
�
�
�
�
��
�
��
�
��
�
��
�
�
evenisTTLifn
oddisTTLifn
TTLnf
,
4
1
,
2
1
),(
5.3 Effectiveness of HPF
HPF selects relay neighbors based on multiple met-
rics in a hybrid way. We use communication cost and
the volume of shared data as two metrics to select relay
neighbors.
Based on the simulation over 10,000 queries, Figure
9 shows the normalized network traffic versus the re-
quired number of response results of four different
search mechanisms: BFS, RPF, DBFS and HPF. DBFS
reduces the network traffic by 30~50% compared with
BFS. HPF outperforms DBFS by up to 20%. Figure 10
compares the normalized response time of four different
search mechanisms over 10,000 queries versus the re-
quired number of response results. HPF performs the
best compared with RPF and DBFS, but still worse than
BFS. DBFS selects relay neighbors who have the larg-
est volume of shared files. Each query may get more re-
sults by reaching fewer peers. HPF needs to query more
peers to obtain the same amount of results than DBFS
but much less than BFS and RPF. That is because we
use multiple metrics instead of a single metric used in
DBFS, expecting to obtain better overall performance,
which has been shown in Figs. 9 and 10.
5.4 Alleviating the Partial Coverage Problem
HPF can effectively address the partial coverage
problem discussed in Section 2.4. Figure 11 shows the
percentage of queried peers as TTL increases. BFS can
quickly cover 100% peers, while DBFS can only cover
up to 77% peers in our simulation because of the partial
coverage problem. DBFS still covers only around 77%
when the value of TTL is set to infinity in our simula-
tion. However, HPF and RPF can cover more than 96%
peers as TTL is increased to 10.
Figure 12 compares the peer coverage size of DBFS
and HPF. In DBFS, most nodes can cover 760-780
peers out of 1,000 nodes. The coverage size is increased
to 950-970 in HPF.

0 5 10 15 20 25 30 35 40
0
10
20
30
40
50
60
70
80
90
100
NormallizedResponseTime
BFS
RPF
DBFS
HPF
0 2 4 6 8 10 12 14
0
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
TTL
PercentageofCoveredNodes
BFS
HPF
DBFS
RPF
600 650 700 750 800 850 900 950 1000
0
2%
4%
6%
8%
10%
12%
14%
16%
18%
Coverage Size
NodesDistribution
DBFS
HPF
Figure 10. Normalized response
time comparison
Figure 11. Coverage percentage
comparison
Figure 12. Partial coverage
comparison
6 Conclusion
In this paper, we have proposed an efficient and
adaptive search mechanism, Hybrid Periodical Flooding.
HPF improves the efficiency of blind flooding by re-
taining the advantages of statistics-based search mecha-
nisms and by alleviating the partial coverage problem.
We summarize our contributions as follows:
� Analyze the current search mechanisms used and
proposed in unstructured P2P networks.
� Qualitatively and quantitatively analyze the partial
coverage problem caused by statistics-based search
mechanisms, such as DBFS.
� Propose to use a periodical flooding function to de-
fine the number of relay neighbors, which can be
adaptively changed. This is the first technique used
in HPF.
� Propose to use multiple metrics to select relay
neighbors to obtain better overall performance or
adaptively meet different performance requirements,
which is the second technique used in HPF.
We have shown the performance of HPF using two
metrics to select relay neighbors. HPF provides the
flexibility to use more metrics and allows the applica-
tion to define multiple metrics and give them different
weights, thereby the algorithm is more flexible in prac-
tice to meet different performance requirements.
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