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\title{Proposal of a Flooding-Based Flexible Search Method for Chord Networks}
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\begin{document}

             \author[1]{Keiichi  Endo}

             \author[2]{Kensuke  Kanetada}

             \author[3]{Dai  Okano}

             \affil[1]{  Ehime University}

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\date{\small \em Received: 7 June 2011 Accepted: 27 June 2011 Published: 12 July 2011}

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\begin{abstract}
        


Recently, peer-to-peer (P2P) network models have been attracting considerable attention. P2P models can be classified into structured and unstructured P2P models. Representative search methods for structured and unstructured P2P networks are Chord and Flooding, respectively. It is difficult to realize flexible search in Chord networks. On the other hand, a large number of query transmissions are required for Flooding. In this study, we propose a Flooding-based search method for Chord networks. Our method works separately from the traditional search method for Chord networks. It suppresses the transmission of redundant queries by considering the topological properties of the structured networks and enables flexible search in Chord networks. Through simulation experiments, we evaluate the performance of the proposed search method and show its effectiveness.

\end{abstract}


\keywords{P2P, overlay networks, distributed hash tables, Chord, Flooding}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
n recent years, various types of services are provided on the Internet. In most of the services, the clientserver model, which is illustrated in Figure 1, is adopted. However, providing a satisfactory service in the client-server model is getting more and more difficult because of the increase of Internet users and the large amount of transferred data. Therefore, many researchers are exploring the ways to provide various types of services in the peer-to-peer (P2P) model, which is illustrated in Figure 2. In this model, a node (user's computer) shares some files with other nodes.\par
Flooding (Figure 3) is the most basic search method for P2P networks. The requester transmits a search query to all the adjacent nodes, and the query is continuously forwarded to adjacent nodes until the TTL (Time To Live) is reduced to 0. However, in this search method, many messages are transmitted, which include redundant queries sent to the nodes that have already received the same queries.\par
The Distributed Hash Table (DHT) enables file search in a P2P network with much smaller number of messages. In the DHT, shared files are associated with nodes by using a hash function. Since the network is constructed in certain rules, a requested file can be found with high probability and without redundant In this paper, we propose a Flooding-based flexible search method for a structured network organized by a DHT algorithm. Our method suppresses the transmission of redundant queries by considering the structure of the organized network.\par
The rest of this paper is organized as follows. Section II describes structured and unstructured P2P models. In Section III, we explain the proposed search method. We evaluate the performance of the proposed method in Section IV. We conclude this paper and discuss future work in Section V.    \hyperref[b1]{[2]}, Chord \hyperref[b2]{[3]}, Pastry \hyperref[b3]{[4]}, Tapestry \hyperref[b4]{[5]}, and Kademlia \hyperref[b5]{[6]}. Since we propose a search method for Chord networks, we explain Chord in more detail below.\par
In Chord, the node ID that is calculated from node's IP address using a hash function is assigned to each node. The names of shared files are also hashed by using the same hash function, and each node manages the index information of the files whose hash values are less than or equal to the node ID and greater than the smaller adjacent node ID. For example, if the nodes in a Chord network are assigned node IDs as shown in Figure 4, the index information of shared files is placed according to Table \hyperref[tab_0]{1}. It should be noted that the nodes in a Chord network are considered to be circularly arranged. Therefore, the node ID 0 is often considered to be greater than the node ID 15.\par
We consider m-bit hash space, which means that node IDs are nonnegative integers less than 2 m . We define node S 's i-th neighbor (i = 0, 1, ?, m -1) as the node assigned the ID next ((S + 2 i ) mod 2 m ), where next(X) denotes the smallest node ID greater than or equal to X. In the following discussion, we omit the remainder operation "mod 2 m ."As an example, we show the neighbors of node 0 in Figure 5. We refer to node (S + 2 i ) and node next(S + 2 i ) as calculated neighbor and actual neighbor, respectively.\par
When a node searches for a file, a query is transmitted and forwarded to the neighbor whose ID is the closest to (and except for the last hop, not greater than) the hash value calculated from the name of the requested file until it reaches the node that should manage the index information of the requested file. For example, a query is transmitted and forwarded as shown in Figure 6 when node 0 searches for a file whose hash value is 10. Since node 10 does not exist, node 11 replies to node 0 (with index information of the requested file if available).\par
In a Chord network, a requested file is found within log 2 N hops (N denotes the number of nodes) if the file exists in the network. In addition, the communication cost is low because queries are not replicated. However, it is difficult to realize flexible search because the destination node ID of a query is calculated basically from the name of the requested file, which is a mutual problem of the DHT.\par
A DHT algorithm that uses a locality-preserving hash function is proposed in \hyperref[b6]{[7]}. Skip Graphs \hyperref[b8]{[8]}, SkipNet \hyperref[b9]{[9]}, and Skip Tree Graphs \hyperref[b10]{[10]} do not use hash functions to construct structured P2P networks or to search in the networks. These methods enable range queries; however, it is still difficult to realize as flexible search as search methods for unstructured P2P networks such as Flooding. Moreover, load balancing is difficult if we adopt these methods.    for unstructured P2P networks are Flooding \hyperref[b12]{[11]}, k-Walker Random Walk \hyperref[b13]{[12]}, and the hybrid search scheme incorporating Flooding and Random Walk \hyperref[b14]{[13]}.\par
In Flooding (and many other search methods for unstructured P2P networks), TTL is used to control the propagation of queries. By using Flooding, a node searches for a file in the following procedure:\par
1. The TTL of a query is initially set to a certain positive integer. 2. The requester transmits the query to all the adjacent nodes. The TTL of the transmitted query is decremented. 3. If the receiver of the query possesses the requested file, the receiver replies to the requester. Otherwise, the receiver forwards the query to all the adjacent nodes except for the sender of the query unless the receiver has received the same query before. In the same manner as step 2, the TTL of the forwarded query is decremented. 4. Step 3 is repeated until the TTL is reduced to 0.\par
Since the paths of queries do not depend on the names (or the keywords) of requested files, various types of queries can be supported in unstructured P2P networks. However, the communication cost is high mainly because of redundant queries. Additionally, a node often fails to find a requested file that exists in the network because the spread of queries is restricted by TTL. 
\section[{III.}]{III.} 
\section[{PROPOSED METHOD}]{PROPOSED METHOD}\par
In this section, we propose a flexible search method for Chord networks. Although our method is based on Flooding, it suppresses the transmission of redundant queries by considering the topological properties of the structured networks. Our method works separately from the traditional search method for Chord networks. Therefore, the traditional search method is still valid for exact match search when our method is adopted. 
\section[{a) Basic Algorithm}]{a) Basic Algorithm}\par
In the proposed method, LTS (Limit To Send) is used instead of TTL in order to control the propagation of queries. A node searches for a file in the following procedure:\par
1. The LTS of a query is initially set to m. 2. The requester transmits the query to the requester's i -th neighbors such that i < LTS. The LTS of the query that is transmitted to the i-th neighbor is changed to i.\par
3. If the receiver of the query possesses the requested file or the index information of the requested file, the receiver replies to the requester. Otherwise, the receiver forwards the query to the receiver's i-th neighbors such that i < LTS unless the receiver has received the same query before. In the same manner as step 2, the LTS of the query that is forwarded to the i-th neighbor is changed to i. 
\section[{4.}]{4.}\par
Step 3 is repeated until the LTS is reduced to 0.\par
In this method, search terminates within m hops because the LTS is decreased by at least one every time the query is forwarded. In addition, as shown in Figure 7, all the nodes can receive the query even if the number of nodes is 2 m , which is the maximum number supported by the m-bit hash space. Furthermore, no redundant queries are transmitted in this case.\par
However, in practice, the i-th actual neighbors for different i 's can be the same node because some node IDs are absent in a Chord network. For instance, in Figure 8, node 0's 0th, 1st, and 2nd actual neighbors are node 4. In this case, if the LTS of the query transmitted by node 0 to node 4 is changed to 0 (the smallest of 0, 1, and 2), node 6 cannot receive any queries as shown in Figure 8. Therefore, the LTS should be changed to 2 (the largest of 0, 1, and 2). Although all the nodes can receive the query in this policy, some redundant queries are transmitted as shown in Figure 9. In the case of Figure 10, the number of transmitted messages is doubled by redundant queries.     
\section[{b) Redundant Query Suppression}]{b) Redundant Query Suppression}\par
We suppress the transmission of redundant queries by including StopID in the query. The query is not forwarded to any node whose ID is greater than or equal to StopID. After this modification is applied, no redundant queries are transmitted. In the case of Figure 10, StopID of the query transmitted by node 0 to node 4 (the 2nd neighbor) is set to 8 (the 3rd neighbor) because node 0 transmits the same query to node 8 at the same time. In this manner, the transmission of redundant queries can be completely suppressed. 
\section[{c) Index Information Replication}]{c) Index Information Replication}\par
In this subsection, we consider how to decrease the number of transmitted messages. If we change the initial LTS from m to m -1, the number of messages for search is approximately halved. However, since only half of the nodes in the network can receive the query, search success ratio becomes lower unless index information is replicated. If replicated index information is placed in the diagonal node (2 m -1 larger node ID), search success ratio is not deteriorated. However, the number of messages for index information placement is doubled if the replicated index information is transmitted independently from the original. We propose a more efficient method to place replicated index information.\par
1. When a new file is shared, the hash value of the file, HashA, is calculated. 2. The diagonal node ID, HashB = HashA + 2 m -1 , is calculated. 
\section[{We let HashNear be the closer node ID of HashA and}]{We let HashNear be the closer node ID of HashA and}\par
HashB from the holder of the newly shared file. We also let HashFar be the farther node ID of the two. 
\section[{4.}]{4.}\par
A message for index information placement is transmitted to the neighbor whose ID is the closest to HashNear.\par
5. The receiver of the message forwards it to the neighbor where the index information should be placed (i.e., the neighbor whose ID is the smallest and not less than HashNear). If it is not possible, the message is forwarded to the neighbor whose ID is the closest to HashNear. 6. In step 5, if HashNear lies on or between the calculated neighbor ID and the actual neighbor ID, another message for index information placement is transmitted to HashFar. Figure 11 illustrates this procedure. In this figure, the numbers in parenthesis correspond to the steps described above. This method enables efficient placement of index information because diagonal links are utilized.  
\section[{SIMULATIONS}]{SIMULATIONS}\par
Through simulation experiments, we evaluate the performance of the proposed method and the effect of the modifications described in the previous section. We compare the following four methods:\par
-Chord0: traditional Flooding described in Section II-B. (Flooding is usually used in an unstructured network; however, in this section, we use Flooding in a structured Chord network.) -ChordA: the proposed method described in Section III-A. -ChordB: the proposed method with redundant query suppression described in Section III-B. -ChordC: the proposed method with redundant query suppression and index information replication described in Section III-C.\par
Table \hyperref[tab_1]{2} shows the common parameters used in the simulations. The initial TTL or LTS for each method is shown in Table \hyperref[tab_2]{3}. All the results shown in this section are based on the average of five experimental results in the same condition.\par
Figure 12 shows the ratio of redundant messages to all the messages transmitted for search.\par
The ratio in ChordA is much lower than the ratio in Chord0, which implies that the basic algorithm of the proposed method achieves much more efficient search than traditional Flooding in Chord networks. No redundant messages are transmitted in ChordB because the redundant query suppression takes effect. We omit showing the result of ChordC because the search algorithm of ChordC is the same as that of ChordB.\par
Figure 13 shows the number of messages transmitted for search. Compared with Chord0 and ChordA, ChordB achieves much lower communication cost. The number of messages for search in ChordC is half the number of messages in ChordB because only half of the nodes in the network receive the query. In Figure 14, we show the number of messages transmitted for index information placement. The results of ChordA and ChordB are the same as that of Chord0. This figure shows that the number of messages for index information placement increases if index information is replicated; however, the difference is independent of the number of nodes in the network.\par
Figure 15 shows the maximum number of hops that queries travel in a search. (For example, in the case of Figure 9, the maximum number of hops is three because the search terminates after the queries travel at most three hops.) The maximum number of hops in Chord0 is the smallest of the four methods in most cases. This is because the query is forwarded to all the adjacent nodes in Chord0. However, Chord0 suffers from high communication cost as we have shown in Figure 13. The maximum number of hops in ChordC is one hop smaller than that of ChordA or ChordB. This is because the search area is half of the network in ChordC.     V. 
\section[{CONCLUSION}]{CONCLUSION}\par
In this paper, we have proposed a Floodingbased flexible search method for Chord networks. We have also described two modifications (redundant query suppression and index information replication) for improving the performance of the proposed method. The results of simulation experiments show that the proposed method enables efficient search.\par
In the future, we plan to investigate the method for reducing the communication cost with the search success ratio kept as high as possible. Since two parameters (LTS and StopID) are used for query forwarding in our method, the propagation of queries can be controlled more flexibly than other simpler methods such as \hyperref[b15]{[14]}. We also plan to consider Flooding-based flexible and efficient search methods for various structured P2P networks constructed by other DHT algorithms such as Pastry \hyperref[b3]{[4]}, or non-DHT algorithms such as Skip Graphs \hyperref[b8]{[8]} and BATON \hyperref[b17]{[15]}.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
                \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.37777777777777777\textwidth}P{0.4722222222222222\textwidth}}
Node\tabcellsep Hash values of files\\
Node 0\tabcellsep 14, 15, 0\\
Node 1\tabcellsep 1\\
Node 5\tabcellsep 2, 3, 4, 5\\
Node 7\tabcellsep 6, 7\\
Node 9\tabcellsep 8, 9\\
Node 11\tabcellsep 10, 11\\
Node 13\tabcellsep 12, 13\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.5540178571428571\textwidth}P{0.29598214285714286\textwidth}}
Size of hash space\tabcellsep 30 bits\\
Number of nodes\tabcellsep 2 i (i = 5, 6, ..., 15)\\
Number of unique files\tabcellsep 10000\\
Number of searches\tabcellsep 1000\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.2602040816326531\textwidth}P{0.3903061224489796\textwidth}P{0.19948979591836735\textwidth}}
Method\tabcellsep Initial value\tabcellsep Search area\\
Chord0\tabcellsep TTL = 30\tabcellsep all\\
ChordA\tabcellsep LTS = 30\tabcellsep all\\
ChordB\tabcellsep LTS = 30\tabcellsep all\\
ChordC\tabcellsep LTS = 29\tabcellsep 1/2\end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 			\footnote{© 2011 Global Journals Inc. (US)} 			\footnote{July:} 			\footnote{July} 			\footnote{July} 			\footnote{July} 			\footnote{July} 			\footnote{July} 			\footnote{July} 			\footnote{Proposal of a Flooding-based Flexible Search Method for Chord Networks July} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
