[ieee 2010 2nd international conference on future computer and communication - wuhan, china...

May 12, 2010 17:39 RPS : Trim Size: 8.50in x 11.00in (IEEE) icfcc2010-lineup˙vol-3: F715

Key-peers Based Topology Control for Unstructured P2P Networks

Cuihua Zuo, Hongcai Feng, Cao Yuan Department of Computer and Information Engineering

Wuhan Polytechnic University Wuhan 430074, P.R.China

E-mail: [email protected], [email protected], [email protected]

Abstract—One of the essential problems in unstructured peer-to-peer (P2P) network is enhancing the efficiency of resource retrieval. Previous researches either have poor response speed, or generate too much network overhead. In order to reduce the traffic load and improve the availability of the sharing resources in unstructured P2P networks, a key-peers based topology control mechanism is presented in this paper. Due to inherent heterogeneity of peers in P2P network, a few peers (called key-peers) directly affect the connectivity of P2P overlay topology. Therefore, it is particularly important to explore these peers. Here, we regard P2P overlay topology as an undirected graph, and analyze the similarities and differences between cut-nodes in graph theory and key-peers in P2P networks. Then we use the related principles about cut-nodes and the reachability relationship of nodes to detect the key-peers of P2P network. Furthermore, we adjust P2P overlay topology based on these key-peers. Finally, experimental results show that compared to the original P2P overlay topology, the modified topology using our approach can perform much better in success rate and respond speed, especially for rare resources.

Keywords-peer-to-peer (P2P) network; key-peer; topology control; connectivity; reachability relationship

I. INTRODUCTION

P2P networks have become a dominant part of the Internet traffic due to the tremendous success of file-sharing systems like Guntella [1] and KaZaA [2]. There are mainly two types of P2P overlays: structured and unstructured ones. Structured overlays [3, 4] tag the peers with peer identifiers thus providing an efficient support for distributed hash table (DHT). The shared data placement and topology characteristics of the network are tightly controlled based on the DHT. In contrast to structured overlays, unstructured overlays do not follow any specific topology characteristics, so no clue emerges as to where content is located. In spite of this apparent disadvantage, unstructured P2P networks have several desirable properties not easily achieved by structured counterparts — they support inherent heterogeneity of peers, are highly resilient to peers’ failure and incur low overhead at peer arrivals and departures. Besides, they are simple to implement and nearly incur no overhead in topology maintenance. Consequently, unstructured networks are becoming more and more popular as they are flexible enough to be optimized for specific applications [5].

The predominating search mechanism in unstructured networks is message flooding with a fixed TTL restriction. This simple flooding along original overlay does not provide guarantee that an object existing in the highly dynamic and heterogeneous P2P network can be found. Moreover, with the increase of TTL value, a large number of redundant messages are generated. Hence, the search scheme or the overlay topology needs to be optimized.

The ultimate goal of our research is to construct an efficient P2P overlay topology, which can reduce the network traffic with high attainability. Towards this end, we analyze the topology characteristic of unstructured P2P networks, and then we propose a topology control mechanism based on key-peers which can be detected using the principles of graph theory. Finally, the experimental results show that the proposed approach offers high success rate and low response time.

II. RELATED WORK

Self-organizing P2P networks develop to an enormous scale at an alarming rate in recent years, and are widely applied to many fields. Research has shown that a large fraction of traffic in the Internet is occupied by peer-to-peer applications [6]. Many efforts have been devoted to improve the performance of retrieving resources in unstructured P2P networks. Overlay optimization [7, 8] is an efficient method.

Traditional topology optimization techniques identify physically closer nodes to connect as overlay neighbors, but could significantly shrink the search scope. Location-aware Topology Matching (LTM) [9] and Scalable Bipartite Overlay (SBO) [10] address the mismatch problem between logic overlay and physic overlay without sacrificing the search scope. In [11], a sub-overlay FloodNet is constructed for the purpose of reducing the number of redundant messages. Though it can reduce network traffic effectively, it needs more hops to reach all peers of the network. Additionally, computing the secondary degree of each peer is very hard because of the dynamic characteristic of P2P networks. [12] presents a fault-tolerant overlay in unstructured P2P systems, which uses local information at each node to construct an overlay that can improve search performance and reduce bandwidth consumption. [13] outlines a novel protocol that directly maintains a tree overlay in the presence of churn. It simultaneously achieves some beneficial properties such as limiting the maximum node degree, minimizing the extent of the tree topology

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changes resulting from failures, and limiting the number of nodes affected by each topology’s change. [14] proposes to structure the P2P overlay topology using a heterogeneity-aware multi-tier topology to better balance the load of peers with heterogeneous capacities and prevent low-capability nodes from throttling the performance of the system.

Different from the aforementioned approaches, the proposed overlay control in this paper is based on the overall characteristic of the original P2P overlay. Since the logical network of unstructured P2P community shows evidence of power-law characteristic which means that very few peers (called key-peers later) have a big influence on the connectivity of the network. In this paper, we use the related principles about cut-node and reachability relationship in graph theory to detect these key-peers, and then adjust P2P overlay topology based on them.

III. KEY-PEERS ANALYSIS AND DETECTION

A P2P topology is a logical overlay network on top of a physical network. Each peer corresponds to a node in the peer-to-peer network and is resided in a node (host) in the physical network. All peers of P2P network are of equal roles in function, but in fact, a few peers have a special significance for the entire network. On the one hand, the failure of these peers can cause that the entire network topology is divided into several independent sub-topologies. On the other hand, these peers often become the “bottleneck” of P2P networks, which will affect the performance of resource retrieving in both search success rate and response latency. In this paper, we call these peers as key-peers, defined as follows.

Definition 1 (Key-peer): In unstructured P2P networks, if after deleting a peer P, one of the following two cases occurs: (1) the original topology is divided into two or more sub-topology; (2) the shortest path between two peers of P2P topology becomes bigger than the Time-to-Live (TTL) limitation, then the peer P will be regard as a key-peer.

In the research of P2P network, the network topology including peers and connections between them is often mapped into an undirected graph. Each peers of P2P network corresponds to a node of undirected graph and each connection between peers corresponds to an edge of undirected graph. Hence, we can adopt the related principles about cut-node in graph theory to research key-peers.

Theorem 1: According to graph theory, assuming v is a node of connected graph G and V is the set of nodes of graph G, if V-{v} can be divided into two or more sets of nodes (including the sets U and W), and as to any node u∈U, ∀w∈W, node v exists in all paths Puw which means the path from node u to w along the graph G, then node v will be regarded as a cut-node.

Proof: Since node v exists in all paths from u to w, there will be no path between u and w after deleting node v. Hence, the graph G will be divided into separate sub-graphs.

Inference 1: Consider a P2P network topology T as an undirected graph G and V is the set of nodes. If a node v∈V is a cut-node of the graph G, then its corresponding peer p in P2P network is a key-peer.

Proof: Since node v is a cut-node of the graph G, V-{v} will be divided into two or more unconnected parts. Correspondingly, after deleting the corresponding peer p in the P2P network topology T of node v in the graph G, the following case occurs: the topology T is divided into two or more sub-topologies. Therefore, peer p is a key-peer of the P2P network.

For example, in figure 1, you can see a connected graph G with several nodes. After deleting node A, the graph G will be partitioned into two parts, where U and W are the sets of nodes in these two parts, respectively. Hence, the node A is a cut-node.

Figure 1. Node A is a cut-node of graph G

However, considering the communication cost, overlay networks need set limited hops for routing messages by TTL in practical applications, so there are differences between key-peers and cut-nodes. For instance, in figure 2, if the sum of TTL1 which means the least hops of routing a message from A to B and TTL2 which expresses the least hops of routing a message from D to B is bigger than the fixed TTL value, and the sum of TTL3 which means the least hops of routing a message from E to C and TTL 4 which denotes the least hops of routing a message from F to C is not more than the TTL value, it’s quite obvious to figure out that peer C belongs to a key-peer of the topology T according to definition 1. However, according to theorem 1, both node B and C are not cut-nodes.

Figure 2. Node C is a key-peer of topology T

Therefore, besides cut-nodes, other key-peers also exist in the P2P network. In order to find all key-peers, we present the concept of reachability relationship which is defined as follows.

Definition 2 (Reachability Relationship): In a P2P topology T limited by a fixed TTL value, peer A could reach

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peer B if A can locate B by sending routing messages in restricted hops (TTL). It is denoted by A→B.

Reachability relationship is not transitive but is symmetric because a topology is mapped into an undirected graph. In other words, if A→B, then B→A. Figure 3 shows an example of reachability relationship. As to peer A, it can reach the peers B, C, D, E, F, G, but can not reach the peer H with TTL=3.

Figure 3. The reachability relationship of peer A

Theorem 2: As to each peer P in P2P topology T, assuming {P1, P2, …, Pn} (n is the number of peer P’s neighbors) is the set of peer P’s neighbors, if P1, P2, …, Pn can not reach each other after deleting peer P, then P is a key-peer. Otherwise, P is not a key-peer.

Proof: After deleting peer P, its neighbors P1, P2, …, Pn can not reach each other, that is, there exist two peers Pi, Pj (1≤i≠j≤n), and Pi can not locate Pj by sending routing messages with TTL limitation. So the shortest path between Pi and Pj along P2P topology T becomes bigger than the TTL limitation. Accordingly, the peer P is a key-peer. On the contrary, if P1, P2, …, Pn can still reach each other, any two peers can locate each other by sending routing messages with TTL limitation, that is, the shortest path between them is not more than TTL. Hence, peer P is not a key-peer.

We split peers into two types, namely, leaf peers and non-leaf peers. Obviously, a leaf peer in the network can’t be a key-peer because it will not behave as the single route way of other peers due to its only one connection. Each non-leaf peer may be a key-peer, so all non-leaf peers are key-peer candidates.

Based on the above analysis, each key-peer candidate probes whether it belongs to a key-peer depending on whether all of its neighbors can still reach each other when it fails. Therefore, it need probe reachability relationship between any two of its neighbors.

In this paper, the probe process can be made by means of the method used in [15]. At the beginning of the detection, each key-peer candidate sends a component probe message (including the candidate’s ID, a timestamp, a TTL value and a neighbor ID) to each of its neighbors. Each key-peer candidate in the network maintains a reachable list. The format of each entry in the reachable list is <candidate’s ID, timestamp, <neighbor ID1, TTL1>, <neighbor ID2, TTL2>, …>. Additionally, each peer has a connection list to store the probing message from candidates. Each peer deals with the received message based on the information stored in the connection list. There are five situations as described in the following when a peer receives a message M(candidate’s ID, timestamp, TTL value, neighbor ID).

(1) If the peer has already received the message and the TTL value in the new message is not bigger than the old, or the message is old, the peer will drop the message. Certainly, if the TTL value of the message is zero, the peer will also drop it.

(2) If the timestamp and neighbor ID of the message are the same as the old one stored in the connection list and the TTL value in the new message is bigger than the old, the peer will replace the old by the new message and forward this message to all its neighbors except the message sender.

(3) If the message is a new one for the peer, it will add the message to its connection list and transmit this message to all its neighbors except the message sender.

(4) If the timestamp in the received message is newer than the one stored in the peer’s connection list, the peer will replace the old information by the new message and forward this message to all its neighbors except the message sender.

(5) If the timestamp of the message is the same as an entry stored in the connection list, but the neighbor ID of the message is not the same as the entry, the peer will add the new pair of neighbor ID and TTL value to the entry and send an arrival message <candidate’s ID, timestamp, <neighbor ID1, TTL1>, <neighbor ID2, TTL2>, …> back to the corresponding candidate. When a candidate receives an arrival message, it will immediately add the message to its reachable list.

TTL value of a message will be reduced by one when it is forwarded. The last situation is valuable for us to analyze the reachability relationship of a candidate’s neighbors. Each arrival message contains two or more pairs of <neighbor ID, TTL>. As to any two pairs <neighbor ID1, TTL1> and <neighbor ID2, TTL2>, if the limited hops for routing messages is TTL, and TTL1 + TTL2 + 2 ≥ TTL which means that without the candidate, the peer with ID1 can locate another peer with ID2 within limited TTL. Therefore, after deleting the candidate, its two neighbors with ID1 and ID2 can reach each other. Similarly, we can get the reachability relationship of any two neighbors of the candidate when it fails. Based on the reachability relationship of its neighbors, a candidate can make decision whether it is a key-peer by theorem 2.

IV. TOPOLOGY CONTROL BASED ON KEY-PEERS

In this paper, the process of topology control is changing key-peers into normal peers. Based on the key-peers described in the above section, we adjust P2P original topology by two phases. In the first phase, extra connections will be added to avoid key-peers. After a peer A has made sure that it is a key-peer, new connections need to be added among its neighbors so that their reachability relationship could be changed. If A’s neighbors are partitioned into m unconnected parts noted by sets S1, S2, …, Sm according to their reachability relationship, that is, ∀C∈Si, ∀H∈Si, 1≤i≤m, there is C→H; but ∀C∈Si, ∀D∈Sj, 1≤j≠i≤m, there is not C→D, peer A will choose one or more delegate peers from each set Si, and then connect these delegate peers in some way.

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There is one principle in selecting the delegate peers. In order to balance the network load and improve the fault tolerance of P2P network, we select the peers with low degree as delegate peers from each set Si. For example, figure 4(a) shows an original topology with ten peers and several connections among them. In the light of the analysis in the above section, A is a key-peer and the reachability relationship of its neighbors is C→H, D→F, shown in figure 4(b). In order to change the reachability relationship among its neighbors, a new connection is added between peer H who owns a lower degree in the set S1 and peer F who also has a lower degree in the set S2, as shown in figure 4(c). After adding the new connection, the peer A needs to analyze whether it is a key-peer again. If A is still a key-peer, another new connection is added, shown in figure 4(d). Once the peer A is no longer a key-peer, the process of adding new connections for its neighbors will be stopped.

(a) P2P original topology

(b) Unconnected parts after deleting A

(c) Add a new connection for the topology

(d) Add another new connection for the topology

Figure 4. The process of topology control

In the second phase, we must prune away some of surplus connections so as to save network overhead and reduce redundant messages. Due to the page limitation of this paper, we only give two principles of deleting a connection: (1) the degrees of two peers linked by the

connection are both more than the average degree of the network; (2) the connection which links a previous key-peer and one of its neighbors that has been added a new connection, such as the connection HA in figure 4(c).

V. PERFORMANCE EVALUATION

We use the simulator PeerSim [16] for evaluating the performance of our approach. In the simulation, we use BRITE [17] to generate the original overlay based on the BA (Barabasi-Albert) model [18] with 10000 nodes and 20000 links. Based on the original overlay, we adjust it by topology control based on key-peers described in the above section. The simulation starts by uniformly placing 10000 distinct files into the network, and queries to files are generated according to a Zipf-like distribution with parameter α = 1. We distribute 10000 files to these 10000 peers and each peer has about 10 different files initially. In other words, each file has nearly10 replicas. We assume that each peer can only cache 40 replicas. Besides, we use traditional LRU algorithms as the replacement strategy of replication. For each experiment in the following, every peer, in turn, starts a searching procedure for a file. We use the most popular search algorithm—Flooding as our routing scheme.

In this paper, we mainly focus on two performance metrics: response time and success rate. Besides, we also analyze the performance of the adjusted topology using our approach compared with the original topology in terms of success rate and response speed. We set the total number of queries to 30000. We observe the appropriate values of TTL for Flooding scheme is five by a series of experiments, which will not be detailed here. Therefore, in the following experiments, we use this value as the default value of TTL. All data shown in the following figures are average values.

Figure 5 lists the average response speed (“hops”) with the increase of query times. Obviously, we can see that the performance of our approach is superior to that of original topology. This is because that there are many key-peers in original topology. Hence, it is harder for a message to spread to the whole network. Additionally, we can also find that the number of average hops is changed in a small range from this figure. This is because the search scope increases very quickly with the flooding search scheme.

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Figure 5. The average hops versus query times

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Figure 6 lists the average success rate with the increase of query times. Obviously, we can see that the success rate in our approach is bigger to that of original overlay all the time. It is understood that the bigger the query times is, the larger the success rate is. The reason is that as the increase of query times, there is more replication for hot resources. Simultaneously, our topology can distribute these replicas of resources more reasonable than the original topology. Furthermore, the success rate using our topology is nearly 100% when the query times is 30000, but in the original topology, it is nearly 93%, which implies that the success rate of rare resources in our topology is much better than that of the original topology.

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Figure 6. The success rate versus query times

VI. CONCLUSION AND FUTURE WORK

In this paper, we first advance the concept of key-peer whose failure may potentially lead the P2P topology to be partitioned, and then propose a detection mechanismdepending on the reachability relationship of peers in the network. Accordingly, we modify the original P2P overlay topology upon these key-peers. The experiments show that the proposed topology structure is more efficient than the existing original one, including response speed and success rate. Although we use flooding scheme to investigate its efficiency, there are still further problems to be explored. Firstly, we can take other search schemes into account. In addition, we don’t discuss how the size of P2P topology affects its performance. We will address these issues in our future work.

ACKNOWLEDGMENT

This work is supported by National Natural Science Foundation of China under Grant 60873225, 60773191, 70771043, National High Technology Research and Development Program of China under Grant 2007AA01Z403, Natural Science Foundation of Hubei Province under Grant 2009CDB298, Open Foundation of

State Key Laboratory of Software Engineering under Grant SKLSE20080718.

REFERENCES

[1] Gnutella, http://www. .limewire.com/, 2007.

[2] KaZaA, http://www.kazaa.com/, 2007.

[3] I. Stoica, R. Morris, D. Karger, M. F. Kaashoek, etc, “Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications,” In Proceedings of the ACM SIGCOMM, San Diego, California, USA, 2001, pp. 149-160.

[4] S. Ratnasamy, P. Francis, M. Handley, etc, “A Scalable Content-Addressable Network,” In Proceedings of the ACM SIGCOMM, San Diego, California, USA, 2001, pp. 161-172.

[5] Hongbo Jiang, Shudong Jin, “Exploiting Dynamic Querying like Flooding Techniques in Unstructured Peer-to-Peer Networks,” In Proceedings of the 13th IEEE International Conference on Network Protocols (ICNP 2005), Boston, MA, USA, 2005, pp. 122-131.

[6] Chen Tian, Hongbo Jiang, Xue Liu, etc, “Towards Minimum Traffic Cost and Minimum Response Latency: A Novel Dynamic Query Protocol in Unstructured P2P Networks,” In Proceedings of the 37thInternational Conference on Parallel Processing (ICPP 2008), Portland, Oregon, USA, 2008, pp. 1-8.

[7] Hasan Guclu, Murat Yuksel, “Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks,” Proceedings of the 27th International Conference on Distributed Computing Systems (ICDCS'07), 2007.

[8] Hai Zhuge, Liang Feng, “Distributed Suffix Tree Overlay for Peer-to-Peer Search,” IEEE Trans. Knowledge and Data Engineering, Vol. 20, No. 2, pp. 276-285, 2008.

[9] Y. Liu, L. Xiao, X. Liu, L.M. Ni, etc, “Location Awareness in Unstructured Peer-to-Peer Systems,” IEEE Trans. Parallel and Distributed Systems, Vol. 16, No. 2, pp. 163-174, 2005.

[10] Y. Liu, L. Xiao, and L.M. Ni, “Building a Scalable Bipartite P2P Overlay Network,” IEEE Trans. Parallel and Distributed Systems, Vol. 18, No. 9, pp. 1296-1306, 2007.

[11] Song Jiang, Lei Guo, Xiaodong Zhang, etc, “LightFlood: Minimizing Redundant Messages and Maximizing the Scope of Peer-to-Peer Search,” IEEE Trans. Parallel and Distributed Systems, Vol. 19, No. 5, pp. 601-614, 2008.

[12] William Acosta, Surendar Chandra, “Improving Search Using a Fault-Tolerant Overlay in Unstructured P2P Systems,” In Proceedings of the 36th International Conference on Parallel Processing (ICPP 2007), Xi-An, China, IEEE Computer Society, 2007, pp. 1-10.

[13] Davide Frey, Amy L. Murphy, “Failure-Tolerant Overlay Trees for Large-Scale Dynamic Networks,” In Proceedings of 8th International Conference on Peer-to-Peer Computing (P2P 2008), Aachen, Germany, 2008, pp. 351-361.

[14] Mudhakar Srivatsa, Bugra Gedik, Ling Liu, “Large Scaling Unstructured Peer-to-Peer Networks with Heterogeneity-Aware Topology and Routing,” Proc. IEEE Transctions on Parallel and Distributed Systems, Vol. 17, No. 11, 2006.

[15] Xiaomei Liu, Li Xiao, Andrew Kreling, etc, “Optimizing Overlay Topology by Reducing Cut Vertices,” Proceedings of ACM International Workshop on Network and Operating System Support for Digital Audio and Video (NOSSDAV), 2006.

[16] PeerSim, http://peersim.sourceforge.net/, 2007.

[17] BRITE, http://www.cs.bu.edu/brite/, 2007.

[18] A.-L. Barabasi, R. Albert, “Emergence of Scaling in Random Networks,” Science, 286, pp. 509-512, 1999.

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