點對點(Peer to Peer)系統是一種分散式系統，其中的參與者扮演相似的角色。在點對點系統中，每個使用者便是一個節點(Peer)，彼此皆能分享資源。每個節點會動態地進出這個點對點系統，系統中的資料也跟隨地增減而有所變化。給定個範圍，範圍搜尋 (range search)將會找任何值在此範圍內的資料。例如，一個範圍查詢(range query)可幫我們找到所有披頭四在1961年至1968年間的作品。然而，一旦區間資料透過廣泛運用在各點對點系統的雜湊函數而分佈在這個點對點系統上時，區間資料本有的連續特性並不保證會存在。因此，找散布在各區域的區間資料是相當耗成本的。分散區段樹(Distributed Segment Tree，簡稱DST)藉由區段樹的結構保留了每個節點上區間資料的區域連續性，且能將一個完整的區間拆解成許多較小並能對應至區段樹中的節點區間(Node Interval) 。此方法運用了分散雜湊表(Distributed Hash Table，簡稱DHT)的邏輯，因此可在任何使用分散雜湊表的點對點系統上(DHT-based P2P System)運作。然而，DST的資料分佈方法會有Overlapping的問題。進行搜尋時，可能比實際需要送出更多的要求訊息(request)。雖然DST提出了Downward Load Stripping 的機制，但資料負載仍然未必見得平衡。主要原因便是DST使用了分散雜湊表的邏輯。因此，在本篇的論文中，我們提出了結構區段樹(Structured Segment Tree，簡稱SST)的方法。SST不再運用分散雜湊表，而且能將區段樹的結構在點對點系統中表現出來。在我們的方法中，點對點系統所構成的拓樸即是區段樹的結構，它能充份反映出區段樹有的特性。在我們的方法中，每個節點便是一顆區段樹上的節點。相同層級的資料區間聯集便是一顆區段樹所能支援的範圍區間。進行搜尋時，節點能送出如實際需要之等量的要求訊息。此外，我們還加入了sibling link來保留空間區域性(spatial locality)和增進搜尋效率。關於負載平衡的議題，我們的方法表現得比DST來得更為平衡。在我們的模擬實驗中，顯示出了SST比DST走訪較少的節點數目，便能搜尋到資料。模擬實驗也顯示出資料負載在SST中來得比DST更加平衡。

A Peer-to-Peer system is a distributed system whose component nodes participate in similar roles. Every user node (the peer) can exchange and contribute its resources to another one in the system. Similar to the case that peers may dynamically join and leave the system, the data will also be inserted into and removed from the system dynamically. Given a certain range, a range query will find any data item whose value within the range. For example, a range query can find all the Beatle's works between 1961 and 1968 for us. However, once the range data is distributed over a P2P system through the hash function which has been used largely in many P2P systems, the continuity of the range data is not guaranteed to exist. Therefore, finding the scattered data whose value within a certain range costs much in a P2P system. The Distributed Segment Tree method (DST) preserves the local continuity of the range data at each node by using a segment tree and can break any given range into minimum number of node intervals whose union constitutes the whole requested range. The DST method works based on the Distributed Hash Table (DHT) logic; therefore, it can be applied in any DHT-based P2P system. However, data distribution of the DST method may cause overlapping. When searching a data range, the DST method sends more number of requests than what is really needed. Although the DST method designs the Downward Load Stripping Mechanism, the load on peers still may not be balanced. The main reason of these problems is that the DST method applies the DHT logic to the P2P systems. Therefore, in this thesis, we propose a
method called Structured Segment Tree (SST) that does not use the DHT logic but embeds the structure of the segment tree into the P2P systems. In fact, the P2P network topology of an SST is the structure of a segment tree. Unlike a DST, an SST can fully reflect the properties of the original segment tree. Each peer in our
proposed P2P system represents a node of a segment tree. Data intervals at the same level are continuous and will not overlap with each other. The union of data intervals at a level with full nodes is totally the whole data range which the P2P system can support. When searching a data range, the SST method sends as many number of requests as needed. In addition, we add sibling links to preserve
the spatial locality and speed up the search efficiency. For the issue of load balance, our SST method also performs better than the DST method. From our simulation, we show that the SST method routes less number of peers to locate the requested range data than the DST method. We also show that the load based on our method is more
balanced than that based on the DST method.

TABLE OF CONTENTS
Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Client-Server System . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Peer-to-Peer System . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Searching Methods in P2P Systems . . . . . . . . . . . . . . . . . . . 3
1.4 Range Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Systems and Indexing Methods for Range Queries . . . . . . . . . . . 6
1.6 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Unstructured P2P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Napster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Gnutella . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Structured P2P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Distributed Hash Table . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Range Query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Range Addressable Network . . . . . . . . . . . . . . . . . . . 18
2.3.2 Range Addressable DAG . . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Distributed Segment Tree . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Tree Vector Index . . . . . . . . . . . . . . . . . . . . . . . . . 23
ii
Page
3. The Structured Segment Tree Method . . . . . . . . . . . . . . . . . 27
3.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Position Identifier . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 Sibling Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.3 Ascendant Link . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Peer Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Finding the Maximum Position Identifier . . . . . . . . . . . . 33
3.2.2 Joining of Peers . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.3 Leaving of Peers . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Data Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Data Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Data Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Data Lookup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5.1 Exact Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.2 Range Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
iii
LIST OF FIGURES
Figure Page
1.1 A client-server system . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 A classification of P2P systems . . . . . . . . . . . . . . . . . . . . . 3
1.3 Range search in the Chord system . . . . . . . . . . . . . . . . . . . . 9
1.4 The covered data intervals of each peer . . . . . . . . . . . . . . . . . 10
1.5 The covered data intervals of each peer in the Chord system . . . . . 11
1.6 A structured segment tree . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 An illustration of the Napster architecture . . . . . . . . . . . . . . . 14
2.2 Searching keyword “Snoopy” from node A . . . . . . . . . . . . . . . 15
2.3 The response from node B which has “Snoopy.avi” . . . . . . . . . . 16
2.4 Direct file transfer from node B to Node A . . . . . . . . . . . . . . . 16
2.5 The base Chord protocol: (a) the Chord architecture; (b) looking up
K55 from N14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Scalable key location: (a) Chord’s finger table; (b) looking up K55
from N14 by its finger table. . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 The basic tree topology on 8 leaves . . . . . . . . . . . . . . . . . . . 20
2.8 The zone of a peer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.9 Distributed segment tree of length 8 . . . . . . . . . . . . . . . . . . . 23
2.10 Mapping from DST nodes to network peers . . . . . . . . . . . . . . . 24
iv
Figure Page
2.11 Result of mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.12 Result of mapping in view of DST . . . . . . . . . . . . . . . . . . . . 24
2.13 Lookup for [2,6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.14 Usage of BitIdx: (a) the whole data range of ”Taiwanese History”; (b)
the BitIdx of ”Taiwanese Recent History”. . . . . . . . . . . . . . . . 26
3.1 A structured segment tree . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 A structured segment tree with sibling links . . . . . . . . . . . . . . 29
3.3 Function Get Data Interval . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Sibling links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Ascendant links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Function Find MaxPID . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.7 Function Who Has Children . . . . . . . . . . . . . . . . . . . . . . 36
3.8 Function Find MaxPID2 . . . . . . . . . . . . . . . . . . . . . . . . 37
3.9 Joining of a peer: (a) sending a Joining request; (b) finding MaxPID;
(c) joining; (d) after joining. . . . . . . . . . . . . . . . . . . . . . . . 38
3.10 Leaving of a peer: (a) finding MaxPID; (b) leaving and replacement. 40
3.11 Data Insertion: (a) standard; (b) threshold. . . . . . . . . . . . . . . 41
3.12 Procedure Data Insertion . . . . . . . . . . . . . . . . . . . . . . . . 42
3.13 Procedure Store Data . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.14 Procedure Data Deletion . . . . . . . . . . . . . . . . . . . . . . . . 43
3.15 Procedure Remove Data . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.16 Function Get Data Interval . . . . . . . . . . . . . . . . . . . . . . . 45
3.17 Function Exact Lookup . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.18 An example of data lookup . . . . . . . . . . . . . . . . . . . . . . . . 47
v
Figure Page
3.19 Function Is Neighbor . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.20 Function Range Lookup . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.21 A lookup for data interval [2, 6] used by the DST method . . . . . . . 50
4.1 A comparison of the exact search with variable RS . . . . . . . . . . 54
4.2 A comparison of variance of the exact search with variable RS . . . . 54
4.3 A comparison of the exact search with variable N . . . . . . . . . . . 55
4.4 A comparison of variance of the exact search with variable N . . . . . 56
4.5 A comparison of the range search with RS = 1024 and N = 31 . . . 57
4.6 A comparison of the range search with RS = 1024 and N = 63 . . . 57
4.7 A comparison of the range search with RS = 512 and N = 63 . . . . 58
4.8 A comparison of the load balance . . . . . . . . . . . . . . . . . . . . 59
4.9 A comparison of the load balance . . . . . . . . . . . . . . . . . . . . 60
4.10 A comparison of the load balance with
= 1500 . . . . . . . . . . . . 60
4.11 A comparison of the load balance with
= 1500 . . . . . . . . . . . . 61
vi
LIST OF TABLES
Table Page
4.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 A comparison of the exact search with variable RS (= 2x) . . . . . . 54

[1] K. Aberer and M. Hauswirth, “An Overview on Peer-to-Peer Information System,”Proc. of Int. Workshop on Distributed Data and Structures (WDAS), pp. 171–188, 2002.
[2] S. Alaei, M. Toossi, and M. Ghodsi, “Skiptree: A Scalable Range-Queriable Distributed Data Structure for Multidimensional Data,” Proc. of the 16th Annual
Int. Symposium on Algorithms and Computation, pp. 298–307, 2005.
[3] M. Cai, J. C. M. Frank, and P. Szekely, “MAAN: A Multiattribute Addressable Network for Grid Information Services.,” Proc. of the 4th Int. Workshop on Grid Computing, pp. 184–191, 2003.
[4] A. H. Cheng and Y. J. Joung, “Probabilistic File Indexing and Searching in Unstructured
Peer-to-Peer Networks,” Computer Networks, Vol. 50, No. 1, pp. 106–127, Jan. 2006.
[5] I. Clarke, S. G. Miller, T. W. Hong, O. Sandberg, and B. Wiley, “Protecting Free Expression Online with Freenet,” IEEE Internet Computing, Vol. 6, No. 1,
pp. 40–49, Jan./Feb. 2002.
[6] A. Crespo and H. Garcia-Molina, “Routing Indices for Peer-to-Peer Systems,”Proc. of the 22nd IEEE Int. Conf. on Distributed Computing, pp. 23–35, 2002.
[7] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, ch. More Geometric Data Structures,
pp. 106–127. SpringerVerlag, 1997.
[8] C. H. Ding, S. Nutanong, and R. Buyya, Peer-to-Peer Networks for Content Sharing, ch. Peer-to-Peer Computing: Evolution of a Disruptive Technology,
pp. 28–65. Idea Group Publishing, Jan. 2005.
[9] S. Fanning, “Napster,” http://www.napster.com/, 1999.
[10] P. Ganesan, B. Yang, and H. Garcia-Molina, “One Torus to Rule Them All:
Multi-Dimensional Queries in P2P Systems,” Proc. of the 7th Int. Workshop on the Web and Databases, pp. 19–24, 2004. 64
[11] K. Gummadi, R. Gummadi, S. Gribble, S. Ratnasamy, S. Shenker, and I. Stoica,
“The Impact of DHT Routing Geometry on Resilience and Proximity,” Proc. of Int. Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 381–394, 2003.
[12] M. Handley, P. Francis, R. Karp, S. Shenker, and S. Ratnasamy, “A Scalable Content-Addressable Network,” Proc. of the ACM SIGCOMM, pp. 161–172,
2001.
[13] N. Harvey, M. B. Jones, S. Saroiu, M. Theimer, and A. Wolman, “Skipnet: A Scalable Overlay Network with Practical Locality Properties,” Proc. of the 4th
USENIX Symposium on Internet Technologies and Systems, pp. 113–126, 2003.
[14] H. C. Hsiao and C. T. King, “Tornado: A Capability-Aware Peer-to-Peer Storage
Overlay,” Parallel and Distributed Computing, Special Issue on Middleware, Vol. 64, No. 6, pp. 747–758, June 2004.
[15] V. Kalogeraki, D. Gunopulos, and D. Zeinalipour-Yazti, “A Local Search Mechanism for Peer–to–Peer Networks,” Proc. of the 11th ACM Conf. on Information and Knowledge Management.
[16] T. Klingberg and R. Manfredi, “The Gnutella 0.6 Protocol Draft,” http://rfcgnutella. sourceforge.net/, 2002.
[17] A. Kothari, D. Agrawal, A. Gupta, and S. Suri, “Range Addressable Network: A
P2P Cache Architecture for Data Ranges,” Proc. of Int. Conf. on Peer-to-Peer Computing, pp. 14–25, 2003.
[18] O. Kwon, J. W. Moon, and K. J. Li, “Distin - A Distributed Spatial Index for P2P Environment,” Proc. of Data Engineering Workshop, pp. 14–25, 2006.
[19] X. Li and J. Wu, “Searching Techniques in Peer-to-Peer Networks,” Handbook of Theoretical and Algorithmic Aspects of Ad Hoc, Sensor, and Peer-to-Peer Networks, Auerbach Publications, pp. 613–642, 2006.
[20] A. Luther, R. Buyya, R. Ranjan, and S. Venugopal, High Performance Computing: Paradigm and Infrastructure, ch. Resource Discovery in Peer-to-Peer
Infrastructure, pp. 1–28. Wiley, Jan. 2005.
[21] Q. Lv, P. Cao, E. Cohen, K. Li, and S. Shenker, “Search and Replication in
Unstructured Peer–to–Peer Networks,” Proc. of the 16th ACM Int. Conf. on Supercomputing, pp. 84–95, June 2002.
[22] M. Marzolla, M. Mordacchini, and S. Orlando, “Tree Vector Indexes: Efficient
Range Queries for Dynamic Content on Peer-to-Peer Networks,” Proc. of the 14th Int. Conf. on Parallel, Distributed, and Network-Based Processing, pp. 11–
18, 2006.
[23] P. Maymounkov and D. Mazieres, “Kademlia: A Peer-to-Peer Information System Based on the Xor Metric,” Proc. of the First Int. Workshop on Peer-to-Peer Systems, pp. 53–65, 2005.
[24] H. Nazerzadeh and M. Ghodsi, “RAQ: A Range-Queriable Distributed Data Structure,” Proc. of Sofsem 2005, 31st Annual Conf. on Current Trends in Theory and Practice of Informatics, pp. 264–272, 2005.
[25] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and S. Shenker, “A Scalable Content-Addressable Network,” Proc. of Int. Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 161–172,
2001.
[26] J. Risson and T. Moors, “Survey of Research Towards Robust Peer-to-Peer Networks:
Search Methods,” Technical Report, University of New South Wales, pp. UNSW–EE–P2P–1–1, 2004. [27] M. Roussopoulos, M. Baker, D. Rosenthal, T. Giuli, P. Maniatis, and J. Mogul,
“2 P2P or Not 2 P2P?,” Proc. of the 3rd International Workshop on Peer-to-Peer Systems, pp. 5–15, 2004.
[28] A. Rowstron and P. Druschel, “Pastry: Scalable, Distributed Object Location and Routing for Large-Scale Peer-to-Peer Systems,” Proc. of IFIP/ACM Int.
Conf. on Distributed Systems Platforms, pp. 329–350, 2001.
[29] C. Schmidt and M. Parashar, “Enabling Flexible Queries with Guarantees in P2p Systems,” IEEE Internet Computing, No. 3, pp. 19–26, May–June.
[30] I. Stoica, D. Adkins, S. Zhuang, S. Shenker, and S. Surana, “Internet Indirection Infrastructure,” Proc. of the ACM SIGCOMM, pp. 73–86, 2002.
[31] I. Stoica, R. Morris, D. Karger, M. F. Kaashoek, F. Dabek, and H. Balakrishnan, “Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications,”
Proc. of the 9th Int. Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 149–160, 2001.
[32] J. Stribling, I. G. Councill, J. Li, M. F. Kaashoek, D. R. Karger, R. Morris, and S. Shenker, “Overcite: A Cooperative Digital Research Library,” Proc. of
the 4th Int. Workshop on Peer-To-Peer Systems, pp. 5–15, Aug. 2005.

[33] Taiwandc, “Taiwan’s 400 Years of History.” www.taiwandc.org, June 2006.
[34] Webopedia, “All About Peer-to-Peer,” http://www.webopedia.com/, pp. 171–
188, 2005.
[35] B. Yang and H. Garcia-Molina, “Improving Search in Peer-to-Peer Networks,”
Proc. of the 22nd IEEE Int. Conf. on Distributed Computing Systems, pp. 5–15, 2002.
[36] M. Zhang and K.-L. Tan, “Supporting Rich Queries in DHT-Based Peer-to-Peer
Systems,” Proc. of the 20th IEEE Int. Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises, pp. 95–100, 2003.
[37] B. Y. Zhao, L. Huang, J. Stribling, S. C. Rhea, A. D. Joseph, and J. Kubiatowicz,“Tapestry: A Global-Scale Overlay for Rapid Service Deployment,” IEEE
Journal on Selected Areas in Communications, Vol. 22, No. 1, pp. 41–53, Jan. 2004.
[38] C. Zheng, G. Shen, S. Li, and S. Shenker, “Distributed Segment Tree: Support
of Range Query and Cover Query over DHT,” Proc. of the 5th Int. Workshop on Peer-To-Peer Systems, pp. 5–15, Feb. 2006.