MAAN: A Multi-Attribute Addressable Network for Grid Information Services

Recent structured Peer-to-Peer (P2P) systems such as Distributed Hash Tables (DHTs) offer scalable key-based lookup for distributed resources. However, they cannot be simply applied to grid information services because grid resources need to be registered and searched using multiple attributes. This paper proposes a Multi-Attribute Addressable Network (MAAN) that extends Chord to support multi-attribute and range queries. MAAN addresses range queries by mapping attribute values to the Chord identifier space via uniform locality preserving hashing. It uses an iterative or single attribute dominated query routing algorithm to resolve multi-attribute based queries. Each node in MAAN only has O(logN) neighbors for N nodes. The number of routing hops to resolve a multi-attribute range query is O(logN+N×s_min), where s_min is the minimum range selectivity on all attributes. When s_min=, it is logarithmic to the number of nodes, which is scalable to a large number of nodes and attributes. We also measured the performance of our MAAN implementation and the experimental results are consistent with our theoretical analysis.     

Re-Chord: A Self-stabilizing Chord Overlay Network

The Chord peer-to-peer system is considered, together with CAN, Tapestry and Pastry, as one of the pioneering works on peer-to-peer distributed hash tables (DHT) that inspired a large volume of papers and projects on DHTs as well as peer-to-peer systems in general. Chord, in particular, has been studied thoroughly, and many variants of Chord have been presented that optimize various criteria. Also, several implementations of Chord are available on various platforms. Though Chord is known to be very efficient and scalable and it can handle churn quite well, no protocol is known yet that guarantees that Chord is self-stabilizing, i.e., the Chord network can be recovered from any initial state in which the network is still weakly connected. This is not too surprising since it is known that the Chord network is not locally checkable for its current topology. We present a slight extension of the Chord network, called Re-Chord (reactive Chord), that turns out to be locally checkable, and we present a self-stabilizing distributed protocol for it that can recover the Re-Chord network from any initial state, in which the n peers are weakly connected. in O(nlogn) communication rounds. We also show that our protocol allows a new peer to join or an old peer to leave an already stable Re-Chord network so that within O((logn)²) communication rounds the Re-Chord network is stable again.     

DHT协议设计选项与抖动问题关联分析

因节点加入和离开引起的抖动是增加结构化P2P网络路由表更新代价的主要原因。为了找出影响网络抖动的关键因素,分析了影响抖动的路由方式、邻居选择、节点加入和节点离开以及并行查找等策略因素,发现任意两种DHT网络分别采用的五种策略都至少有两种不同,对两种DHT网络直接进行比较就很难确定哪些策略能更有效地降低抖动。因此,提出在同一网络内用不同的单个策略对网络抖动进行比较和分析的方法,称之为CSP。通过对现有DHT算法进行改进,使用CSP方法对不同的单个策略进行比较,得出以下结论:迭代路由、快速加入和周期性恢复策略和有效的邻居选择算法能更有效地降低网络的抖动。     

一种改进的Chord网络模型

经典的Chord模型中为维护Chord环路由信息而周期性执行的Stabilize操作产生了大量的消息转发。提出一种改进的Chord模型,通过使用优化的双向Finger表,使得只在节点加入或离开时才进行路由更新,降低了消息转发的开销,同时优化了路由定位算法。     

P2P网络中基于DHT的自适应Chord风险模型

针对Chord模型在节点加入或离开时产生大量消息,不适用于动态网络的问题,提出一种基于分布式哈希表（Distribute Hash Table,DHT）的自适应Chord模型,即Self-adaptive Chord。方法是该模型在节点加入或离开的时候暂不考虑整个网络逻辑拓扑的一致性,只简单更新其前驱节点和后继节点的路由表,而在节点转发消息时动态地调整各节点路由表,使得网络逻辑拓扑动态地趋向于一致。通过实验对比评估了自适应Chord和Chord性能,结果表明自适应Chord能有效降低由于网络动荡引发的消息数量,同时基本保留了Chord的高效率查询。结论为自适应Chord提供了一种在节点动荡频繁的环境下的候选解决方案。     

The Flexible Hypercube: A New Fault-Tolerant Architecture for Parallel Computing

This paper presents the new Flexible Hypercube architecture. The Flexible Hypercube is a fault-tolerant network topology that can be constructed for an arbitrary number of nodes and is incrementally expandable. This topology maintains the strong features of the Hypercube while overcoming deficiencies in expandability. It is shown to have strong node connectivity, a small diameter, and to be tolerant of faults. The Flexible Hypercube is a suitable architecture for the design of both tightly coupled parallel systems and distributed systems. Efficient fault-free and fault-tolerant algorithms for message routing and broadcasting are presented for the architecture. The fault-free algorithm guarantees successful routing inO(logN) time, whereNis the number of nodes in the system, and the fault-tolerant algorithm guarantees routing to functioning nodes if a route exists. The fault-free and fault-tolerant broadcasting algorithms have time complexityO(logN), and the fault-tolerant algorithm guarantees success if no two faulty nodes are adjacent and no functioning node is adjacent to two faults.     

基于混合结构的Chord系统研究

Chord是一种比较有效的P2P路由算法,它能够快速地查找到该资源的位置,但是当节点能力差异较大时会影响网络的稳定性;Chord环上的节点ID与实际物理地址不一致会造成信息的延迟现象;混合式的P2P能够较好的管理能力较差的节点,但是查询具有盲目性。该文通过分析它们两者的优缺点提出了基于混合结构的Chord系统,在一定程度上解决了传统Chord的稳定性、绕路问题和混合P2P结构的查询效率问题。     

Ad-hoc limited scale-free models for unstructured peer-to-peer networks

Several protocol efficiency metrics (e.g., scalability, search success rate, routing reachability and stability) depend on the capability of preserving structure even over the churn caused by the ad-hoc nodes joining or leaving the network. Preserving the structure becomes more prohibitive due to the distributed and potentially uncooperative nature of such networks, as in the peer-to-peer (P2P) networks. Thus, most practical solutions involve unstructured approaches while attempting to maintain the structure at various levels of protocol stack. The primary focus of this paper is to investigate construction and maintenance of scale-free topologies in a distributed manner without requiring global topology information at the time when nodes join or leave. We consider the uncooperative behavior of peers by limiting the number of neighbors to a pre-defined hard cutoff value (i.e., no peer is a major hub), and the ad-hoc behavior of peers by rewiring the neighbors of nodes leaving the network. We also investigate the effect of these hard cutoffs and rewiring of ad-hoc nodes on the P2P search efficiency.     

Index-based query processing on distributed multidimensional data

This work introduces decentralized query processing techniques based on MIDAS, a novel distributed multidimensional index. In particular, MIDAS implements a distributed k-d tree, where leaves correspond to peers, and internal nodes dictate message routing. MIDAS requires that peers maintain little network information, and features mechanisms that support fault tolerance and load balancing. The proposed algorithms process point and range queries over the multidimensional indexed space in only O(log n) hops in expectance, where n is the network size. For nearest neighbor queries, two processing alternatives are discussed. The first, termed eager processing, has low latency (expected value of O(log n) hops) but may involve a large number of peers. The second, termed iterative processing, has higher latency (expected value of O(log² n) hops) but involves far fewer peers. A detailed experimental evaluation demonstrates that our query processing techniques outperform existing methods for settings involving real spatial data as well as in the case of high dimensional synthetic data.     

Towards optimal range medians

We consider the following problem: Given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which needs O(nlogk+klogn) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a comparison lower bound for k=O(n). The space complexity of our simple algorithm is O(nlogn) in the pointer machine model, and O(n) in the RAM model. In the latter model, a more involved O(n) space data structure can be constructed in O(nlogn) time where the time per query is reduced to O(logn/loglogn). We also give efficient dynamic variants of both data structures, achieving O(log²n) query time using O(nlogn) space in the comparison model and O((logn/loglogn)²) query time using O(nlogn/loglogn) space in the RAM model, and show that in the cell-probe model, any data structure which supports updates in O(log^O(1)n) time must have Ω(logn/loglogn) query time.Our approach naturally generalizes to higher-dimensional range median problems, where element positions and query ranges are multidimensional—it reduces a range median query to a logarithmic number of range counting queries.     

Maintaining dynamic sequences under equality tests in polylogarithmic time

We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests inO(1) time. The randomized version supports new sequence creations inO(log² n) expected time wheren is the length of the sequence created. The deterministic solution supports sequence creations inO(logn(logmlog^* m+logn)) time for themth operation. This work was supported by the ESPRIT Basic Research Actions Program, under Contract No. 7141 (Project ALCOM II).     

Study of General Icomplete Star Interconnection Networks

The star networks,which were originally proposed by Akers and Harel,have suffered from a rigorous restriction on the number of nodes.The general incomplete star networks(GISN) are proposed in this paper to relieve this restriction.An efficient labeling scheme for GISN is given,and routing and broadcasting algorithms are also presented for GIS.The communication diameter of GISN is shown to be bounded by 4n-7.The proposed single node broadcasting algorithm is optimal with respect to time complexity O(nlog2n).     

Stochastic analysis of a churn-tolerant structured peer-to-peer scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to “convert” a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a O(logN) degree connected network, in which every search succeeds in O(logN) hops w.h.p., using O(logN) messages, where N is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an O(logN) overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p.     

Robust algorithms for packet routing in a mesh

This paper considers the problem of permutation packet routing on a n×n mesh-connected array of processors. Each node in the array is assumed to be independently faulty with a probability bounded above by a valuep. This paper gives a routing algorithm which, ifp 0.29, will with very high probability route every packet that can be routed inO(n logn) steps with queue lengths that areO(log² n). Extensions to higher-dimensional meshes are given.     

Connected component and simple polygon intersection searching

Efficient data structures are given for the following two query problems: (i) preprocess a setP of simple polygons with a total ofn edges, so that all polygons ofP intersected by a query segment can be reported efficiently, and (ii) preprocess a setS ofn segments, so that the connected components of the arrangement ofS intersected by a query segment can be reported quickly. In these problems we do not want to return the polygons or connected components explicitly (i.e., we do not wish to report the segments defining the polygon, or the segments lying in the connected components). Instead, we assume that the polygons (or connected components) are labeled and we just want to report their labels. We present data structures of sizeO(n ¹⁺) that can answer a query in timeO(n ¹⁺+k), wherek is the output size. If the edges ofP (or the segments inS) are orthogonal, the query time can be improved toO(logn+k) usingO(n logn) space. We also present data structures that can maintain the connected components as we insert new segments. For arbitrary segments the amortized update and query time areO(n ^1/2+) andO(n ^1/2++k), respectively, and the space used by the data structure isO(n ¹⁺. If we allowO(n ^4/3+ space, the amortized update and query time can be improved toO(n ^1/3+ andO(n ^1/3++k, respectively. For orthogonal segments the amortized update and query time areO(log² n) andO(log² n+klogn), and the space used by the data structure isO (n logn). Some other related results are also mentioned.Part of this work was done while the second author was visiting the first author on a grant by the Dutch Organization for Scientific Research (N.W.O.). The research of the second author was also supported by the ESPRIT Basic Research Action No. 3075 (project ALCOM). The research of the first author was supported by National Science Foundation Grant CCR-91-06514.     

Exact Solutions to Diameter and Routing Problems in PEC Networks

Recently, the diameter problem for packed exponential connections (PEC) networks was addressed by Cho-Chin Lin and V. K. Prasanna [Proc. Symposium on Parallel and Distributed Processing, 1992, pp. 368–375], who presented asymptotically tight bounds for the diameter and showed asymptotically optimal routing algorithms. In this paper exact, solutions to the diameter and routing problems of PEC networks are derived, thereby strengthening the asymptotic bounds of Lin and Prasanna. For anN= 2ⁿnode PEC network, with[formula]an integer, it is shown that the diameter is given by the simple expression[formula]An exact expression for the diameter of PEC networks for generalNis also derived. Efficient algorithms for shortest-path routing between nodes in a PEC network are then developed. These algorithms use at mostO(log²N) time for computing the lengths of minimal routes between nodes. Finally, a simple modification to obtain symmetric PEC networks is suggested.     

Eclecticism shrinks even small worlds

We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a d-dimensional mesh by adding links chosen at random according to the d-harmonic distribution. In these graphs, greedy routing performs in O(log ² n) expected number of steps. We introduce indirect-greedy routing. We show that giving O(log ² n) bits of topological awareness per node enables indirect-greedy routing to perform in O(log ^1+1/d n) expected number of steps in d-dimensional augmented meshes. We also show that, independently of the amount of topological awareness given to the nodes, indirect-greedy routing performs in Ω(log ^1+1/d n) expected number of steps. In particular, augmenting the topological awareness above this optimum of O(log ² n) bits would drastically decrease the performance of indirect-greedy routing. Our model demonstrates that the efficiency of indirect-greedy routing is sensitive to the “world’s dimension,” in the sense that high dimensional worlds enjoy faster greedy routing than low dimensional ones. This could not be observed in Kleinberg’s routing. In addition to bringing new light to Milgram’s experiment, our protocol presents several desirable properties. In particular, it is totally oblivious, i.e., there is no header modification along the path from the source to the target, and the routing decision depends only on the target, and on information stored locally at each node. A preliminary version of this paper appeared in the proceedings of the 23rd ACM Symposium on Principles of Distributed Computing (PODC), St. Johns, Newfoundland, Canada, July 25–28, 2004.     

数据仓库系统中层次式Cube存储结构

区域查询是数据仓库上支持联机分析处理(on-line analytical processing,简称OLAP)的重要操作.近几年,人们提出了一些支持区域查询和数据更新的Cube存储结构.然而这些存储结构的空间复杂性和时间复杂性都很高,难以在实际中使用.为此,提出了一种层次式Cube存储结构HDC(hierarchical data cube)及其上的相关算法.HDC上区域查询的代价和数据更新代价均为O(log^dn),综合性能为O((logn)^2d)(使用C_qC_u模型)或O(K(logn)^d)(使用C_qn_q+C_un_u模型).理论分析与实验表明,HDC的区域查询代价、数据更新代价、空间代价以及综合性能都优于目前所有的Cube存储结构.     

一种具有能力约束性能的任意源覆盖多播方法

近年来提出的许多面向单个数据源设计的多播树并不能简单扩展到任意源多播系统中,因为针对每个源建立一个树代价高昂.而已存在的一些允许多数据源的P2P(peer-to-peer)系统的维护量大,在体现结点能力差异等方面缺少灵活性.提出一个任意源覆盖多播服务方案,并具有结点能力约束性能.它建立在非DHT(distributed hash table)覆盖网络上,无须建立显式的多播树.设计了两种分布式多播算法,它们将任意源的多播信息传送到所有结点的期望跳数是O(log_cn),其中,c是平均结点能力,n是多播组中的结点个数.     

An adaptive sector-based routing model over structured peer-to-peer networks

It is common that members of a peer-to-peer network join and leave the system at any time. But in a structured peer-to-peer network, frequent joining and leaving may cause huge maintenance overhead. To deal with this churn problem, we proposed a two-tier architecture called adaptive sector-based routing model (ASBRM). In ASBRM the key space is divided into several sectors and each one has a super peer who plays the role of the relay proxy of the sector. When the number of peer members in a sector exceeds a predefined threshold, it will split into two sectors so that the traffic and computational overhead of the super peer can be kept within an acceptable range. For the convenience of explanation, we combine ASBRM with Chord and perform a series of simulations. Both analysis and simulation results show that ASBRM achieves lower communication cost of members’ joining and leaving while at the same time the message routing path length is also shortened.