Skip Graph Research Articles

Building self-stabilizing overlay networks with the transitive closure framework

Overlay networks are expected to operate in hostile environments where node and link failures are commonplace. One way to make overlay networks robust is to design self-stabilizing overlay networks, i.e., overlay networks that can handle node and link failures without any external supervision. In this paper, we first describe a simple framework, which we call the Transitive Closure Framework (TCF), for the self-stabilizing construction of an extensive class of overlay networks. Like previous self-stabilizing algorithms for overlay networks, TCF permits intermediate node degrees to grow to Ω(n), independent of the maximum degree of the target overlay network. However, TCF has several advantages over previous work in this area: (i) it is a “framework” and can be used for the construction of a variety of overlay networks (e.g. Linear, Skip+), not just a particular network, (ii) it runs in an optimal number of rounds for a variety of overlay networks, and (iii) it can easily be composed with other non-self-stabilizing protocols that can recover from specific bad initial states in a memory-efficient fashion. We demonstrate the power of our framework by deriving from TCF a simple self-stabilizing protocol for constructing Skip+ graphs [R. Jacob, A. Richa, C. Scheideler, S. Schmid, H. Täubig, A distributed polylogarithmic time algorithm for self-stabilizing skip graphs, in: PODC ’09: Proceedings of the 28th ACM symposium on Principles of distributed computing, ACM, New York, NY, USA, 2009, pp. 131–140] that guarantees optimal convergence time from any configuration.

Corona: A stabilizing deterministic message-passing skip list

We present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales well. We prove the general necessary conditions limiting the initial states from which a self-stabilizing structured overlay network in a message-passing system can be constructed. The conditions require that initial state information has to form a weakly connected graph and it should only contain identifiers that are present in the system. We formally describe Corona and rigorously prove that it stabilizes from an arbitrary initial state subject to the necessary conditions. We extend Corona to construct a skip graph.

Tiara: A self-stabilizing deterministic skip list and skip graph

We present Tiara—a self-stabilizing peer-to-peer network maintenance algorithm. Tiara is truly deterministic which allows it to achieve exact performance bounds. Tiara allows logarithmic searches and topology updates. It is based on a novel sparse 0–1 skip list. We then describe its extension to a ringed structure and to a skip-graph.

Fast and Cost-Effective Online Load-Balancing in Distributed Range-Queriable Systems

Distributed systems such as Peer-to-Peer overlays have been shown to efficiently support the processing of range queries over large numbers of participating hosts. In such systems, uneven load allocation has to be effectively tackled in order to minimize overloaded peers and optimize their performance. In this work, we detect the two basic methodologies used to achieve load-balancing: Iterative key redistribution between neighbors and node migration. We identify these two key mechanisms and describe their relative advantages and disadvantages. Based on this analysis, we propose NIXMIG, a hybrid method that adaptively utilizes these two extremes to achieve both fast and cost-effective load-balancing in distributed systems that support range queries. We theoretically prove its convergence and as a case study, we offer an implementation on top of a Skip Graph, where we thoroughly validate our findings in a variety of static, dynamic and realistic workloads. We compare NIXMIG with an existing load-balancing algorithm proposed by Karger and Ruhl [1] and our experimental analysis shows that, NIXMIG can be as much as three times faster, requiring only one sixth and one third of message and item exchanges, respectively, to bring the system to a balanced state.

A new and effective hierarchical overlay structure for Peer-to-Peer networks

The tremendous growth of public interest in Peer-to-Peer (P2P) networks in recent years has initiated a lot of research work on how to design efficient overlay structures for P2P systems. Scalable overlay networks such as Chord, CAN, Pastry, and Tapestry provide no control over where data is stored and the location of the peers and resources is determined by the hash values of their identifiers and keys respectively. As a result, these overlays cannot support range queries and other proximity-aware complex queries directly. In this paper, we present a hierarchical P2P overlay network called SkipCluster, which is capable of supporting both exact-match and multi-dimensional range queries efficiently without consumption of extra memory space. SkipCluster is derived from skip graphs and SkipNet, but it has a two-tier hierarchical architecture.In both tiers, peers are connected in sequence according to the order of their peer IDs, and related resources are stored near each other without hashing of their resource keys. We design a novel data structure called Triple Linked List (TLL) to store each super-peer’s pointers in the higher tier, which can be used to find the longest prefix and speed up query routing of inter-cluster. In the lower tier, each intra-cluster peer’s routing table contains pointers with exponentially incremental distance. Experimental results show that SkipCluster can speed up both exact-match and range queries in different network sizes.

A Concurrent Implementation of Skip Graphs

In this extended abstract, we outline a concurrent implementation of a data structure called skip graphs. This data structure, proposed by Aspnes and Shah, has similar functionality to binary search trees, and has also special features that make it suitable for P2P distributed environments. In our implementation, we used non-blockirig locking primitives to synchronize the operations whenever necessary. The resulting implementation performed well in practice, according to our experiments.

Histogram-Based Global Load Balancing in Structured Peer-to-Peer Systems

Over the past few years, peer-to-peer (P2P) systems have rapidly grown in popularity and have become a dominant means for sharing resources. In these systems, load balancing is a key challenge because nodes are often heterogeneous. While several load-balancing schemes have been proposed in the literature, these solutions are typically ad hoc, heuristic based, and localized. In this paper, we present a general framework, HiGLOB, for global load balancing in structured P2P systems. Each node in HiGLOB has two key components: 1) a histogram manager maintains a histogram that reflects a global view of the distribution of the load in the system, and 2) a load-balancing manager that redistributes the load whenever the node becomes overloaded or underloaded. We exploit the routing metadata to partition the P2P network into nonoverlapping regions corresponding to the histogram buckets. We propose mechanisms to keep the cost of constructing and maintaining the histograms low. We further show that our scheme can control and bound the amount of load imbalance across the system. Finally, we demonstrate the effectiveness of HiGLOB by instantiating it over three existing structured P2P systems: Skip Graph, BATON, and Chord. Our experimental results indicate that our approach works well in practice.

The expansion and mixing time of skip graphs with applications

We prove that with high probability a skip graph contains a 4-regular expander as a subgraph and estimate the quality of the expansion via simulations. As a consequence, skip graphs contain a large connected component even after an adversarial deletion of nodes. We show how the expansion property can be used to sample a node in the skip graph in a highly efficient manner. We also show that the expansion property can be used to load balance the skip graph quickly. Finally, it is shown that the skip graph could serve as an unstructured P2P system, making it a good candidate for a hybrid P2P system.

NBDT: an efficient P2P indexing scheme for web service discovery

In this paper, we propose a new infrastructure for web services discovery in P2P networks, the Nested Balanced Distributed Tree (NBDT). Peers that store web services information, such as data item descriptions, are efficiently located using a scalable and robust data indexing structure based on a NBDT. The key innovation is that the solution is based on a totally new infrastructure, which is not vulnerable to classic disadvantages. We present a theoretical analysis backed up by experimental results, which shows that the communication cost of query and update operations scale sublogarithmically in the worst case with the number of NBDT nodes, outperforming three of the most popular decentralised infrastructures: Chord (and some of its successors), BATON (and its successor) and Skip Graphs. Furthermore, we show that the network is robust to failures providing quality of web services requirements.

Skip graphs

Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peer-to-peer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, simple and straightforward algorithms can be used to construct a skip graph, insert new nodes into it, search it, and detect and repair errors within it introduced due to node failures.

Range queries over skip tree graphs

The support for complex queries, such as range, prefix and aggregation queries, over structured peer-to-peer systems is currently an active and significant topic of research. This paper demonstrates how Skip Tree Graph, as a novel structure, presents an efficient solution to that problem area through provision of a distributed search tree functionality on decentralised and dynamic environments. Since Skip Tree Graph is based on skip trees, a concurrent approach to skip lists, it constitutes an augmentation of skip graphs that extends its functionality and allows for important performance improvements. This work presents a thorough comparison between these two related peer-to-peer overlay networks, their construction, search algorithms and properties. Being based on tree structures, skip tree graphs supports aggregation queries and multicast/broadcast operations, which cannot be directly implemented in its predecessor. The repair mechanism for healing the structure in case of failures is more efficient and harnesses the parallelism inherent in P2P networks. Particular consideration is given to the performance of different range-query schemes over the two related structures. Theoretical and experimental results conclude that Skip Tree Graphs outperform skip graphs on both exact-match and range searches.

EXTENDED SKIP GRAPHS FOR EFFICIENT KEY SEARCH IN PEER-TO-PEER ENVIRONMENT

In this paper, we propose three techniques to improve the cost/performance of the skip graph that was recently proposed by Aspnes and Shah. The skip graph, which is a distributed data structure that could efficiently support find, insert, and delete operations of a key drawn from a totally ordered set, consists of N nodes each of which is connected with exactly log 2 N nodes determined by a set of random binary vectors called membership vectors. In the following, we will extend the construction of the skip graph in the following two directions: 1) proposal of a subgraph of the skip graph which realizes a graceful degradation of the routing performance when the number of neighbors reduces from log 2 N, and 2) proposal of a supergraph of the skip graph which realizes a significant performance improvement when the number of neighbors increases from log 2 N. The performance of those extended graphs will be evaluated analytically.

Survey of research towards robust peer-to-peer networks: Search methods

The pace of research on peer-to-peer (P2P) networking in the last five years warrants a critical survey. P2P has the makings of a disruptive technology--it can aggregate enormous storage and processing resources while minimizing entry and scaling costs. Failures are common amongst massive numbers of distributed peers, though the impact of individual failures may be less than in conventional architectures. Thus the key to realizing P2P's potential in applications other than casual file sharing is robustness.P2P search methods are first couched within an overall P2P taxonomy. P2P indexes for simple key lookup are assessed, including those based on Plaxton trees, rings, tori, butterflies, de Bruijn graphs and skip graphs. Similarly, P2P indexes for keyword lookup, information retrieval and data management are explored. Finally, early efforts to optimize range, multiattribute, join and aggregation queries over P2P indexes are reviewed. Insofar as they are available in the primary literature, robustness mechanisms and metrics are highlighted throughout. However, the low-level mechanisms that most affect robustness are not well isolated in the literature. Furthermore, there has been little consensus on robustness metrics. Recommendations are given for future research.