Deke Guo

Theory and Network Applications of Dynamic Bloom Filters

A bloom filter is a simple, space-efficient, randomized data structure for concisely representing a static data set, in order to support approximate membership queries. It has great potential for distributed applications where systems need to share information about what resources they have. The space efficiency is achieved at the cost of a small probability of false positive in membership queries. However, for many applications the space savings and short locating time consistently outweigh this drawback. In this paper, we introduce dynamic bloom filters (DBF) to support concise representation and approximate membership queries of dynamic sets, and study the false positive probability and union algebra operations. We prove that DBF can control the false positive probability at a low level by adjusting the number of standard bloom filters used according to the actual size of current dynamic set. The space complexity is also acceptable if the actual size of dynamic set does not deviate too much from the predefined threshold. Furthermore, we present multidimension dynamic bloom filters (MDDBF) to support concise representation and approximate membership queries of dynamic sets in multiple attribute dimensions, and study the false positive probability and union algebra operations through mathematic analysis and experimentation. We also explore the optimization approach and three network applications of bloom filters, namely bloom joins, informed search, and global index implementation. Our simulation shows that informed search based on bloom filters can obtain higher recall and success rate of query than the blind search protocol.

The Dynamic Bloom Filters

A Bloom filter is an effective, space-efficient data structure for concisely representing a set, and supporting approximate membership queries. Traditionally, the Bloom filter and its variants just focus on how to represent a static set and decrease the false positive probability to a sufficiently low level. By investigating mainstream applications based on the Bloom filter, we reveal that dynamic data sets are more common and important than static sets. However, existing variants of the Bloom filter cannot support dynamic data sets well. To address this issue, we propose dynamic Bloom filters to represent dynamic sets, as well as static sets and design necessary item insertion, membership query, item deletion, and filter union algorithms. The dynamic Bloom filter can control the false positive probability at a low level by expanding its capacity as the set cardinality increases. Through comprehensive mathematical analysis, we show that the dynamic Bloom filter uses less expected memory than the Bloom filter when representing dynamic sets with an upper bound on set cardinality, and also that the dynamic Bloom filter is more stable than the Bloom filter due to infrequent reconstruction when addressing dynamic sets without an upper bound on set cardinality. Moreover, the analysis results hold in stand-alone applications, as well as distributed applications.

Expandable and Cost-Effective Network Structures for Data Centers Using Dual-Port Servers

A fundamental goal of data center networking is to efficiently interconnect a large number of servers with the low equipment cost. Several server-centric network structures for data centers have been proposed. They, however, are not truly expandable and suffer a low degree of regularity and symmetry. Inspired by the commodity servers in todays data centers that come with dual port, we consider how to build expandable and cost-effective structures without expensive high-end switches and additional hardware on servers except the two NIC ports. In this paper, two such network structures, called HCN and BCN, are designed, both of which are of server degree 2. We also develop the low overhead and robust routing mechanisms for HCN and BCN. Although the server degree is only 2, HCN can be expanded very easily to encompass hundreds of thousands servers with the low diameter and high bisection width. Additionally, HCN offers a high degree of regularity, scalability, and symmetry, which conform to the modular designs of data centers. BCN is the largest known network structure for data centers with the server degree 2 and network diameter 7. Furthermore, BCN has many attractive features, including the low diameter, high bisection width, large number of node-disjoint paths for the one-to-one traffic, and good fault-tolerant ability. Mathematical analysis and comprehensive simulations show that HCN and BCN possess excellent topological properties and are viable network structures for data centers.

Moore: An Extendable Peer-to-Peer Network Based on Incomplete Kautz Digraph with Constant Degree

The topological properties of peer-to-peer overlay networks are critical factors that dominate the performance of these systems. Several non-constant and constant degree interconnection networks have been used as topologies of many peer-to-peer networks. One of these has many desirable properties: the Kautz digraph. Unlike interconnection networks, peer-to-peer networks need a topology with an arbitrary size and degree, but the complete Kautz digraph does not possess these properties. In this paper, we propose Moore: the first effective and practical peer-to-peer network based on the incomplete Kautz digraph with <i>O</i>(log<i> _d </i> <i>N</i>) diameter and constant degree under a dynamic environment. The diameter and average routing path length are [log<i> _d </i>(<i>N</i>) - log<i> _d </i>(1 + 1/<i>d</i>)] and log<i> _d </i> <i>N</i>, respectively, and are shorter than that of CAN, butterfly, and cube-connected-cycle. They are close to that of complete de Bruijn and Kautz digraphs. The message cost of node joining and departing operations are at most 2.5 <i>d</i> log<i> _d </i> <i>N</i> and (2.5 <i>d</i> + 1) log<i> _d </i> <i>N</i>, and only <i>d</i> and 2<i>d</i> nodes need to update their routing tables. Moore can achieve optimal diameter, high performance, good connectivity and low congestion evaluated by formal proofs and simulations.

False Negative Problem of Counting Bloom Filter

Bloom filter is effective, space-efficient data structure for concisely representing a data set and supporting approximate membership queries. Traditionally, researchers often believe that it is possible that a Bloom filter returns a false positive, but it will never return a false negative under well-behaved operations. By investigating the mainstream variants, however, we observe that a Bloom filter does return false negatives in many scenarios. In this work, we show that the undetectable incorrect deletion of false positive items and detectable incorrect deletion of multiaddress items are two general causes of false negative in a Bloom filter. We then measure the potential and exposed false negatives theoretically and practically. Inspired by the fact that the potential false negatives are usually not fully exposed, we propose a novel Bloom filter scheme, which increases the ratio of bits set to a value larger than one without decreasing the ratio of bits set to zero. Mathematical analysis and comprehensive experiments show that this design can reduce the number of exposed false negatives as well as decrease the likelihood of false positives. To the best of our knowledge, this is the first work dealing with both the false positive and false negative problems of Bloom filter systematically when supporting standard usages of item insertion, query, and deletion operations.

Control plane of software defined networks

Software Defined Networking (SDN) has been proposed to solve ossifications of Internet. The main motivation of SDN is to separate the control plane and data plane, enabling a centralized control. In this way, the network infrastructure becomes an open and standardized resource. Hence, it can be managed and utilized in a more efficient way. The controller is the key infrastructure in the SDN and provides programming interfaces to the entire network. Then, various applications can be written to perform management tasks and offer new functionalities on the controller. In this survey, we present many essential research issues about the controller, and especially focus on the control architecture, performance, scalability, placement, interface and security. The aim of this paper is to provide an up-to-date view to the SDN controller.

BCN: Expansible network structures for data centers using hierarchical compound graphs

A fundamental challenge in data centers is how to design networking structures for efficiently interconnecting a large number of servers. Several server-centric structures have been proposed, but are not truly expansible and suffer low degree of regularity and symmetry. To address this issue, we propose two novel structures called HCN and BCN, which utilize hierarchical compound graphs to interconnect large population of servers each with two ports only. They own two topological advantages, i.e., the expansibility and equal degree. In addition, HCN offers high degree of regularity, scalability and symmetry, which well conform to the modular design of data centers. Moreover, a BCN of level one in each dimension involves more servers than FiConn with server degree 2 and diameter 7, and is large enough for a single data center. Mathematical analysis and comprehensive simulations show that BCN possesses excellent topology properties and is a viable network structure for data centers.

Maximizing the Lifetime of

Barrier coverage is an essential issue in wireless sensor networks for its various applications. Traditional barrier coverage, however, has a tight requirement that sensor nodes have to form continuous barriers. In many scenarios, this requirement can be relaxed to some extent while supporting the surveillance task well, thus easing the deployment of sensors. In this paper, we focus on maximizing the network lifetime under a novel k-discrete barrier coverage model, whose goal is to cover some specific discrete points of interest (POIs) by deploying sensors in k lines to form barriers. First, we formulate the problem of scheduling sensors with limited moving energy to achieve the maximal network lifetime while ensuring k-discrete barrier coverage as the max-lifetime for k-discrete barrier coverage with limited-moving-cost (KLCML) problem and then analyze the theoretical upper and lower bound of the problem and the coverage probability of the coverage model. Second, we propose a schedule algorithm, called KLCML, which uses the information on redundant sensors to maximize the network lifetime while achieving the k-discrete barrier coverage. Different from the existing works, the KLCML combines the redeployment method and the sleeping schedule method seamlessly to prolong the network lifetime intensively. Comprehensive simulations demonstrate that our analytical result about the coverage probability matches the simulation result well, and that the proposed KLCML algorithm prolongs the network lifetime effectively while achieving the k-discrete barrier coverage under different settings of parameters, such as the number of sensor nodes, the standard deviation of sensor offsets in deployment and the density of the POIs to be monitored.

k

In order to improve scalability and reduce maintenance overhead for structured peer-to-peer systems, researchers design optimal architectures with constant degree and logarithmical diameter. The expected topologies, however, require the number of peers to be some given values determined by the average degree and the diameter. Hence, existing designs fail to address the issue due to the fact that (1) we cannot guarantee how many peers to join a P2P system at a given time, and (2) a P2P system is typically dynamic with peers frequently coming and leaving. In this work, we propose BAKE scheme based on balanced Kautz tree structure with logdn in diameter and constant degree even the number of peers is an arbitrary value. Resources that are similar in single or multi-dimensional attributes space are stored on a same peer or neighboring peers. Through formal analysis and comprehensive simulations, we show that BAKE achieves optimal diameter and good connectivity as the Kautz digraph does. Indeed, the concepts of balanced Kautz tree introduced in this work can also be extended and applied to other interconnection networks after minimal modifications, for example, de Bruijn digraph.

-Discrete Barrier Coverage Using Mobile Sensors

This paper proposes a novel architecture called KCube. KCube is a compound graph of Kautz digraph and hypercube. It employs the hypercube topology as a unit cluster and connects many such clusters by means of a Kautz digraph. It then utilizes the topological properties of hypercube to realize convenient embedding of parallel algorithms, and the short diameter of Kautz graph to support efficient inter-cluster communication. KCube possesses many attractive characteristics, such as modularity, expansibility, and regularity, while these benefits are achieved at the cost of only increasing the degree of any node by one, regardless of the network size. The methodology to construct KCube can also be applied to other compound networks after minimal modifications.