Multi-dimensional Range Queries Research Articles

Authenticating multi‐dimensional query results in outsourced database

In the outsourced database model, the third-party server provides query services to users on behalf of the data owner. However, the service provider may be unreliable or susceptible to attacks. The service provider can also produce inauthentic or incomplete query results. An authentication scheme for multi-dimensional data is proposed in the present study to investigate this problem. The authors introduce a new concept of tower head node based on the k -dimensional skip list and use it to construct a new authenticated data structure. This structure supports both multi-dimensional range query and dynamic maintenance. They also show how to verify the authenticity and completeness of query results on multi-dimensional datasets in the outsourced database model. Moreover, this structure can be fully outsourced, thus the service provider can perform the entire maintenance, which is crucial for users with limited computational resources. The proof of security and the evaluation of experiment demonstrate that the scheme is secure and outperforms previous schemes in terms of the construction cost, proof size, query time, verification time and update cost.

Design of policy-aware differentially private algorithms

The problem of designing error optimal differentially private algorithms is well studied. Recent work applying differential privacy to real world settings have used variants of differential privacy that appropriately modify the notion of neighboring databases. The problem of designing error optimal algorithms for such variants of differential privacy is open. In this paper, we show a novel transformational equivalence result that can turn the problem of query answering under differential privacy with a modified notion of neighbors to one of query answering under standard differential privacy, for a large class of neighbor definitions. We utilize the Blowfish privacy framework that generalizes differential privacy. Blowfish uses a policy graph to instantiate different notions of neighboring databases. We show that the error incurred when answering a workload W on a database x under a Blowfish policy graph G is identical to the error required to answer a transformed workload f G ( W ) on database g G ( x ) under standard differential privacy, where f G and g G are linear transformations based on G. Using this result, we develop error efficient algorithms for releasing histograms and multidimensional range queries under different Blowfish policies. We believe the tools we develop will be useful for finding mechanisms to answer many other classes of queries with low error under other policy graphs.

Dragon: Multidimensional range queries on distributed aggregation trees

Distributed query processing is of paramount importance in next-generation distribution services, such as Internet of Things (IoT) and cyber–physical systems. Even if several multi-attribute range queries supports have been proposed for peer-to-peer systems, these solutions must be rethought to fully meet the requirements of new computational paradigms for IoT, like fog computing. This paper proposes dragon, an efficient support for distributed multi-dimensional range query processing targeting efficient query resolution on highly dynamic data. In dragon nodes at the edges of the network collect and publish multi-dimensional data. The nodes collectively manage an aggregation tree storing data digests which are then exploited, when resolving queries, to prune the sub-trees containing few or no relevant matches. Multi-attribute queries are managed by linearizing the attribute space through space filling curves. We extensively analysed different aggregation and query resolution strategies in a wide spectrum of experimental set-ups. We show that dragon manages efficiently fast changing data values. Further, we show that dragon resolves queries by contacting a lower number of nodes when compared to a similar approach in the state of the art.

Exploiting Massive Parallelism for IndexingMulti-Dimensional Datasets on the GPU

Inherently multi-dimensional n-ary indexing structures such as R-trees are not well suited for the GPU because of their irregular memory access patterns and recursive back-tracking function calls. It has been known that traversing hierarchical tree structures in an irregular manner makes it difficult to exploit parallelism and to maximize the utilization of GPU processing units. Moreover, the recursive tree search algorithms often fail with large indexes because of the GPU's tiny runtime stack size. In this paper, we propose a novel parallel tree traversal algorithm-massively parallel restart scanning (MPRS) for multi-dimensional range queries that avoids recursion and irregular memory access. The proposed MPRS algorithm traverses hierarchical tree structures with mostly contiguous memory access patterns without recursion, which offers more chances to optimize the parallel SIMD algorithm. We implemented the proposed MPRS range query processing algorithm on n-ary bounding volume hierarchies including R-trees and evaluated its performance using real scientific datasets on an NVIDIA Tesla M2090 GPU. Our experiments show braided parallel SIMD friendly MPRS range query algorithm achieves at least 80 percent warp execution efficiency while task parallel tree traversal algorithm shows only 9-15 percent efficiency. Moreover, braided parallel MPRS algorithm accesses 7-20 times less amount of global memory than task parallel parent link algorithm by virtue of minimal warp divergence.

Approach for Constructing Public Key Encryption with Multi-Dimensional Range Query

Approach for Constructing Public Key Encryption with Multi-Dimensional Range Query

DGFIndex for smart grid

In Smart Grid applications, as the number of deployed electric smart meters increases, massive amounts of valuable meter data is generated and collected every day. To enable reliable data collection and make business decisions fast, high throughput storage and high-performance analysis of massive meter data become crucial for grid companies. Considering the advantage of high efficiency, fault tolerance, and price-performance of Hadoop and Hive systems, they are frequently deployed as underlying platform for big data processing. However, in real business use cases, these data analysis applications typically involve multidimensional range queries (MDRQ) as well as batch reading and statistics on the meter data. While Hive is high-performance at complex data batch reading and analysis, it lacks efficient indexing techniques for MDRQ. In this paper, we propose DGFIndex, an index structure for Hive that efficiently supports MDRQ for massive meter data. DGFIndex divides the data space into cubes using the grid file technique. Unlike the existing indexes in Hive, which stores all combinations of multiple dimensions, DGFIndex only stores the information of cubes. This leads to smaller index size and faster query processing. Furthermore, with pre-computing user-defined aggregations of each cube, DGFIndex only needs to access the boundary region for aggregation query. Our comprehensive experiments show that DGFIndex can save significant disk space in comparison with the existing indexes in Hive and the query performance with DGFIndex is 2-50 times faster than existing indexes in Hive and HadoopDB for aggregation query, 2-5 times faster than both for non-aggregation query, 2-75 times faster than scanning the whole table in different query selectivity.

Development of Cloud P2P OLAP system based on balanced quadtree

To make use of the recent distributed OLAP environment, researches on P2P (Peer-to-Peer) OLAP with the dynamic hybrid tree (DHT) and Grid OLAP are actively proposed. In addition, OLAP query execution costs many minutes by its enormous data and OLAP query properties. To adapt OLAP systems to the cloud computing environment, P2P OLAP has problems on executing multi-dimensional range queries because of P2P properties. In this paper, the central management Cloud P2P OLAP is proposed to provide an efficient cloud computing environment which query results are able to be reused with the time-series properties by various users. The Cloud P2P OLAP is grafted onto hierarchical hybrid P2P for fast query results and multi-dimensional range query, so that the index loads are distributed and the performance is improved.

Supporting multidimensional range queries in Hierarchically Distributed Tree

SummaryAn examination of the multidimensional range query in existing peer‐to‐peer (P2P) overlay networks indicates that multidimensional range queries are sensitive to underlying topologies; this is because partitioning and mapping of multidimensional data space are two interconnected parts of a process that must be carried out cooperatively. The first section focuses on how to preserve data localities, whereas the second section concerns how to accommodate and maintain data localities at the P2P overlay layer. There are many studies that have been conducted on the first section since 1966, and those works that are well accepted are mostly based on recursive decomposition, which forms a tree structure in nature. However, less effort has been made to provide comparable support from the P2P overlay layer. In our previous work, we proposed the Hierarchically Distributed Tree (HD Tree) in order to better support multidimensional range queries in the P2P overlay network. This paper further explores error‐resilient routing and load balancing strategies that can be employed in the HD Tree. We also provide a complete set of experimental results for all routing operations: Join and Leave of nodes, range queries at different levels of selectivity, and the dynamic load balancing scheme. Comparisons are made by conducting simulations under both the ideal and the error‐prone routing environment and within various ary HD Trees. The experimental results show that load balancing in the HD Tree can be adjusted dynamically and globally, and it is actually a trade‐off between distributing the basic load and the involvement of nodes in range querying. The experimental results also indicate that a maximum of 10 percent of routing nodes’ failures do not have significant effects on the performance of range queries. However, a lower ary HD Tree appears to have better routing performance, whereas a higher ary HD Tree achieves a higher fault‐tolerant capacity. Nevertheless, the performance of range queries in a higher ary HD Tree can be further optimized if all possible routing options can be fully explored in the error‐prone routing environment. Copyright © 2013 John Wiley & Sons, Ltd.

Parallel multi-dimensional range query processing with R-trees on GPU

The general purpose computing on graphics processing unit (GP-GPU) has emerged as a new cost effective parallel computing paradigm in high performance computing research that enables large amount of data to be processed in parallel. Large scale scientific data intensive applications have been playing an important role in modern high performance computing research. A common access pattern into such scientific data analysis applications is multi-dimensional range query, but not much research has been conducted on multi-dimensional range query on the GPU. Inherently multi-dimensional indexing trees such as R-Trees are not well suited for GPU environment because of its irregular tree traversal. Traversing irregular tree search path makes it hard to maximize the utilization of massively parallel architectures. In this paper, we propose a novel MPTS (Massively Parallel Three-phase Scanning) R-tree traversal algorithm for multi-dimensional range query, that converts recursive access to tree nodes into sequential access. Our extensive experimental study shows that MPTS R-tree traversal algorithm on NVIDIA Tesla M2090 GPU consistently outperforms traditional recursive R-trees search algorithm on Intel Xeon E5506 processors.

$\mathcal{MD}$ -HBase: design and implementation of an elastic data infrastructure for cloud-scale location services

The ubiquity of location enabled devices has resulted in a wide proliferation of location based applications and services. To handle the growing scale, database management systems driving such location based services (LBS) must cope with high insert rates for location updates of millions of devices, while supporting efficient real-time analysis on latest location. Traditional DBMSs, equipped with multi-dimensional index structures, can efficiently handle spatio-temporal data. However, popular open-source relational database systems are overwhelmed by the high insertion rates, real-time querying requirements, and terabytes of data that these systems must handle. On the other hand, key-value stores can effectively support large scale operation, but do not natively provide multi-attribute accesses needed to support the rich querying functionality essential for the LBSs. We present the design and implementation of $\mathcal {MD}$ -HBase, a scalable data management infrastructure for LBSs that bridges this gap between scale and functionality. Our approach leverages a multi-dimensional index structure layered over a key-value store. The underlying key-value store allows the system to sustain high insert throughput and large data volumes, while ensuring fault-tolerance, and high availability. On the other hand, the index layer allows efficient multi-dimensional query processing. Our optimized query processing technique accesses only the index and storage level entries that intersect with the query region, thus ensuring efficient query processing. We present the design of $\mathcal {MD}$ -HBase that demonstrates how two standard index structures--the K-d tree and the Quad tree--can be layered over a range partitioned key-value store to provide scalable multi-dimensional data infrastructure. Our prototype implementation using HBase, a standard open-source key-value store, can handle hundreds of thousands of inserts per second using a modest 16 node cluster, while efficiently processing multi-dimensional range queries and nearest neighbor queries in real-time with response times as low as few hundreds of milliseconds.

Secure Cooperative Data Storage and Query Processing in Unattended Tiered Sensor Networks

We consider an unattended tiered sensor network (UTSN) consisting of resource-rich master nodes at the upper tier and resource-poor sensor nodes at the lower tier. Sensor nodes submit data to nearby master nodes which store the data and answer the queries from the network owner on behalf of sensor nodes. Such a cooperative data storage and query processing paradigm offers a number of advantages over traditional Homogeneous unattended sensor networks. Relying on master nodes for data storage and query processing, however, raises severe concerns about data confidentiality and query-result correctness when the sensor network is deployed in hostile environments. In particular, a compromised master node may leak hosted sensitive data to the adversary; it may also return juggled or incomplete query results to the network owner. In this paper, we take multidimensional range queries as an example to investigate secure cooperative data storage and query processing in UTSNs. We present a suite of novel schemes that can ensure data confidentiality against master nodes and also enable the network owner to verify with very high probability the authenticity and completeness of any query result by inspecting the spatial and temporal relationships among the returned data. Detailed performance evaluations confirm the high efficacy and efficiency of the proposed schemes.

Continuous Skyline Query on Sensor Network

Data centric storages for sensor networks have been proposed to efficiently process multi-dimensional range queries as well as exact matches. Usually, a sensor network does not process only one type of the query but supports various types of queries such as range queries, exact matches and skyline queries. Therefore, a sensor network based on a data centric storage for range queries and exact matches should process skyline queries efficiently. However, existing algorithms for skyline queries have not considered the features of data centric storages. Some of the data centric storages store similar data in sensor nodes that are placed on geographically similar locations. Consequently, all data are ordered in a sensor network. In this paper, we propose a new skyline query processing algorithm that exploits the above features of data centric storages.

Skyline Query Processing in Sensor Network Based on Data Centric Storage

Data centric storages for sensor networks have been proposed to efficiently process multi-dimensional range queries as well as exact matches. Usually, a sensor network does not process only one type of the query, but processes various types of queries such as range queries, exact matches and skyline queries. Therefore, a sensor network based on a data centric storage for range queries and exact matches should process skyline queries efficiently. However, existing algorithms for skyline queries have not considered the features of data centric storages. Some of the data centric storages store similar data in sensor nodes that are placed on geographically similar locations. Consequently, all data are ordered in a sensor network. In this paper, we propose a new skyline query processing algorithm that exploits the above features of data centric storages.

Secure multidimensional range queries over outsourced data

In this paper, we study the problem of supporting multidimensional range queries on encrypted data. The problem is motivated by secure data outsourcing applications where a client may store his/her data on a remote server in encrypted form and want to execute queries using server's computational capabilities. The solution approach is to compute a secure indexing tag of the data by applying bucketization (a generic form of data partitioning) which prevents the server from learning exact values but still allows it to check if a record satisfies the query predicate. Queries are evaluated in an approximate manner where the returned set of records may contain some false positives. These records then need to be weeded out by the client which comprises the computational overhead of our scheme. We develop a bucketization procedure for answering multidimensional range queries on multidimensional data. For a given bucketization scheme, we derive cost and disclosure-risk metrics that estimate client's computational overhead and disclosure risk respectively. Given a multidimensional dataset, its bucketization is posed as an optimization problem where the goal is to minimize the risk of disclosure while keeping query cost (client's computational overhead) below a certain user-specified threshold value. We provide a tunable data bucketization algorithm that allows the data owner to control the trade-off between disclosure risk and cost. We also study the trade-off characteristics through an extensive set of experiments on real and synthetic data.

HD Tree: A novel data structure to support multi-dimensional range query for P2P networks

There are two basic concerns for supporting multi-dimensional range query in P2P overlay networks. The first is to preserve data locality in the process of data space partitioning, and the second is the maintenance of data locality among data ranges with an exponentially expanding and extending rate. The first problem has been well addressed by using recursive decomposition schemes, such as Quad-tree, K-d tree, Z -order, and Hilbert curve. On the other hand, the second problem has been recently identified by our novel data structure: HD Tree. In this paper, we explore how data locality can be easily maintained, and how range query can be efficiently supported in HD Tree. This is done by introducing two basic routing strategies: hierarchical routing and distributed routing. Although hierarchical routing can be applied to any two nodes in the P2P system, it generates high volume traffic toward nodes near the root, and has very limited options to cope with node failure. On the other hand, distributed routing concerns source and destination pairs only at the same depth, but traffic load is bound to some nodes at two neighboring depths, and multiple options can be found to redirect a routing request. Because HD Tree supports multiple routes between any two nodes in the P2P system, routing in HD Tree is very flexible; it can be designed for many purposes, like fault tolerance, or dynamic load balancing. Distributed routing oriented combined routing (DROCR) algorithm is one such routing strategy implemented so far. It is a hybrid algorithm combining advantages from both hierarchical routing and distributed routing. The experimental results show that DROCR algorithm achieves considerable performance gain over the equivalent tree routing at the highest depth examined. For supporting multi-dimensional range query, the experimental results indicate that the exponentially expanding and extending rate have been effectively controlled and minimized by HD Tree overlay structure and DROCR routing.

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.

Replica-aware, multi-dimensional range queries in Distributed Hash Tables

In this paper, we present and evaluate a protocol that enables fast and accurate range-query execution in Distributed Hash Tables (DHTs). Range queries are of particular importance when the network is populated with groups or collections of data items, whose respective identifiers are generated in a way that encodes semantic relationships into key distances. Contrary to related work in the same direction, our proposed query engine is aware of data replicas at the DHT level and by grouping related nodes into replica neighborhoods, resolves queries with the minimum amount of messaging overhead. Moreover, we suggest pairing respective operations with the core DHT routing mechanics, which allows for reusing existing management and monitoring structures and automatically adapting the query path to the dynamic characteristics of the overlay. We also present an application scenario and the respective deployment details of a prototype implementation in the context of the Gredia project.

Data storage and range query mechanism for multi-dimensional attributes in wireless sensor networks

Wireless sensor networking (WSN) is an emerging technology that enables remote monitoring on a large scale. Data-centric storage is an effective and important technique in WSNs. Its function is to store sensed events according to their attribute values by mapping them to some nodes in order to avoid routing all the values outside the network and flooding the queries. There are many attributes with range values in an event, so the sensor will need to use multi-dimensional range queries to retrieve data. The authors propose a data storage and range query method for multi-dimensional attributes in WSNs. The main idea is to map multi-dimensional events to their corresponding range spaces and build an in-network distributed data structure to efficiently gather the data of multi-dimensional range queries. The performance evaluation shows that the proposed scheme can reduce message cost and hotspot problems to achieve load balancing even when a vast number of the events and sensor nodes are present in a sensor network.

HRing: A Structured P2P Overlay Based on Harmonic Series

This paper presents Harmonic Ring (HRing), a structured peer-to-peer (P2P) overlay where long links are built along the ring with decreasing probabilities coinciding with the Harmonic Series. HRing constructs routing tables based on the distance between node positions instead of node IDs in order to eliminate the effect of node ID distribution on the long link distribution and load balance. It supports leave-and-rejoin load balance without incurring uneven long link distribution. In addition, node IDs can be any form, like number, string, address, and date, without the prerequisite of uniform distribution, so they can preserve the semantics and range locality of data objects. HRing supports multidimensional range queries. Each node is expected to have O(ln(n)) long links. The construction of O(ln(n)) long links for a node costs (O(ln(n)) messages. Routing queries achieve O(ln(n)) hops. Analyses and simulations demonstrate the efficiency of query routing and the effectiveness of the long link construction method.

Parity-based inference control for multi-dimensional range sum queries

This paper studies the inference control of multi-dimensional range (MDR) sum queries. We show that existing inference control methods are usually inefficient for MDR queries. We then consider parity-based inference control that restricts users to queries involving an even number of sensitive values. Such a restriction renders inferences significantly more difficult, because an even number is closed under addition and subtraction, whereas inferences target at one value. However, more sophisticated inferences are still possible with only even MDR queries. We show that the collection of all even MDR queries causes inferences if and only if a special collection of sum-two queries (that is, the summation of exactly two values) does so. The result leads to an inference control method with an improved computational complexity O(mn) (over the previous result of O(m 2n)) for m MDR queries over n values. We show that no odd MDR queries can be answered without causing inferences. We show how to check non-MDR queries for inferences in linear time. We also show how to find large inference-free subsets of even MDR queries when they do cause inferences.