Receiver-oriented design of Bloom filters for data-centric routing

Abstract

Bloom filter (BF) is a space-efficient data structure that represents a large set of items and supports efficient membership queries. It has been widely proposed to employ Bloom filters in the routing entries so as to facilitate data-centric routing in network applications. The existing designs of Bloom filters, however, cannot effectively support in-network queries. Given a query for a data item at a node in the network, the noise in unrelated routing entries very likely equals to the useful information of the item in the right routing entries. Consequently, the majority of queries are routed towards many wrong nodes besides those destinations, wasting large quantities of network traffic. To address this issue, we classified the existing designs as CUBF (Cumulative Bloom filters) and ABF (Aggregated Bloom filters), and then evaluate their performance in routing queries under the noisy environments. Based on the evaluation results, we propose a receiver-oriented design of Bloom filters to sufficiently restrict the probability of a wrong routing decision. Moreover, we significantly decrease the delay of a routing decision in the case of CUBF by using the bit slice approach, and reduce the transmission size of each BF in the case of ABF by using the compression approach. Both the theoretical analysis and experimental results demonstrate that our receiver-oriented design of Bloom filters apparently outperforms the existing approaches in terms of the success probability of routing and network traffic cost.

Introduction

Bloom filter (BF) [1] is a space-efficient data structure that represents a large set of items and supports efficient membership queries. BF outperforms other data structures such as binary search trees and tries, as the time needed to insert an item or check whether an item belongs to the filtering set is constant, irrespective of the cardinality of the set. Hence BF has been widely adopted in database and networking applications [1], [2], such as web cache sharing [3] and routing [4], [5], [6]. Moreover, BF has great potential in memory management, such as summarizing streaming data in memory [7], storing the states of a large number of flows in the on-chip memory of the routers [8], and speeding up the Bayesian filters [9].

The space efficiency of BF, however, is achieved at the cost of false positive judgments. False positive judgment is a unnegligible drawback of BF, which refers to the case that an item does not belong to a set but the BF makes the contrary judgment. In many applications, the savings in storage and computational costs brought by BF outweigh such a drawback, on condition that the false positive probability is sufficiently low. Many efforts have been made to reduce the probability of false positive in stand-alone and distributed systems [10], [11], [12], [13] during the past years.

In the last few years, it has been proposed to employ BF in supporting data-centric routing in overlay networks [4], [5], [14], [15], [16], wireless sensor networks [17], ad hoc networks [18], [19], and mesh networks [20]. The common idea of those proposals is that every node uses a BF to represent the information of all its data items and broadcasts the BF to the nodes in its propagation range, i.e. the nodes within d hops from the node. Correspondingly, a node receives a number of BFs via each link of it. The link, associated with the BFs received via it or the union of them, is then maintained as a routing entry. The union of BFs is defined as the logic or operation among their bit vectors [21]. For any intermediate node routing a query, it forwards the query through the link whose corresponding routing entry satisfies the query. Ideally, a query will be propelled towards its destination once it enters the propagation range of the destination. For example, a query at node E for a data item at node A is routed to the right destination node along a single path $E\to C\to B\to A$, as shown in Fig. 1a.

False positive judgments exist in data-centric routing with BFs. The necessary condition for the BF-based routing schemes outperforming the blind routing schemes is that the false positive probability in the routing entries is sufficiently low. Otherwise, given any query for a data item x at a node in the network, the noise in unrelated routing entries very likely equals to the useful information of the item in the right routing entries. The noise in a unrelated routing entry is defined as the amount of membership information of x in it, if the node does not receive a BF from the destination of x via the corresponding link. Being misled, the majority of queries are routed towards many wrong nodes besides the right destinations, and result in huge amount of redundant but useless queries in the network. For example, a query at node E for a data item at node A is routed to both the right destination node and other two nodes G and H which do not hold the desired data item, as shown in Fig. 1b. The network in turn presents poor efficiency of query processing and suffers scalability problem.

In this paper, we reveal through theoretical analysis that the existing designs of BF cannot satisfy the aforementioned necessary condition. Specifically, we classified the existing BF-based routing schemes as CUBF (Cumulative Bloom filters) and ABF (Aggregated Bloom filters), and then evaluate their performance in routing queries under the noisy environments. Based on the evaluation results, we propose a receiver-oriented design of Bloom filters, with which the false positive probability of any routing entry is low enough so that a node can correctly distinguish the right out-going link from the others. We further conduct extensive simulations to evaluate the performance of the proposed scheme. Both the theoretical analysis and experimental results demonstrate that our receiver-oriented design of BF apparently outperforms the existing designs in terms of success probability of routing and network traffic cost, as shown in Fig. 1.

The rest of this paper is organized as follows. In Section 2, we briefly introduce BF and its traditional design. In Section 3, we summarize the state-of-arts designs of BF-based data-centric routing schemes, and then propose the receiver-oriented design of BF. In Section 4, we further optimize the transmission and storage strategies of BF, and present our study on how to ensure that the false positive probability of any routing entry does not exceed an upper bound in practice. Section 5 presents the performance evaluation results. We concludes this work in Section 6.