Range Queries in Trie-Structured Overlays

Abstract

Among the open problems in P2P systems, support for non-trivial search predicates, standardized query languages, distributed query processing, query load balancing, and quality of query results have been identified as some of the most relevant issues. This paper describes how range queries as an important non-trivial search predicate can be supported in a structured overlay network that provides O(log n) search complexity on top of a trie abstraction. We provide analytical results that show that the proposed approach is efficient, supports arbitrary granularity of ranges, and demonstrate that its algorithmic complexity in terms of messages is independent of the size of the queried ranges and only depends on the size of the result set. In contrast to other systems which provide evaluation results only through simulations, we validate the theoretical analysis of the algorithms with large-scale experiments on the PlanetLab infrastructure using a fully-fledged implementation of our approach.

Scalable distributed indexing and query processing over Linked Data

“…Since the query is split into multiple parallel queries which appear to trickle down to all the key-space partitions in the range, it is called shower algorithm. A detailed discussion of this algorithm is provided in [13]. The efficiency of P-Grid in terms of ranges queries compared to related P2P systems such as [20,21] is also shown by performance evaluation studies such as [22] where P-Grid is among the best performing systems.…”

“…There are several systems providing all three of the capabilities listed above. Meanwhile, many popular DHT systems support efficient processing of range queries, either by nature [13,14,15] or by extension [16,17,18] (if the required data semantics are not kept during hashing). Queried ranges are mapped to according key ranges and these key ranges are looked up accordingly.…”

“…Overall, our choice of P-Grid as the underlying infrastructure is well justified as P-Grid supports prefix queries as an underlying concept [19], provides efficient load balancing [3] and includes efficient support for range queries by means of its shower algorithm [13]. In this algorithm the range query is first forwarded to an arbitrary peer responsible for any of the key-space partitions within the range, and then the query is forwarded to other possible partitions recursively using the current peer's routing table.…”

“…ξ S EQ , as illustrated in the top line of Figure 3, which means contacting all nodes responsible for property <A> in sequence (|p r A | denotes the number of responsible nodes) 2. ξ RQ , as illustrated in the top line of Figure 4, which means contacting all nodes responsible for property <A> using the parallel shower algorithm [13] (as outlined in Section 3.1)…”

A Repair Mechanism for Fault-Tolerance for Tree-Structured Peer-to-Peer Systems

“…Among them, Nodewiz [4] assumes a set of static reliable nodes to host the trie, which is unfortunately hard to ensure on peer-to-peer platforms. P-Grid [7] builds a trie on the whole key-space (i.e., the whole set of potential keys). Each leaf of this trie corresponds to a subset of the key-space.…”