A fault tolerant peer-to-peer spatial data structure

Abstract

In recent years, many layered indexing techniques over distributed hash table (DHT)-based peer-to-peer (P2P) systems have been proposed to realize distributed range search. In this paper, we present a fault tolerant constant degree dynamic Distributed Spatial Data Structure called DSDS that supports orthogonal range search on a set of N d-dimensional points published on n nodes. We describe a total order binary relation algorithm to publish points among supernodes and determine supernode keys. A non-redundant rainbow skip graph is used to coordinate message passing among nodes. The worst case orthogonal range search cost in a d-dimensional DSDS with n nodes is \(O\left (\log n+m+\frac {K}{B}\right )\) messages, where m is the number of nodes intersecting the query, K is the number of points reported in range, and B is the number of points that can fit in one message. A complete backup copy of data points stored in other nodes provides redundancy for our DSDS. This redundancy permits answering a range search query in the case of failure of a single node. For single node failure, the DSDS routing system can be recovered to a fully functional state at a cost of O(log n) messages. Backup sets in DSDS nodes are used to first process a query in the most efficient dimension, and then used to process a query containing the data in a failed node in d-dimensional space. The DSDS search algorithm can process queries in d-dimensional space and still tolerate failure of one node. Search cost in the worst case with a failed node increases to \(O\left (d\log n+dm+\frac {K}{B}\right )\) messages for d dimensions.