Distributed frameworks are gaining increasingly widespread use in applications that process large amounts of data. One important example application is large scale similarity search, for which Locality Sensitive Hashing (LSH) has emerged as the method of choice, specially when the data is high-dimensional. At its core, LSH is based on hashing the data points to a number of buckets such that similar points are more likely to map to the same buckets. To guarantee high search quality, the LSH scheme needs a rather large number of hash tables. This entails a large space requirement, and in the distributed setting, with each query requiring a network call per hash bucket look up, this also entails a big network load. The Entropy LSH scheme proposed by Panigrahy significantly reduces the number of required hash tables by looking up a number of query offsets in addition to the query itself. While this improves the LSH space requirement, it does not help with (and in fact worsens) the search network efficiency, as now each query offset requires a network call. In this paper, focusing on the Euclidian space under @math norm and building up on Entropy LSH, we propose the distributed Layered LSH scheme, and prove that it exponentially decreases the network cost, while maintaining a good load balance between different machines. Our experiments also verify that our scheme results in a significant network traffic reduction that brings about large runtime improvement in real world applications.
@cite_22: In this paper we consider distributed K-Nearest Neighbor (KNN) search and range query processing in high dimensional data. Our approach is based on Locality Sensitive Hashing (LSH) which has proven very efficient in answering KNN queries in centralized settings. We consider mappings from the multi-dimensional LSH bucket space to the linearly ordered set of peers that jointly maintain the indexed data and derive requirements to achieve high quality search results and limit the number of network accesses. We put forward two such mappings that come with these salient properties: being locality preserving so that buckets likely to hold similar data are stored on the same or neighboring peers and having a predictable output distribution to ensure fair load balancing. We show how to leverage the linearly aligned data for efficient KNN search and how to efficiently process range queries which is, to the best of our knowledge, not possible in existing LSH schemes. We show by comprehensive performance evaluations using real world data that our approach brings major performance and accuracy gains compared to state-of-the-art.
@cite_22 describe the Sum and Cauchy schemes which map LSH buckets to peers in p2p networks in order to minimize network costs. However, in contrast to Layered LSH, no guarantees on network cost and load balance are provided. In this paper, we show via MapReduce experiments on the Wiki data set that Sum distributes data unevenly and thus may load some of the reduce tasks. In addition we also describe experiments which demonstrate that Layered LSH compares favorably with Cauchy on this data set.