The elimination tree for unsymmetric matrices is a recent model playing important roles in sparse LU factorization. This tree captures the dependencies between the tasks of some well-known variants of sparse LU factorization. Therefore, the height of the elimination tree corresponds to the critical path length of the task dependency graph in the corresponding parallel LU factorization methods. We investigate the problem of finding minimum height elimination trees to expose a maximum degree of parallelism by minimizing the critical path length. This problem has recently been shown to be NP-complete. Therefore, we propose heuristics, which generalize the most successful approaches used for symmetric matrices to unsymmetric ones. We test the proposed heuristics on a large set of real world matrices and report 28% reduction in the elimination tree heights with respect to a common method, which exploits the state of the art tools used in Cholesky factorization.

In a shared-nothing, distributed text retrieval system, queries are processed over an inverted index that is partitioned among a number of index servers. In practice, the index is either document-based or term-based partitioned. This choice is made depending on the properties of the underlying hardware infrastructure, query traffic distribution, and some performance and availability constraints. In query processing on retrieval systems that adopt a term-based index partitioning strategy, the high communication overhead due to the transfer of large amounts of data from the index servers forms a major performance bottleneck, deteriorating the scalability of the entire distributed retrieval system. In this work, to alleviate this problem, we propose a novel inverted index partitioning model that relies on hypergraph partitioning. In the proposed model, concurrently accessed index entries are assigned to the same index servers, based on the inverted index access patterns extracted from the past query logs. The model aims to minimize the communication overhead that will be incurred by future queries while maintaining the computational load balance among the index servers. We evaluate the performance of the proposed model through extensive experiments using a real-life text collection and a search query sample. Our results show that considerable performance gains can be achieved relative to the term-based index partitioning strategies previously proposed in literature. In most cases, however, the performance remains inferior to that attained by document-based partitioning.

Concurrently processing thousands of web queries, each with a response time under a fraction of a second, necessitates maintaining and operating massive data centers. For large-scale web search engines, this translates into high energy consumption and a huge electric bill. This work takes the challenge to reduce the electric bill of commercial web search engines operating on data centers that are geographically far apart. Based on the observation that energy prices and query workloads show high spatio-temporal variation, we propose a technique that dynamically shifts the query workload of a search engine between its data centers to reduce the electric bill. Experiments on real-life query workloads obtained from a commercial search engine show that significant financial savings can be achieved by this technique.

Query forwarding is an important technique for preserving the result quality in distributed search engines where the index is geographically partitioned over multiple search sites. The key component in query forwarding is the thresholding algorithm by which the forwarding decisions are given. In this paper, we propose a linear-programming-based thresholding algorithm that significantly outperforms the current state-of-the-art in terms of achieved search efficiency values. Moreover, we evaluate a greedy heuristic for partial index replication and investigate the impact of result cache freshness on query forwarding performance. Finally, we present some optimizations that improve the performance further, under certain conditions. We evaluate the proposed techniques by simulations over a real-life setting, using a large query log and a document collection obtained from Yahoo!.