Upper Bound Approximations for BlockMaxWand

BlockMaxWand is a recent advance on the Wand dynamic pruning technique, which allows efficient retrieval without any effectiveness degradation to rank K. However, while BMW uses docid-sorted indices, it relies on recording the upper bound of the term weighting model scores for each block of postings in the inverted index. Such a requirement can be disadvantageous in situations such as when an index must be updated. In this work, we examine the appropriateness of upper-bound approximation – which have previously been shown suitable for Wand– in providing efficient retrieval for BMW. Experiments on the ClueWeb12 category B13 corpus using 5000 queries from a real search engine’s query log demonstrate that BMW still provides benefits w.r.t. Wand when approximate upper bounds are used, and that, if approximations on upper bounds are tight, BMW with approximate upper bounds can provide efficiency gains w.r.t.Wand with exact upper bounds, in particular for queries of short to medium length

Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Our method employs a branch and bound strategy with novel and aggressive pruning techniques. For instance, we use the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space. In addition, we parallelize the exploration of the search tree. During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes. We apply the algorithm to two problems: to compute temporal strong components and to compress graphs.Comment: 11 page

Efficient & Effective Selective Query Rewriting with Efficiency Predictions

To enhance effectiveness, a user's query can be rewritten internally by the search engine in many ways, for example by applying proximity, or by expanding the query with related terms. However, approaches that benefit effectiveness often have a negative impact on efficiency, which has impacts upon the user satisfaction, if the query is excessively slow. In this paper, we propose a novel framework for using the predicted execution time of various query rewritings to select between alternatives on a per-query basis, in a manner that ensures both effectiveness and efficiency. In particular, we propose the prediction of the execution time of ephemeral (e.g., proximity) posting lists generated from uni-gram inverted index posting lists, which are used in establishing the permissible query rewriting alternatives that may execute in the allowed time. Experiments examining both the effectiveness and efficiency of the proposed approach demonstrate that a 49% decrease in mean response time (and 62% decrease in 95th-percentile response time) can be attained without significantly hindering the effectiveness of the search engine

Parallelized reliability estimation of reconfigurable computer networks

A parallelized system, ASSURE, for computing the reliability of embedded avionics flight control systems which are able to reconfigure themselves in the event of failure is described. ASSURE accepts a grammar that describes a reliability semi-Markov state-space. From this it creates a parallel program that simultaneously generates and analyzes the state-space, placing upper and lower bounds on the probability of system failure. ASSURE is implemented on a 32-node Intel iPSC/860, and has achieved high processor efficiencies on real problems. Through a combination of improved algorithms, exploitation of parallelism, and use of an advanced microprocessor architecture, ASSURE has reduced the execution time on substantial problems by a factor of one thousand over previous workstation implementations. Furthermore, ASSURE's parallel execution rate on the iPSC/860 is an order of magnitude faster than its serial execution rate on a Cray-2 supercomputer. While dynamic load balancing is necessary for ASSURE's good performance, it is needed only infrequently; the particular method of load balancing used does not substantially affect performance

Faster Algorithms for Rectangular Matrix Multiplication

Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous record \alpha>0.29462 by Coppersmith (Journal of Complexity, 1997). More generally, we construct a new algorithm for multiplying an n x n^k matrix by an n^k x n matrix, for any value k\neq 1. The complexity of this algorithm is better than all known algorithms for rectangular matrix multiplication. In the case of square matrix multiplication (i.e., for k=1), we recover exactly the complexity of the algorithm by Coppersmith and Winograd (Journal of Symbolic Computation, 1990). These new upper bounds can be used to improve the time complexity of several known algorithms that rely on rectangular matrix multiplication. For example, we directly obtain a O(n^{2.5302})-time algorithm for the all-pairs shortest paths problem over directed graphs with small integer weights, improving over the O(n^{2.575})-time algorithm by Zwick (JACM 2002), and also improve the time complexity of sparse square matrix multiplication.Comment: 37 pages; v2: some additions in the acknowledgment