Given a set of objects$\mathcal {O}$, each with$d$numeric attributes, atop-$k$preferencescores these objects using a linear combination of their attribute values, where the weight on each attribute reflects the interest in this attribute. Given a query preference$q$, atop-$k$queryfinds the$k$objects in$\mathcal {O}$with highest scores with respect to$q$. Given a query object$o$and a set of preferences$\mathcal {Q}$, areverse top-$k$queryfinds all preferences$q\in \mathcal {Q}$for which$o$becomes one of the top$k$objects with respect to$q$. Previous solutions to these problems are effective only in low dimensions. In this paper, we develop a solution for much higher dimensions (up to high tens), if many preferences exhibitsparsity—i.e., each specifies non-zero weights for only a handful (say$5$-$7$) of attributes (though the subsets of such attributes and their weights can vary greatly). Our idea is to select carefully a set of low-dimensionalcore subspacesto “cover” the sparse preferences in a workload. These subspaces allow us to index them more effectively than the full-dimensional space. Being multi-dimensional, each subspace covers many possible preferences; furthermore, multiple subspaces can jointly cover a preference, thereby expanding the coverage beyond each subspace’s dimensionality. Experimental evaluation validates our solution’s effectiveness and advantages over previous solutions.

Given a set of objects O, each with d numeric attributes, a top-k preference scores these objects using a linear combination of their attribute values, where the weight on each attribute reflects the interest in this attribute. Given a query preference q, a top-k query finds the k objects in O with highest scores with respect to q. Given a query object o and a set of preferences Q, a reverse top-k query finds all preferences q ∈ Q for which o becomes one of the top k objects with respect to q. Previous solutions to these problems are effective only in low dimensions. In this paper, we develop a solution for much higher dimensions (up to high tens), if many preferences exhibit sparsity-i.e., each specifies non-zero weights for only a handful (say 5-7) of attributes (though the subsets of such attributes and their weights can vary greatly). Our idea is to select carefully a set of low-dimensional core subspaces to “cover” the sparse preferences in a workload. These subspaces allow us to index them more effectively than the full-dimensional space. Being multi-dimensional, each subspace covers many possible preferences; furthermore, multiple subspaces can jointly cover a preference, thereby expanding the coverage beyond each subspace's dimensionality. Experimental evaluation validates our solution's effectiveness and advantages over previous solutions.

We consider how to support a large number of users over a wide-area network whose interests are characterised by range top-k continuous queries. Given an object update, we need to notify users whose top-k results are affected. Simple solutions include using a content-driven network to notify all users whose interest ranges contain the update (ignoring top-k), or using a server to compute only the affected queries and notifying them individually. The former solution generates too much network traffic, while the latter overwhelms the server. We present a geometric framework for the problem that allows us to describe the set of affected queries succinctly with messages that can be efficiently disseminated using content-driven networks. We give fast algorithms to reformulate each update into a set of messages whose number is provably optimal, with or without knowing all user interests. We also present extensions to our solution, including an approximate algorithm that trades off between the cost of server-side reformulation and that of user-side post-processing, as well as efficient techniques for batch updates.

Given a set of objects, each with multiple numeric attributes, a (preference) top-k query retrieves the k objects with the highest scores according to a user preference, defined as a linear combination of attribute values. We consider the problem of processing a large number of continuous top-k queries, each with its own preference. When objects or user preferences change, the query results must be updated. We present a dynamic index that supports the reverse top k query, which is of independent interest. Combining this index with another one for top-k queries, we develop a scalable solution for processing many continuous top-k queries that exploits the clusteredness in user preferences. We also define an approximate version of the problem and present a solution significantly more efficient than the exact one with little loss in accuracy.

We study the problem of assigning subscribers to brokers in a wide-area content-based publish/subscribe system. A good assignment should consider both subscriber interests in the event space and subscriber locations in the network space, and balance multiple performance criteria including bandwidth, delay, and load balance. The resulting optimization problem is NP-complete, so systems have turned to heuristics and/or simpler algorithms that ignore some performance criteria. Evaluating these approaches has been challenging because optimal solutions remain elusive for realistic problem sizes. To enable proper evaluation, we develop a Monte Carlo approximation algorithm with good theoretical properties and robustness to workload variations. To make it computationally feasible, we combine the ideas of linear programming, randomized rounding, coreset, and iterative reweighted sampling. We demonstrate how to use this algorithm as a yardstick to evaluate other algorithms, and why it is better than other choices of yardsticks. With its help, we show that a simple greedy algorithm works well for a number of workloads, including one generated from publicly available statistics on Google Groups. We hope that our algorithms are not only useful in their own right, but our principled approach toward evaluation will also be useful in future evaluation of solutions to similar problems in content-based publish/subscribe.

We study the problem of assigning subscribers to brokers in a wide-area content-based publish/subscribe system. A good assignment should consider both subscriber interests in the event space and subscriber locations in the network space, and balance multiple performance criteria including bandwidth, delay, and load balance. The resulting optimization problem is NP-complete, so systems have turned to heuristics and/or simpler algorithms that ignore some performance criteria. Evaluating these approaches has been challenging because optimal solutions remain elusive for realistic problem sizes. To enable proper evaluation, we develop a Monte Carlo approximation algorithm with good theoretical properties and robustness to workload variations. To make it computationally feasible, we combine the ideas of linear programming, randomized rounding, coreset, and iterative reweighted sampling. We demonstrate how to use this algorithm as a yardstick to evaluate other algorithms, and why it is better than other choices of yardsticks. With its help, we show that a simple greedy algorithm works well for a number of workloads, including one generated from publicly available statistics on Google Groups. We hope that our algorithms are not only useful in their own right, but our principled approach toward evaluation will also be useful in future evaluation of solutions to similar problems in content-based publish/subscribe.

We demonstrate ProSem, a scalable wide-area publish/subscribe system that supports complex, stateful subscriptions as well as simple ones. One unique feature of ProSem is its cost-based joint optimization of both subscription processing and notification dissemination. ProSem uses novel reformulation techniques to expose new alternatives for processing and disseminating data using standard stateless content-driven network components.