Efficient Bundle Sorting

AMS subject classification. 68W01 DOI. 10.1137/S0097539704446554Many data sets to be sorted consist of a limited number of distinct keys. Sorting such data sets can be thought of as bundling together identical keys and having the bundles placed in order; we therefore denote this as bundle sorting. We describe an efficient algorithm for bundle sorting in external memory, which requires at most c(N/B) logM/B k disk accesses, where N is the number of keys, M is the size of internal memory, k is the number of distinct keys, B is the transfer block size, and 2 < c < 4. For moderately sized k, this bound circumvents the Θ((N/B) logM/B(N/B)) I/O lower bound known for general sorting. We show that our algorithm is optimal by proving a matching lower bound for bundle sorting. The improved running time of bundle sorting over general sorting can be significant in practice, as demonstrated by experimentation. An important feature of the new algorithm is that it is executed “in-place,” requiring no additional disk space

Efficient Bundle Sorting

This is the published version. Copyright © 2006 Society for Industrial and Applied MathematicsMany data sets to be sorted consist of a limited number of distinct keys. Sorting such data sets can be thought of as bundling together identical keys and having the bundles placed in order; we therefore denote this as bundle sorting. We describe an efficient algorithm for bundle sorting in external memory, which requires at most c(N/B) logM/Bk disk accesses, where N is the number of keys, M is the size of internal memory, k is the number of distinct keys, B is the transfer block size, and 2 < c < 4. For moderately sized k, this bound circumvents the Theta((N/B) logM/B (N/B)) I/O lower bound known for general sorting. We show that our algorithm is optimal by proving a matching lower bound for bundle sorting. The improved running time of bundle sorting over general sorting can be significant in practice, as demonstrated by experimentation. An important feature of the new algorithm is that it is executed "in-place," requiring no additional disk space

The Mobility Case for Regionalism

In the discourse of local government law, the idea that a mobile populace can “vote with its feet” has long served as a justification for devolution and decentralization. Tracing to Charles Tiebout’s seminal work in public finance, the legal-structural prescription that follows is that a diversity of independent and empowered local governments can best satisfy the varied preferences of residents metaphorically shopping for bundles of public services, regulatory environment, and tax burden. This localist paradigm generally presumes that fragmented governments are competing for residents within a given metropolitan area. Contemporary patterns of mobility, however, call into question this foundational assumption. People today move between — and not just within — metropolitan regions, domestically and even internationally. This is particularly so for a subset of residents — high human-capital knowledge workers and the so-called “creative class” — that is prominently coveted in this interregional competition. These modern mobile residents tend to evaluate the policy bundles that drive their locational decisions on a regional scale, weighing the comparative merits of metropolitan areas against each other. And local governments are increasingly recognizing that they need to work together at a regional scale to compete for these residents.This Article argues that this intermetropolitan mobility provides a novel justification for regionalism that counterbalances the strong localist tendency of the traditional Tieboutian view of local governance. Contrary to the predominant assumption in the legal literature, competition for mobile residents is as much an argument for regionalism as it has been for devolution and decentralization. In an era of global cities vying for talent, the mobility case for regionalism has significant doctrinal consequences for debates in local government law and public finance, including the scope of local authority, the nature of regional equity, and the structure of metropolitan collaboration

Training linear ranking SVMs in linearithmic time using red-black trees

We introduce an efficient method for training the linear ranking support vector machine. The method combines cutting plane optimization with red-black tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time complexity, where m is the number of training examples, and s the average number of non-zero features per example. Best previously known training algorithms achieve the same efficiency only for restricted special cases, whereas the proposed approach allows any real valued utility scores in the training data. Experiments demonstrate the superior scalability of the proposed approach, when compared to the fastest existing RankSVM implementations.Comment: 20 pages, 4 figure

The Mobility Case for Regionalism

In the discourse of local government law, the idea that a mobile populace can “vote with its feet” has long served as a justification for devolution and decentralization. Tracing to Charles Tiebout’s seminal work in public finance, the legal-structural prescription that follows is that a diversity of independent and empowered local governments can best satisfy the varied preferences of residents metaphorically shopping for bundles of public services, regulatory environment, and tax burden. This localist paradigm generally presumes that fragmented governments are competing for residents within a given metropolitan area. Contemporary patterns of mobility, however, call into question this foundational assumption. People today move between — and not just within — metropolitan regions, domestically and even internationally. This is particularly so for a subset of residents — high human-capital knowledge workers and the so-called “creative class” — that is prominently coveted in this interregional competition. These modern mobile residents tend to evaluate the policy bundles that drive their locational decisions on a regional scale, weighing the comparative merits of metropolitan areas against each other. And local governments are increasingly recognizing that they need to work together at a regional scale to compete for these residents.This Article argues that this intermetropolitan mobility provides a novel justification for regionalism that counterbalances the strong localist tendency of the traditional Tieboutian view of local governance. Contrary to the predominant assumption in the legal literature, competition for mobile residents is as much an argument for regionalism as it has been for devolution and decentralization. In an era of global cities vying for talent, the mobility case for regionalism has significant doctrinal consequences for debates in local government law and public finance, including the scope of local authority, the nature of regional equity, and the structure of metropolitan collaboration

A heuristic approach for the allocation of resources in large-scale computing infrastructures

An increasing number of enterprise applications are intensive in their consumption of IT, but are infrequently used. Consequently, organizations either host an oversized IT infrastructure or they are incapable of realizing the benefits of new applications. A solution to the challenge is provided by the large-scale computing infrastructures of Clouds and Grids which allow resources to be shared. A major challenge is the development of mechanisms that allow efficient sharing of IT resources. Market mechanisms are promising, but there is a lack of research in scalable market mechanisms. We extend the Multi-Attribute Combinatorial Exchange mechanism with greedy heuristics to address the scalability challenge. The evaluation shows a trade-off between efficiency and scalability. There is no statistical evidence for an influence on the incentive properties of the market mechanism. This is an encouraging result as theory predicts heuristics to ruin the mechanism’s incentive properties. Copyright © 2015 John Wiley & Sons, Ltd