Ranking Functions for Size-Change Termination II

Size-Change Termination is an increasingly-popular technique for verifying program termination. These termination proofs are deduced from an abstract representation of the program in the form of "size-change graphs". We present algorithms that, for certain classes of size-change graphs, deduce a global ranking function: an expression that ranks program states, and decreases on every transition. A ranking function serves as a witness for a termination proof, and is therefore interesting for program certification. The particular form of the ranking expressions that represent SCT termination proofs sheds light on the scope of the proof method. The complexity of the expressions is also interesting, both practicaly and theoretically. While deducing ranking functions from size-change graphs has already been shown possible, the constructions in this paper are simpler and more transparent than previously known. They improve the upper bound on the size of the ranking expression from triply exponential down to singly exponential (for certain classes of instances). We claim that this result is, in some sense, optimal. To this end, we introduce a framework for lower bounds on the complexity of ranking expressions and prove exponential lower bounds.Comment: 29 pages

On the Complexity of List Ranking in the Parallel External Memory Model

We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the list, on the one hand, and its close relationship to the problem of permuting data, which is known to be hard for the external memory models, on the other hand. By carefully defining the power of the computational model, we prove a permuting lower bound in the PEM model. Furthermore, we present a stronger \Omega(log^2 N) lower bound for a special variant of the problem and for a specific range of the model parameters, which takes us a step closer toward proving a non-trivial lower bound for the list ranking problem in the bulk-synchronous parallel (BSP) and MapReduce models. Finally, we also present an algorithm that is tight for a larger range of parameters of the model than in prior work

Measuring economic complexity of countries and products: which metric to use?

Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applications, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products -- typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a Generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable

Scalable Probabilistic Similarity Ranking in Uncertain Databases (Technical Report)

This paper introduces a scalable approach for probabilistic top-k similarity ranking on uncertain vector data. Each uncertain object is represented by a set of vector instances that are assumed to be mutually-exclusive. The objective is to rank the uncertain data according to their distance to a reference object. We propose a framework that incrementally computes for each object instance and ranking position, the probability of the object falling at that ranking position. The resulting rank probability distribution can serve as input for several state-of-the-art probabilistic ranking models. Existing approaches compute this probability distribution by applying a dynamic programming approach of quadratic complexity. In this paper we theoretically as well as experimentally show that our framework reduces this to a linear-time complexity while having the same memory requirements, facilitated by incremental accessing of the uncertain vector instances in increasing order of their distance to the reference object. Furthermore, we show how the output of our method can be used to apply probabilistic top-k ranking for the objects, according to different state-of-the-art definitions. We conduct an experimental evaluation on synthetic and real data, which demonstrates the efficiency of our approach

The Blacklisting Memory Scheduler: Balancing Performance, Fairness and Complexity

In a multicore system, applications running on different cores interfere at main memory. This inter-application interference degrades overall system performance and unfairly slows down applications. Prior works have developed application-aware memory schedulers to tackle this problem. State-of-the-art application-aware memory schedulers prioritize requests of applications that are vulnerable to interference, by ranking individual applications based on their memory access characteristics and enforcing a total rank order. In this paper, we observe that state-of-the-art application-aware memory schedulers have two major shortcomings. First, such schedulers trade off hardware complexity in order to achieve high performance or fairness, since ranking applications with a total order leads to high hardware complexity. Second, ranking can unfairly slow down applications that are at the bottom of the ranking stack. To overcome these shortcomings, we propose the Blacklisting Memory Scheduler (BLISS), which achieves high system performance and fairness while incurring low hardware complexity, based on two observations. First, we find that, to mitigate interference, it is sufficient to separate applications into only two groups. Second, we show that this grouping can be efficiently performed by simply counting the number of consecutive requests served from each application. We evaluate BLISS across a wide variety of workloads/system configurations and compare its performance and hardware complexity, with five state-of-the-art memory schedulers. Our evaluations show that BLISS achieves 5% better system performance and 25% better fairness than the best-performing previous scheduler while greatly reducing critical path latency and hardware area cost of the memory scheduler (by 79% and 43%, respectively), thereby achieving a good trade-off between performance, fairness and hardware complexity

Hierarchical meta-rules for scalable meta-learning

The Pairwise Meta-Rules (PMR) method proposed in [18] has been shown to improve the predictive performances of several metalearning algorithms for the algorithm ranking problem. Given m target objects (e.g., algorithms), the training complexity of the PMR method with respect to m is quadratic: (formula presented). This is usually not a problem when m is moderate, such as when ranking 20 different learning algorithms. However, for problems with a much larger m, such as the meta-learning-based parameter ranking problem, where m can be 100+, the PMR method is less efficient. In this paper, we propose a novel method named Hierarchical Meta-Rules (HMR), which is based on the theory of orthogonal contrasts. The proposed HMR method has a linear training complexity with respect to m, providing a way of dealing with a large number of objects that the PMR method cannot handle efficiently. Our experimental results demonstrate the benefit of the new method in the context of meta-learning