Abstract The computational cost of transfer matrix methods for the Potts model is related to the question in how many ways can two layers of a lattice be connected? Answering the question leads to the generation of a combinatorial set of lattice configurations. This set defines the configuration space of the problem, and the smaller it is, the faster the transfer matrix can be computed. The configuration space of generic ( q , v ) transfer matrix methods for strips is in the order of the Catalan numbers, which grows asymptotically as O ( 4 m ) where m is the width of the strip. Other transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the structure of the lattice. In this paper we propose a parallel algorithm that uses a sub-Catalan configuration space of O ( 3 m ) to build the generic ( q , v ) transfer matrix in a compressed form. The improvement is achieved by grouping the original set of Catalan configurations into a forest of family trees, in such a way that the solution to the problem is now computed by solving the root node of each family. As a result, the algorithm becomes exponentially faster than the Catalan approach while still highly parallel. The resulting matrix is stored in a compressed form using O ( 3 m × 4 m ) of space, making numerical evaluation and decompression to be faster than evaluating the matrix in its O ( 4 m × 4 m ) uncompressed form. Experimental results for different sizes of strip lattices show that the parallel family trees (PFT) strategy indeed runs exponentially faster than the Catalan Parallel Method (CPM) , especially when dealing with dense transfer matrices. In terms of parallel performance, we report strong-scaling speedups of up to 5.7 × when running on an 8-core shared memory machine and 28 × for a 32-core cluster. The best balance of speedup and efficiency for the multi-core machine was achieved when using p = 4 processors, while for the cluster scenario it was in the range p ∈ [ 8 , 10 ] . Because of the parallel capabilities of the algorithm, a large-scale execution of the parallel family trees strategy in a supercomputer could contribute to the study of wider strip lattices.
In this subsection we compare the (PFT) strategy against the (CPM) @cite_28 by using the following metrics: (1) running time (2) matrix evaluation time and (3) matrix space. Figure shows the results. and the .
@cite_28
2269992556 2172261094 2534596111 2608928574
We study digital-goods auctions for items in unlimited supply introduced by Goldberg, Hartline and Wright. Since no deterministic algorithms are competitive for this class of auctions, one of the central research issues is how to obtain a nice probabilistic distribution over truthful algorithms. In this paper, we introduce a rather systematic approach to this goal: Consider for example the Sampling Cost Share (SCS) auction. It is well known that SCS works well if the the current bid vector produces many winners against F(2), the standard benchmark algorithm for competitive analysis. In fact, its competitive ratio is approaching to 2.0 as k (= the number of F(2) winners) grows. On the other hand, its competitive ratio becomes as bad as 4.0 for k = 2. Our new approach is to develop a sequence of similar cost-share type algorithms, DCSk, which work well for small k. Now we choose a sufficiently large constant N and run DCS1, DCS2, ..., DCSN and SCS with probabilities p1, p2, ..., pN and q, respectively. It should be noted that we can use LP to obtain optimal p1, p2,..., pN and q. By this averaging method, we can improve the competitive ratio of SCS from 4.0 to 3.531 and that of the currently best Aggregated γ3 algorithm due to Hartline and McGrew from 3.243 to 3.119. We present an any-time concurrent probabilistic temporal planner (CPTP) that includes continuous and discrete uncertainties and metric functions. Rather than relying on dynamic programming our approach builds on methods from stochastic local policy search. That is, we optimise a parameterised policy using gradient ascent. The flexibility of this policy-gradient approach, combined with its low memory use, the use of function approximation methods and factorisation of the policy, allow us to tackle complex domains. This factored policy gradient (FPG) planner can optimise steps to goal, the probability of success, or attempt a combination of both. We compare the FPG planner to other planners on CPTP domains, and on simpler but better studied non-concurrent non-temporal probabilistic planning (PP) domains. We present FPG-ipc, the PP version of the planner which has been successful in the probabilistic track of the fifth international planning competition. In this paper we introduce a response time analysis technique for Synchronous Data Flow programs mapped to multiple parallel dependent tasks running on a compute cluster of the Kalray MPPA-256 many-core processor. The analysis we derive computes a set of response times and release dates that respect the constraints in the task dependency graph. We extend the Multicore Response Time Analysis (MRTA) framework by deriving a mathematical model of the multi-level bus arbitration policy used by the MPPA. Further, we refine the analysis to account for the release dates and response times of co-runners, and the use of memory banks. Further improvements to the precision of the analysis were achieved by splitting each task into two sequential phases, with the majority of the memory accesses in the first phase, and a small number of writes in the second phase. Our experimental evaluation focused on an avionics case study. Using measurements from the Kalray MPPA-256 as a basis, we show that the new analysis leads to response times that are a factor of 4.15 smaller for this application, than the default approach of assuming worst-case interference on each memory access. Optimizing multivariate performance measure is an important task in Machine Learning. Joachims (2005) introduced a Support Vector Method whose underlying optimization problem is commonly solved by cutting plane methods (CPMs) such as SVM-Perf and BMRM. It can be shown that CPMs converge to an e accurate solution in O(1 λe) iterations, where λ is the trade-off parameter between the regularizer and the loss function. Motivated by the impressive convergence rate of CPM on a number of practical problems, it was conjectured that these rates can be further improved. We disprove this conjecture in this paper by constructing counter examples. However, surprisingly, we further discover that these problems are not inherently hard, and we develop a novel smoothing strategy, which in conjunction with Nesterov's accelerated gradient method, can find an e accurate solution in O* (min 1 e, 1 √λe ) iterations. Computationally, our smoothing technique is also particularly advantageous for optimizing multivariate performance scores such as precision recall break-even point and ROCArea; the cost per iteration remains the same as that of CPMs. Empirical evaluation on some of the largest publicly available data sets shows that our method converges significantly faster than CPMs without sacrificing generalization ability.