Cellular Array Morphology During Directional Solidification

Cellular array morphology has been examined in the shallow cell, deep cell, and cell-to-dendrite transition regime in Pb-2.2 wt pct Sb and Al-4.1 wt pct Cu alloy single-crystal samples that were directionally solidified along [100]. Statistical analysis of the cellular spacing distribution on transverse sections has been carried out using minimum spanning tree (MST), Voronoi polygons, radial distribution factor, and fast Fourier transform (FFT) techniques. The frequency distribution of the number of nearest neighbors and the MST parameters suggest that the arrangement of cells may be visualized as a hexagonal tessellation with superimposed 50 pct random noise. However, the power spectrum of the Fourier transform of the cell centers shows a diffused single-ring pattern that does not agree with the power spectrum from the hexagonal tessellation having a 50 pct superimposed random (uniformly distributed or Gaussian) noise. The radial distribution factor obtained from the cells is similar to that of liquids. An overall steady-state distribution in terms of the mean primary spacing is achieved after directional solidification of about three mushy-zone lengths. However, the process of nearest-neighbor interaction continues throughout directional solidification, as indicated by about 14 pct of the cells undergoing submerging in the shallow cell regime or by an increasing first and second nearest-neighbor ordering along the growth direction for the cells at the cell-to-dendrite transition. The nature of cell distribution in the Al-Cu alloy appears to be the same as that in the Pb-Sb. The ratio between the upper and lower limits of the primary spacing, as defined by the largest and the smallest 10 pct of the population, respectively, is constant: 1.43 +/- 0.11. It does not depend upon the solidification processing conditions

Engineering Branch-and-Cut Algorithms for the Equicut Problem

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application

Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems

This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches

Discrete Particle Swarm Optimization for Multiple Destination Routing Problems ⋆

Abstract. This paper proposes a discrete particle swarm optimization (DPSO) to solve the multiple destination routing (MDR) problems. The problem has been proven to be NP-complete and the traditional heuristics (e.g., the SPH, DNH and ADH) are inefficient in solving it. The particle swarm optimization (PSO) is an efficient global search algorithm and is promising in dealing with complex problems. This paper extends the PSO to a discrete PSO and uses the DPSO to solve the MDR problem. The global search ability and fast convergence ability of the DPSO make it efficient to the problem. Experiments based on the benchmarks from the OR-library show that the DPSO obtains better results when compared with traditional heuristic algorithms, and also outperforms the GA-based algorithm with faster convergence speed

Conclusion

Abstract. History independent data structures, presented by Micciancio, are data structures that possess a strong security property: even if an intruder manages to get a copy of the data structure, the memory layout of the structure yields no additional information on the data structure beyond its content. In particular, the history of operations applied on the structure is not visible in its memory layout. Naor and Teague proposed a stronger notion of history independence in which the intruder may break into the system several times without being noticed and still obtain no additional information from reading the memory layout of the data structure. An open question posed by Naor and Teague is whether these two notions are equally hard to obtain. In this paper we provide a separation between the two requirements for comparison based algorithms. We show very strong lower bounds for obtaining the stronger notion of history independence for a large class of data structures, including, for example, the heap and the queue abstract data structures. We also provide complementary upper bounds showing that the heap abstract data structure may be made weakly history independent in the comparison based model without incurring any additional (asymptotic) cost on any of its operations. (A similar result is easy for the queue.) Thus, we obtain the first separation between the two notions of history independence. The gap we obtain is exponential: some operations may be executed in logarithmic time (or even in constant time) with the weaker definition, but require linear time with the stronger definition