205001001
The Towers of Hanoi Problem with Parallel Moves
Abstract This paper proposes a variant of the towers of Hanoi problem allowing parallel moves. An algorithm for this problem is presented and proved to be optimal.
33647867
Manipulating multiple stacks with ordered-heap
Abstract A new method for manipulating multiple stacks based on dynamic data structure is proposed in this paper. A simple data structure called ordered-heap is developed, in which nodes are preserved as a heap, and kept inorder traversal sequence remains unchanged. By employing ordered-heap to a multiple-stacks environment, it is easy and efficient to simultaneously handle several variable-size stacks in a sequential memory area. Our experiments show that not only the total number of item movements in the proposed method is much smaller than in the previous methods, but also the overhead for maintaining data structure in the proposed method is kept within a reasonable range.
412842
Location problems with costs being sums of powers of euclidean distances
The Cooper problem of minimizing the sum of weighted powers of the Euclidean distances is further studied. The practical significance of this problem is that instead of the Weber problem where the weighted sum of the Euclidean distances is minimized, here economies and diseconomies of scale are allowed for, which results in a problem of minimizing the sum of weighted powers of the Euclidean distances. The original Cooper solution has been a modification of the Weiszfeld method for the Weber problem; it can be shown to be a steepest descent method with a step size determined by an expression depending on the weights and distances, which is not optimal in any sense. In the present work, the matter of the best step size to be taken is investigated. It is shown that multiplying the step size given by Cooper by 2n where n is the power of the Euclidean distances, improves the iterative process substantially. For the cases with n≥l considered by Cooper, namely 1≤n≤3, the number of steps needed to reach a certain termination criterion is reduced. For higher values of n, the original Cooper step size is usually too large and there is no convergence. With the present amended method, the problem can be solved, using an appropriate normalization, even for powers of 100 and more. A semi-intuitive proof for this step size is given as well as numerical examples of solutions with n = 1,10 and 100. The method can easily be extended to location problems in three (and more) dimensions.
5664320
MCM interconnect design using two-pole approximation
In this paper, an optimization scheme is proposed for interconnect design with wire width and series resistance being design variables. Due to the distributed nature of interconnects, poles of such systems are transcendental and infinite in number. First, a two-pole approximation is used to capture the system behavior. Lower-order moments are employed to obtain two approximate dominant poles. Then, the two parameters, damping ratio and natural undamped frequency, are expressed as functions of the two dominant poles. Since the output response is characterized by the two parameters, the parameters are used to define the objective function and constraints, which form a constrained multivariable nonlinear optimization problem. After that, the optimization problem is solved using the gradient projection method. One advantage of our approach is the ability to explicitly control the maximum overshoot of the observation points. Two numerical examples are given.
18768668
Phylophenetic properties of metabolic pathway topologies as revealed by global analysis
BackgroundAs phenotypic features derived from heritable characters, the topologies of metabolic pathways contain both phylogenetic and phenetic components. In the post-genomic era, it is possible to measure the "phylophenetic" contents of different pathways topologies from a global perspective.ResultsWe reconstructed phylophenetic trees for all available metabolic pathways based on topological similarities, and compared them to the corresponding 16S rRNA-based trees. Similarity values for each pair of trees ranged from 0.044 to 0.297. Using the quartet method, single pathways trees were merged into a comprehensive tree containing information from a large part of the entire metabolic networks. This tree showed considerably higher similarity (0.386) to the corresponding 16S rRNA-based tree than any tree based on a single pathway, but was, on the other hand, sufficiently distinct to preserve unique phylogenetic information not reflected by the 16S rRNA tree.ConclusionWe observed that the topology of different metabolic pathways provided different phylogenetic and phenetic information, depicting the compromise between phylogenetic information and varying evolutionary pressures forming metabolic pathway topologies in different organisms. The phylogenetic information content of the comprehensive tree is substantially higher than that of any tree based on a single pathway, which also gave clues to constraints working on the topology of the global metabolic networks, information that is only partly reflected by the topologies of individual metabolic pathways.
681079
Coronoid Systems with Perfect Matchings
Abstract A hexagonal system is a finite 2-connected plane graph in which every interior face is bounded by a regular hexagon. A coronoid system is obtained from a hexagonal system by deleting some interior vertices and/or interior edges such that a unique interior face which is bounded by a polygon with more than six edges emerges, and each edge on the outer perimeter belongs to a hexagon. In this paper, a necessary and sufficient condition is given for a coronoid system to have perfect matchings. Moreover, a criterion is established for those coronoid systems with perfect matchings that possess some edges which do not belong to any perfect matching.
41515158
Error resilience for block loss with overlapped motion compensation
A new error resilience algorithm for recovering the lost blocks or motion vectors is presented. It combines the overlapped motion compensation and the side match criterion to make the effect of lost blocks subjectively imperceptible. The side match criterion takes advantage of the spatial contiguity and interpixel correlation of image to select the best-fit replacement among the motion vectors of spatially contiguous candidate blocks. Particularly, to mask the blocking artifacts, we incorporate an overlapping technique to create a subjectively closer approximation to the true error-free image.