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In the next decade, the high-performance supercomputers will consist of several millions of CPUs. The interconnection networks in such supercomputers play an important role for achieving high performance. In this paper, we introduce the Metacube (MC), a versatile family of interconnection network that can connect an extremely large number of nodes with a small number of links per node and keep the diameter rather low. An MC network has a 2-level hypercube structure. An MC( k, m) network can connect $2^{2^{k}m+k}$ nodes with m+ k links per node, where k is the dimension of the high-level hypercubes (classes) and m is the dimension of the low-level hypercubes (clusters). An MC is a symmetric network with short diameter, easy and efficient routing and broadcasting similar to that of the hypercube. However, the MC network can connect millions of nodes with up to 6 links per node. An MC(2,3) with 5 links per node has 16,384 nodes and an MC(3,3) with 6 links per node has 134,217,728 nodes. We describe the MC network’s structure, topological properties, routing and broadcasting algorithms, and the Hamiltonian cycle embedding in the Metacube networks. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze a fast algorithm that determines the possible molecular formulae corresponding to the resolved peaks in the spectral data obtained from a mass analyzer like an FT-ICR-MS. In contrast to our approach, most known algorithms and software that attempt to solve this important problem are brute-force in nature and consequently, highly prone to combinatorial explosion when dealing with the volume of real data. We also present an object-oriented implementation of our algorithm in a general-purpose, user-friendly, interactive, and easily extensible software tool PG C ompound M atch F inder. A run-time performance analysis of our software shows that even when dealing with several billion theoretical possibilities matched against tens of thousands of resolved peaks, a complete analysis using today’s standard desktop machines can take only a few minutes. [ABSTRACT FROM AUTHOR]

According to the features of manufacturing grid (MGrid) resources, some resources should be reserved jointly to schedulers before executing a complex MGrid task. We define it as a co-reservation. In order to support co-reservation, we design a framework, a workflow, and a series of application programming interfaces of co-reservation in the MGrid system. The processing of co-reservation requests may be expensive due to a number of cell reservations, the complex relationships, and the large number of eligible resources in the MGrid system. In this paper, the processing of co-reservation requests is transferred to the subgraph isomorphism problem and an improved algorithm is introduced to solve it efficiently. Finally, we implement a prototype of co-reservation in the magnetic bearing resource and service sharing platform under MGrid. The experiment results show that the improved algorithm is effective to co-reservation. [ABSTRACT FROM AUTHOR]

An important query for spatio-temporal databases is to find nearest trajectories of moving objects. Existing work on this topic focuses on the closest trajectories in the whole data space. In this paper, we introduce and solve constrained k-nearest neighbor (C kNN) queries and historical continuous C kNN (HCC kNN) queries on R-tree-like structures storing historical information about moving object trajectories. Given a trajectory set D, a query object (point or trajectory) q, a temporal extent T, and a constrained region CR, (i) a C kNN query over trajectories retrieves from D within T, the k (≥ 1) trajectories that lie closest to q and intersect (or are enclosed by) CR; and (ii) an HCC kNN query on trajectories retrieves the constrained k nearest neighbors (C kNNs) of q at any time instance of T. We propose a suite of algorithms for processing C kNN queries and HCC kNN queries respectively, with different properties and advantages. In particular, we thoroughly investigate two types of C kNN queries, i.e., C kNNP and C kNNT, which are defined with respect to stationary query points and moving query trajectories, respectively; and two types of HCC kNN queries, namely, HCC kNNP and HCC kNNT, which are continuous counterparts of C kNNP and C kNNT, respectively. Our methods utilize an existing data-partitioning index for trajectory data (i.e., TB-tree) to achieve low I/O and CPU cost. Extensive experiments with both real and synthetic datasets demonstrate the performance of the proposed algorithms in terms of efficiency and scalability. [ABSTRACT FROM AUTHOR]

An automated general purpose method is introduced for computing a rigorous estimate of a bounded region in ℝ n whose points satisfy a given property. The method is based on calculations conducted in interval arithmetic and the constructed approximation is built of rectangular boxes of variable sizes. An efficient strategy is proposed, which makes use of parallel computations on multiple machines and refines the estimate gradually. It is proved that under certain assumptions the result of computations converges to the exact result as the precision of calculations increases. The time complexity of the algorithm is analyzed, and the effectiveness of this approach is illustrated by constructing a lower bound on the set of parameters for which an overcompensatory nonlinear Leslie population model exhibits more than one attractor, which is of interest from the biological point of view. This paper is accompanied by efficient and flexible software written in C++ whose source code is freely available at . [ABSTRACT FROM AUTHOR]

This paper considers the problem of scheduling n jobs on a single machine to minimize the total weighted completion time in the presence of sequence-dependent setup times and release times. To the best of our knowledge, little research has been devoted to this scheduling problem. Therefore, we developed two exact algorithms, including a constraint programming model and a branch-and-bound method for small problems. The obtained optimal solutions can be used as a benchmark for evaluating the performance of heuristics. With the complexity in mind, two heuristics, including a best index dispatch (BID) and a modified weighted shortest processing time (MWSPT) based on non-delay concepts are also proposed for large problems. The time complexities of the two proposed heuristics are O( n4) and O( n3), respectively. The computational results showed that the branch-and-bound method could solve most instances with 40 jobs under the time limit of 7,200 s. The BID heuristic is superior to the MWSPT in solution quality, although both can efficiently and effectively obtain near-optimal solutions for large instances. [ABSTRACT FROM AUTHOR]

In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied extensively in computer science. In particular, we demonstrate that the search for weighing matrices constructed from two circulants using the power spectral density criterion and exploiting structural patterns for the locations of the zeros in candidate solutions, can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. This allows us to bring into bear efficient algorithms from the string sorting literature. We also state and prove some new enhancements to the power spectral density criterion, that allow us to treat successfully the rounding error effect and speed up the algorithm. Finally, we use these ideas to find new weighing matrices of order 2 n and weights 2 n – 13, 2 n – 17 constructed from two circulants. [ABSTRACT FROM AUTHOR]

In this paper, the maximal abelian dimension is computationally obtained for an arbitrary finite-dimensional Lie algebra, defined by its nonzero brackets. More concretely, we describe and implement an algorithm which computes such a dimension by running it in the symbolic computation package MAPLE. Finally, we also show a computational study related to this implementation, regarding both the computing time and the memory used. [ABSTRACT FROM AUTHOR]

In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zeroth Betti number, and the Euler–Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zeroth one. As a consequence we also obtain algorithms for computing semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in singly exponential time, which improves on the complexity of the previously published algorithms for this problem. [ABSTRACT FROM AUTHOR]

Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w:E → R + a function which assigns a positive weight or length to each edge of G. G is called a realization of a finite metric space (M,d), with M = { 1,...,n} if and only if { 1,...,n} ⫅ V and d(i,j) is equal to the length of the shortest chain linking i and j in G ∀ i,j = 1,...,n. A realization G of (M,d), is said optimal if the sum of its weights is minimal among all the realizations of (M,d). Consider a partition of M into two nonempty subsets K and L, and let e be an edge in a realization G of (M,d); we say that e is a bridge linking K with L if e belongs to all chains in G linking a vertex of K with a vertex of L. The Metric Bridge Partition Problem is to determine if the elements of a finite metric space (M,d) can be partitioned into two nonempty subsets K and L such that all optimal realizations of (M,d) contain a bridge linking K with L. We prove in this paper that this problem is polynomially solvable. We also describe an algorithm that constructs an optimal realization of (M,d) from optimal realizations of (K,d|K) and (L,d|L). [ABSTRACT FROM AUTHOR]

Manual monitoring and seam tracking through welding images in real-time, by naked eye or industrial TV are experience-dependant, subjective, labor-intensive, and sometimes biased. So it is necessary to realize computer-aided seam tracking. We have developed a plasma arc welding (PAW) seam-tracking system, which senses the molten and the seam in a frame using a vision sensor, and then detects the seam deviation to adjust the work piece motion adaptively to the seam position sensed by the vision sensor with our collaborator. In this paper, we propose a novel molten pool area image-processing algorithm based on machine vision. The algorithm processes each image at a speed of 20 frames/s in real-time to extract three feature variables to get the seam deviation. It is proved experimentally that the algorithm is very fast and effective. Issues related to the algorithm are also discussed. [ABSTRACT FROM AUTHOR]

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata and McCormick (2002) with the aid of a novel technique of changing the potential by solving maximum submodular flow problems. [ABSTRACT FROM AUTHOR]

The tool switching problem is used to determine a job sequence and the tools to be loaded on a machine with the objective of minimising the total number of tool switches. In this paper, in order to develop a practical and efficient approach to solving this problem, a beam-search-based algorithm is introduced to formulate the solution space of the problem. The performance of the heuristic algorithm is compared with the heuristic developed by Bard. The proposed algorithm is then tested on some random test problems. The results show that the beam-search-based algorithm performs well in terms of computational efficiency and solution quality. [ABSTRACT FROM AUTHOR]

A CAD application tool kit interfacing with a Unigraphics (UG) system was developed for disintegrating large and complex rapid prototyping objects into smaller and simpler components which can be fabricated by a rapid prototyping system. As the core of the tool kit, the algorithm of such disintegration is described in detail in this paper. The algorithm combines the flat planar parting method and feature-based volume decomposition. Due consideration is also given to the optimisation of the surface accuracy, the build time, and the strength and number of segments generated. Based on the algorithm and the CAD application tool kit, the disintegration of two RP objects was realised in a selective laser sintering system. [ABSTRACT FROM AUTHOR]

It is a difficult task to manually cluster a large software system into loosely coupled modules with a large number of highly cohesive classes. On the other hand clustering is a NP-Hard problem. In this paper the design and implementation of a flexible software environment, called DAGC, to assemble and experiment with genetic clustering algorithms, for software (re)modularization, is described. The main idea behind the design of the DAGC is to define a general genetic clustering algorithm which may invoke different implementations for the parts from an extendable list of components. The DAGC provides visualization facilities to compare and evaluate different genetic clustering algorithms, regarding the two parameters of running time and the quality of clusters generated by the algorithms. [ABSTRACT FROM AUTHOR]

The paper is an exposition of the author's talk on the Seminar on Differential Geometry in IMPA in Rio de Janeiro. It presents a short survey of some recent results in the metric theory of polyhedra in 3-space. Namely we emphasize on some applicatons of the theorem which is a vast generalization of the Heron's formule for the area of a triangle to volumes of polyhedra. [ABSTRACT FROM AUTHOR]

In his famous book “Combinatory Analysis” MacMahon introduced Partition Analysis (“Omega Calculus”) as a computational method for solving problems in connection with linear diophantine inequalities and equations. The technique has recently been given a new life by G.E. Andrews and his coauthors, who had the idea of marrying it with the tools of to-day’s Computer Algebra. The theory consists of evaluating a certain type of rational function of the form A(λ)-1B(1/λ)-1 by the MacMahon Ω operator. So far, the case where the two polynomials A and B are factorized as products of polynomials with two terms has been studied in details. In this paper we study the case of arbitrary polynomials A and B. We obtain an algorithm for evaluating the Ω operator using the coefficients of those polynomials without knowing their roots. Since the program efficiency is a persisting problem in several-variable polynomial Calculus, we did our best to make the algorithm as fast as possible. As an application, we derive new combinatorial identities. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm for determining satisfiability of general Boolean formulas which are not necessarily in conjunctive normal form. The algorithm extends the well-known Davis–Putnam algorithm to work on Boolean formulas represented using Boolean Expression Diagrams (BEDs). The BED data structure allows the algorithm to take advantage of the built-in reduction rules and the sharing of sub-formulas. Furthermore, it is possible to combine the algorithm with traditional BDD construction (using Bryant’s Apply-procedure). By adjusting a single parameter to the BedSat algorithm, it is possible to control to what extent the algorithm behaves like the Apply-algorithm or like a SAT-solver. Thus, the algorithm can be seen as bridging the gap between standard SAT-solvers and BDDs. We present promising experimental results for 566 non-clausal formulas obtained from the multi-level combinational circuits in the ISCAS’85 benchmark suite and from performing model checking of a shift-and-add multiplier. [ABSTRACT FROM AUTHOR]