Efficient Out of Core Sorting Algorithms for the Parallel Disks Model

In this paper we present efficient algorithms for sorting on the Parallel Disks Model (PDM). Numerous asymptotically optimal algorithms have been proposed in the literature. However many of these merge based algorithms have large underlying constants in the time bounds, because they suffer from the lack of read parallelism on PDM. The irregular consumption of the runs during the merge affects the read parallelism and contributes to the increased sorting time. In this paper we first introduce a novel idea called the dirty sequence accumulation that improves the read parallelism. Secondly, we show analytically that this idea can reduce the number of parallel I/O's required to sort the input close to the lower bound of [Formula: see text]. We experimentally verify our dirty sequence idea with the standard R-Way merge and show that our idea can reduce the number of parallel I/Os to sort on PDM significantly.     

Solving large FPT problems on coarse-grained parallel machines

Fixed-parameter tractability (FPT) techniques have recently been successful in solving NP-complete problem instances of practical importance which were too large to be solved with previous methods. In this paper, we show how to enhance this approach through the addition of parallelism, thereby allowing even larger problem instances to be solved in practice. More precisely, we demonstrate the potential of parallelism when applied to the bounded-tree search phase of FPT algorithms. We apply our methodology to the k-Vertex Cover problem which has important applications in, for example, the analysis of multiple sequence alignments for computational biochemistry. We have implemented our parallel FPT method for the k-Vertex Cover problem using C and the MPI communication library, and tested it on a 32-node Beowulf cluster. This is the first experimental examination of parallel FPT techniques. As part of our experiments, we solved larger instances of k-Vertex Cover than in any previously reported implementations. For example, our code can solve problem instances with k?400 in less than .     

Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions

A k-bounded pseudo-Boolean function is a real-valued function on n{0,1} that can be expressed as a sum of functions depending on at most k input bits. The k-bounded functions play an important role in a number of areas including molecular biology, biophysics, and evolutionary computation. We consider the problem of finding the Fourier coefficients of k-bounded functions, or equivalently, finding the coefficients of multilinear polynomials on n{−1,1} of degree k or less. Given a k-bounded function f with m non-zero Fourier coefficients for constant k, we present a randomized algorithm to find the Fourier coefficients of f with high probability in function evaluations. The best known upper bound was , where λ(n,m) is between and n depending on m. Our bound improves the previous bound by a factor of . It is almost tight with respect to the lower bound . In the process, we also consider the problem of finding k-bounded hypergraphs with a certain type of queries under an oracle with one-sided error. The problem is of self interest and we give an optimal algorithm for the problem.     

The Kolmogorov Expression Complexity of Logics

The purpose of the paper is to propose a completely new notion of complexity of logics in finite-model theory. It is the Kolmogorov variant of the Vardi'sexpression complexity. We define it by considering the value of the Kolmogorov complexityC(L[]) of the infinite stringL[] of all truth values of sentences ofLin . The higher is this value, the more expressive is the logicLin . If is a class of finite models, then the value ofC(L[]) over all ∈ is a measure of expressive power ofLin . Unboundedness ofC(L[])−C(L′[]) for ∈ implies nonexistence of a recursive interpretation ofLinL′. A version of this statement with complexities modulo oracles implies the nonexistence of any interpretation ofLinL′. Thus the valuesC(L[]) modulo oracles constitute an invariant of the expressive power of logics over finite models, depending on their real (absolute) expressive power, and not on the syntax. We investigate our notion for fragments of the infinitary logic ^ω_∞ω: least fixed point logic (LFP) and partial fixed point logic (PFP). We prove a precise characterization of 0–1 laws for these logics in terms of a certain boundedness condition placed onC(L[]). We get an extension of the notion of a 0–1 law by imposing an upper bound on the value ofC(L[]) growing not too fast with cardinality of , which still implies inexpressibility results similar to those implied by 0–1 laws. We also discuss classes in whichC(PFP^k[]) is very high. It appears that then PFP or its simple extension can define all the PSPACE subsets of .     

Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities

The conjecture that periodically switched stability implies absolute asymptotic stability of random infinite products of a finite set of square matrices, has recently been disproved under the guise of the finiteness conjecture. In this paper, we show that this conjecture holds in terms of Markovian probabilities. More specifically, let S_k∈C^n×n,1≤k≤K, be arbitrarily given K matrices and , where n,K≥2. Then we study the exponential stability of the following discrete-time switched dynamics S: where can be an arbitrary switching sequence.For a probability row-vector and an irreducible Markov transition matrix with , we denote by the Markovian probability on corresponding to . By using symbolic dynamics and ergodic-theoretic approaches, we show that, if S possesses the periodically switched stability then, (i) it is exponentially stable -almost surely; (ii) the set of stable switching sequences has the same Hausdorff dimension as . Thus, the periodically switched stability of a discrete-time linear switched dynamics implies that the system is exponentially stable for “almost” all switching sequences.     

A simpler linear time 2/3−ε approximation for maximum weight matching

We present two approximation algorithms for the maximum weight matching problem that run in time . We give a simple and practical randomized algorithm and a somewhat more complicated deterministic algorithm. Both algorithms are exponentially faster in terms of ε than a recent algorithm by Drake and Hougardy. We also show that our algorithms can be generalized to find a 1−ε approximation to the maximum weight matching, for any ε>0.     

Heavy-baryon spectroscopy from lattice QCD

We use a four-dimensional lattice calculation of the full-QCD (quantum chromodynamics, the non-abelian gauge theory of the strong interactions of quarks and gluons) path integrals needed to determine the masses of the charmed and bottom baryons. In the charm sector, our results are in good agreement with experiment within our systematics, except for the spin-1/2 Ξcc, for which we found the isospin-averaged mass to be Ξcc to be . We predict the mass of the (isospin-averaged) spin-1/2 Ωcc to be . In the bottom sector, our results are also in agreement with experimental observations and other lattice calculations within our statistical and systematic errors. In particular, we find the mass of the Ωb to be consistent with the recent CDF measurement. We also predict the mass for the as yet unobserved to be 5955(27) MeV.     

Polyomino coloring and complex numbers

Usually polyominoes are represented as subsets of the lattice . In this paper we study a representation of polyominoes by Gaussian integers. Polyomino is represented by the set

Then we consider functions of type from the set of all polyominoes to an abelian group G, given by , where v is prime in (N(v) is the norm of v). Using the arithmetic of the ring we find necessary and sufficient conditions for such a function to be a coloring map.     

Computing the nearest polynomial with a zero in a given domain by using piecewise rational functions

For a real univariate polynomial f and a closed complex domain D whose boundary C is a simple curve parameterized by a univariate piecewise rational function, a rigorous method is given for finding a real univariate polynomial such that has a zero in D and is minimal. First, it is proved that the minimum distance between f and polynomials having a zero at α∈C is a piecewise rational function of the real and imaginary parts of α. Thus, on C, the minimum distance is a piecewise rational function of a parameter obtained through the parameterization of C. Therefore, can be constructed by using the property that has a zero on C and computing the minimum distance on C. We analyze the asymptotic bit complexity of the method and show that it is of polynomial order in the size of the input.     

External-memory depth-first search algorithm for solid grid graphs

In this paper, we propose an external memory depth first search algorithm for solid grid graphs, a subclass of grid graphs. The I/O-complexity of the algorithm is O(sort(N)), where N=|V|+|E|, is the sorting I/O-complexity, M is the memory size, and B is the block size. Since grid graphs might be nonplanar (if diagonal edges intersect), they are beyond the reach of existing planar depth first search algorithms. The best known algorithm for this class of graph is the standard (internal memory) DFS algorithm with appropriate block (sub-grid) I/O-access. Its I/O-complexity is .     

Reconstruction of a word from a multiset of its factors

Let be the multiset containing all factors of w of length k including repetitions. One of the main results is that if for all , then w=v. The bound is optimal; however we will also show that if for all , then w and v are structurally similar.     

Full-rank representation of generalized inverse AT,S and its application

In this paper, we introduce a full-rank representation of the generalized inverse of a given complex matrix A, which is based on an arbitrary full-rank decomposition of G, where G is a matrix such that R(G)=T and N(G)=S. Using this representation, we introduce the minor of the generalized inverse ; as a special case of the minor, a determinantal representation of the generalized inverse is obtained. As an application, we use an example to demonstrate that this representation is correct.     

An iterative algorithm for solving a pair of matrix equations over generalized centro-symmetric matrices

A matrix is said to be a symmetric orthogonal matrix if . A matrix is said to be generalized centro-symmetric (generalized central anti-symmetric) with respect to P, if A=PAP (A=−PAP). The generalized centro-symmetric matrices have wide applications in information theory, linear estimate theory and numerical analysis. In this paper, we propose a new iterative algorithm to compute a generalized centro-symmetric solution of the linear matrix equations . We show, when the matrix equations are consistent over generalized centro-symmetric matrix Y, for any initial generalized centro-symmetric matrix Y₁, the sequence {Y_k} generated by the introduced algorithm converges to a generalized centro-symmetric solution of matrix equations . The least Frobenius norm generalized centro-symmetric solution can be derived when a special initial generalized centro-symmetric matrix is chosen. Furthermore, the optimal approximation generalized centro-symmetric solution to a given generalized centro-symmetric matrix can be derived. Several numerical examples are given to show the efficiency of the presented method.     

Combining OWL ontologies using -Connections

The standardization of the Web Ontology Language (OWL) leaves (at least) two crucial issues for Web-based ontologies unsatisfactorily resolved, namely how to represent and reason with multiple distinct, but linked ontologies, and how to enable effective knowledge reuse and sharing on the Semantic Web.In this paper, we present a solution for these fundamental problems based on -Connections. We aim to use -Connections to provide modelers with suitable means for developing Web ontologies in a modular way and to provide an alternative to the owl:imports construct.With such motivation, we present in this paper a syntactic and semantic extension of the Web Ontology language that covers -Connections of OWL-DL ontologies. We show how to use such an extension as an alternative to the owl:imports construct in many modeling situations. We investigate different combinations of the logics , and for which it is possible to design and implement reasoning algorithms, well-suited for optimization.Finally, we provide support for -Connections in both an ontology editor, SWOOP, and an OWL reasoner, Pellet.