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The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of nonlinear constant/variable-order space-fractional problems on one- and two-dimensional rectangular domains. A fast approximation algorithm is developed to deal with the variable-order spectral fractional Laplacian by approximating the variable-indexing Fourier modes, and then combined with saddle dynamics to construct the solution landscape of variable-order space-fractional phase field model. Numerical experiments are performed to substantiate the accuracy and efficiency of fast approximation algorithm and elucidate essential features of the stationary solutions of space-fractional phase field model. Furthermore, we demonstrate that the solution landscapes of spectral fractional Laplacian problems can be reconfigured by varying the diffusion coefficients in the corresponding integer-order problems. • A fast approximation algorithm for variable-order spectral fractional Laplacian. • Construction of solution landscapes of space-fractional phase field models. • Reconfiguration of fractional Laplacian problems by integer-order problems. [ABSTRACT FROM AUTHOR]

In this paper we establish an algorithmic framework between bin packing and strip packing, with which strip packing can be very well approximated by applying some bin packing algorithms. More precisely we obtain the following results: (1) Any off-line bin packing algorithm can be applied to strip packing maintaining almost the same asymptotic worst-case ratio. (2) A class of Harmonic-based algorithms for bin packing, such as Refined Harmonic, Modified Harmonic, Harmonic++, can be applied to online strip packing. In particular, we show that online strip packing admits an upper bound of 1.58889 + ϵ on the asymptotic competitive ratio, for any arbitrarily small ϵ > 0 . This significantly improves the previously best bound of 1.6910 and affirmatively answers an open question posed by Csirik and Woeginger (1997). Moreover, the time complexity mainly depends on a sorting procedure and the bin packing algorithms employed. [ABSTRACT FROM AUTHOR]

This article presents a fast solver for the dense “frontal” matrices that arise from the multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that these matrices can be efficiently represented as a hierarchically off-diagonal low-rank (HODLR) matrix. To construct the low-rank approximation of the off-diagonal blocks, we propose a new pseudo-skeleton scheme, the boundary distance low-rank approximation, that picks rows and columns based on the location of their corresponding vertices in the sparse matrix graph. We compare this new low-rank approximation method to the adaptive cross approximation (ACA) algorithm and show that it achieves better speedup specially for unstructured meshes. Using the HODLR direct solver as a preconditioner (with a low tolerance) to the GMRES iterative scheme, we can reach machine accuracy much faster than a conventional LU solver. Numerical benchmarks are provided for frontal matrices arising from 3D finite element problems corresponding to a wide range of applications. [ABSTRACT FROM AUTHOR]

Peer-to-Peer systems have been introduced as an alternative to the traditional client–server scheme. Distributed Hash Tables, a type of structured Peer-to-Peer system, have been designed for massive storage purposes. In this work we model the behavior of a DHT based system, Cassandra, with focus on its fault tolerance capabilities, and more specifically, on its availability when facing two different situations: (1) transient failures, those in which a node goes off-line for a while and returns on-line maintaining its data, and (2) memory-less failures, those in which a node goes off-line and returns with no data. First, we introduce two analytical models (one for each scenario) that provide approximations to the behavior of Cassandra under different configurations, and secondly, in order to validate our models, we complete a set of experiments over a real Cassandra cluster. Experimental results confirm the validity of the proposed models of the availability of Cassandra. We also provide some examples of how these models can be used to optimize the availability configuration of Cassandra-based applications. [ABSTRACT FROM AUTHOR]

We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously proposed algorithms do not consider the possibly different significance of different matrix entries, our results help measure such significance and suggest where to focus when computing factors. An experimental evaluation of the new algorithm on both synthetic and real data demonstrates its good performance in terms of good coverage by the first few factors as well as a small number of factors needed for an almost exact decomposition and indicates that the algorithm outperforms the available ones in these terms. We also propose future research topics. [ABSTRACT FROM AUTHOR]

Anonymity protocols focus on protecting the identities of senders and/or receivers in a network communication. Most of these protocols rely on randomness to achieve their goal and therefore can very well be represented as noisy channels in the information theoretic sense. In this paper we examine the problem of measuring the anonymity degree of anonymity protocols. We investigate a new idea of measuring anonymity based on how much the rows of the channel probabilities matrix are different from each other. We propose a new and generic approximation algorithm for the open problem of finding where anonymity of a given protocol is minimized. We illustrate how the probabilities matrix is constructed for some known anonymity protocols and we use the information leakage measures to study known attacks on those protocols. The analysis shows counter intuitive results in particular for Timed dynamic pool (Cottrell) mixes. Finally, we discuss the applicability of the proposed measures on Tor Network. [ABSTRACT FROM AUTHOR]

Let P w ( E n ; F ) be the space of all continuous n -homogeneous polynomials from a Banach space E into another F , that are weakly continuous on bounded sets. We give sufficient conditions for the weak sequential completeness of P w ( E n ; F ) . These sufficient conditions are also necessary if both E ⁎ and F have the bounded compact approximation property. We also show that the weak sequential completeness and the reflexivity of P w ( E n ; F ) are equivalent whenever both E and F are reflexive. [ABSTRACT FROM AUTHOR]

We consider the design of dominant strategy incentive compatible, revenue-maximizing auctions for an indivisible good, when bidders' values are drawn from a correlated distribution. For independent distributions, Myerson showed that the optimal auction for risk-neutral bidders remains incentive compatible regardless of bidders' risk attitudes. We show that, for correlated distributions, the same is true when only two bidders are involved, whereas for more bidders, randomization can generate strictly more revenue. However, for risk-neutral bidders, we show this gain is never more than a 5 3 -factor. This is a consequence of two results of independent interest: (1) a polynomial-time derandomization of auctions for two bidders; (2) a polynomial-time computable deterministic auction that 5 3 -approximates the optimal revenue extractable from risk-neutral bidders. Moreover, we give a polynomial-time algorithm to compute optimal auctions for a constant number of bidders, and for any number of bidders we give polynomial-time algorithms with approximation factors arbitrarily close to 3 2 . [ABSTRACT FROM AUTHOR]

We revisit the problem of designing the profit-maximizing single-item auction, solved by Myerson in his seminal paper for the case in which bidder valuations are independently distributed. We focus on general joint distributions, either discrete or Lipschitz-continuous, seeking the optimal deterministic incentive compatible auction. We give a geometric characterization of the optimal auction, resulting in a duality theorem and an efficient algorithm for finding the optimal deterministic auction in the two-bidder case and an NP-completeness result for three or more bidders. [ABSTRACT FROM AUTHOR]

In this article we study questions related to the approximation of Markov functions on a finite set of points on the real line by rational functions with real coefficients. The main results include formulas for the error in best rational approximation. A connection of rational approximation problems with the discrete Hankel operator is also investigated. [ABSTRACT FROM AUTHOR]

The network verification problem is that of establishing the accuracy of a high-level description of its physical topology, by making as few measurements as possible on its nodes. This task can be formalized as an optimization problem that, given a graph and a query model specifying the information returned by a query at a node, asks for finding a minimum-size subset of nodes to be queried so as to univocally identify the graph. This problem has been studied with respect to different query models, assuming that a node had some global knowledge about the network. Here, we propose a new query model based on the local knowledge a node instead usually has. Quite naturally, we assume that a query at a given node returns the associated routing table, i.e., a set of entries which provides, for each destination node, a corresponding (set of) first-hop node(s) along an underlying shortest path. [ABSTRACT FROM AUTHOR]

Broadcast is a fundamental operation in Wireless Sensor Networks (WSNs) and plays an important role in a communication protocol design. In duty-cycled scenarios, a sensor node can receive a message only in its active time slot, which makes it more difficult to design collision-free scheduling for broadcast operations. Recent studies in this area have focused on minimizing broadcast latency and guaranteeing that all nodes receive a broadcast message. This paper investigates the problem of Minimum Latency Broadcast Scheduling in Duty-Cycled (MLBSDC) WSNs. By using special geometric properties of independent sets of a broadcast tree, we reduce the number of transmissions, consequently reducing the possibility of collision. Allowing multiple transmissions in one working period, our proposed Latency Aware Broadcast Scheduling (LABS) scheme provides a latency-efficient broadcast schedule. Theoretical analysis proves that the scheme has the same approximation ratio and complexity as the previous best algorithm for the MLBSDC problem. Moreover, simulation shows that the new scheme achieves up to 34%, 37%, and 21% performance improvement over previous schemes, in terms of latency, number of transmissions, and energy consumption, respectively. [ABSTRACT FROM AUTHOR]

Abstract: Periodic monitoring is sufficient for sweep coverage with a small number of mobile sensor nodes, whereas a continuous monitoring with static sensor nodes is required for the coverage problem in wireless sensor networks. Finding the minimum number of mobile sensor nodes with a uniform speed to guarantee sweep coverage is NP-hard and it cannot be approximated within a factor of 2 (Li et al., 2011). In this paper we have proposed a 2-approximation algorithm for solving the sweep coverage for a given set of points of interest (PoIs). The best known approximation factor is 3 for this problem (Li et al., 2011). Modification of the algorithm is also proposed for extending lifetime of the mobile sensors, sweep coverage in the presence of obstacles and failure of mobile sensors. When all PoIs are static sensor nodes, we have proposed a distributed approximation algorithm with approximation ratio 2, where the static sensor nodes compute the number of mobile sensor nodes and their positions. We have introduced sweep coverage for a given area of interest (AoI) and proved that the problem is NP-complete. A -approximation algorithm is designed in order to solve the problem for a square region. An improvement over the approximation factor is designed for any rectangular region. Based on our simulation study we have shown that less number mobile sensor nodes are required for our point sweep coverage algorithm compared to the algorithm proposed in Du et al. (2010). [Copyright &y& Elsevier]

Abstract: This paper presents a novel algorithm to approximate the long-range electrostatic potential field in the Cartesian coordinates applicable to 3D coarse-grained simulations of biopolymers. In such models, coarse-grained clusters are formed via treating groups of atoms as rigid and/or flexible bodies connected together via kinematic joints. Therefore, multibody dynamic techniques are used to form and solve the equations of motion of such coarse-grained systems. In this article, the approximations for the potential fields due to the interaction between a highly negatively/positively charged pseudo-atom and charged particles, as well as the interaction between clusters of charged particles, are presented. These approximations are expressed in terms of physical and geometrical properties of the bodies such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor about the center of charge of the clusters. Further, a novel substructuring scheme is introduced to implement the presented far-field potential evaluations in a binary tree framework as opposed to the existing quadtree and octree strategies of implementing fast multipole method. Using the presented Lagrangian grids, the electrostatic potential is recursively calculated via sweeping two passes: assembly and disassembly. In the assembly pass, adjacent charged bodies are combined together to form new clusters. Then, the potential field of each cluster due to its interaction with faraway resulting clusters is recursively calculated in the disassembly pass. The method is highly compatible with multibody dynamic schemes to model coarse-grained biopolymers. Since the proposed method takes advantage of constant physical and geometrical properties of rigid clusters, improvement in the overall computational cost is observed comparing to the tradition application of fast multipole method. [Copyright &y& Elsevier]

Abstract: Existing sparse inpainting models often suffer from their over-constraints on the sparsity of the transformed recovered images. Due to the fact that a transformed image of a wavelet or framelet transform is not truly sparse, but approximately sparse, we introduce an approximate sparsity model for inpainting. We formulate the model as minimizing the number of nonzero components of the soft-thresholding operator applied to the transformed image. The key difference of the proposed model from the existing ones is the use of a soft-thresholding operator which shrinkages the components of the transformed image. To efficiently solve the resulting nonconvex optimization problem, we rewrite the norm, which counts the number of nonzero components, as a weighted norm with a nonlinear discontinuous weight function, which is then approximated by a continuous weight function. We overcome the nonlinearity in the weight function by an iteration which leads to a numerical scheme for solving the nonconvex optimization problem. In each iteration, we solve a weighted convex optimization problem. We then focus on understanding the existence of solutions of the weighted convex optimization problem and characterizing them as fixed-points of a nonlinear mapping. The fixed-point formulation allows us to employ efficient iterative algorithms to find the fixed-points. Numerical experiments are shown to demonstrate improvement in performance of the proposed model over the existing models for image inpainting. [Copyright &y& Elsevier]

Abstract: Sparsity-based regularization methods for image restoration assume that the underlying image has a good sparse approximation under a certain system. Such a system can be a basis, a frame, or a general over-complete dictionary. One widely used class of such systems in image restoration are wavelet tight frames. There have been enduring efforts on seeking wavelet tight frames under which a certain class of functions or images can have a good sparse approximation. However, the structure of images varies greatly in practice and a system working well for one type of images may not work for another. This paper presents a method that derives a discrete tight frame system from the input image itself to provide a better sparse approximation to the input image. Such an adaptive tight frame construction scheme is applied to image denoising by constructing a tight frame tailored to the given noisy data. The experiments showed that the proposed approach performs better in image denoising than those wavelet tight frames designed for a class of images. Moreover, by ensuring that the system derived from our approach is always a tight frame, our approach also runs much faster than other over-complete dictionary based approaches with comparable performance on denoising. [Copyright &y& Elsevier]

Abstract: This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach. [Copyright &y& Elsevier]

Abstract: Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a ‘push–pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker–Planck (drift–diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a ‘critical point’ for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm. [Copyright &y& Elsevier]

Abstract: We study -variate approximation problems in the average case setting with respect to a zero-mean Gaussian measure. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. For the absolute error criterion, we obtain the necessary and sufficient conditions in terms of the eigenvalues of its covariance operator and obtain an estimate of the exponent of quasi-polynomial tractability which cannot be improved in general. For the linear tensor product problems, we find that the quasi-polynomial tractability is equivalent to the strong polynomial tractability. For the normalized error criterion, we solve a problem related to the Korobov kernels, which is left open in Lifshits et al. (2012). [Copyright &y& Elsevier]

• A cost function vector of the simultaneous perturbation stochastic approximation algorithm is proposed. • The proposed method reaches a good convergence performance. • The vibration of the inlet pipeline is eliminated by using the proposed method. Active vibration control of stable rotating machinery with a time-variant structure is a research priority in the field. Simultaneous perturbation stochastic approximation (SPSA), a model-free active control strategy, has attracted a lot of attention from researchers. This paper studies the cost function of the SPSA algorithm to improve its performance in controlling periodic vibration. After the weight vector being perturbed by a perturbation vector, the existing cost functions of the SPSA algorithm can reveal the overall energy variation but hardly detail the variation of each harmonic wave. Therefore, the adaptive notch filter with the SPSA algorithm using these cost functions shows a low convergence speed and a bad control effect in active periodic disturbance controlling. In order to detail the energy variation of each harmonic, this paper proposes a cost function using the weighted cross correlation function. When the algorithm calculates the energy of each harmonic wave, the disturbances from other harmonics and background noise are reduced. The interference noises in the estimated gradient of the cost function are reduced indirectly. The algorithm convergence performance improves. To illustrate that, the simulations of controlling harmonic waves and the experiments of eliminating the vibration of the pump inlet pipeline are conducted. The results indicate that the adaptive notch filter with the proposed cost function has reached the fastest convergence speed and the best control effect so far among the use of other cost functions mentioned in this paper. [ABSTRACT FROM AUTHOR]

• A robust deep low-rank feature learning and encoding model for cross-age face recognition is proposed. • A manifold-constrained low-rank approximation algorithm is proposed to learn clean low-rank feature matrix for representation. • A locality-constrained feature encoding framework is proposed to represent the cross-age face images of the same identity by similar codewords. • The proposed method outperforms other state-of-the-art methods in terms of recognition rate. Cross-age face recognition (CAFR) is a challenging task, due to significant intra-personal variations. Furthermore, the training and testing data may contain random noise components. To address these issues, this paper proposes a deep low-rank feature learning and encoding method. Firstly, our method employs manifold learning in the low-rank optimization, which preserves the global and local structure of the data samples, while learning the clean low-rank features. Secondly, we encode the low-rank features using our locality-constrained feature encoding method, which learns an age-insensitive codebook from training data, and enables the intra-class samples to share the same local bases in a codebook. In the testing stage, the gallery and probe features are encoded by the learned codebook, which represents the images of the same identity by similar codewords for recognition. Furthermore, the periocular region of human faces is investigated for CAFR. Extensive experiments on five datasets demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Given a collection of multisets { X 1 , X 2 , ... , X k } (k ≥ 2) of positive integers, a multiset S is a common integer partition for them if S is an integer partition of every multiset X i , 1 ≤ i ≤ k. The minimum common integer partition (k -MCIP) problem is defined as to find a CIP for { X 1 , X 2 , ... , X k } with the minimum cardinality. We present a 6 5 -approximation algorithm for the 2-MCIP problem, improving the previous best algorithm of performance ratio 5 4 designed by Chen et al. in 2006. We then extend it to obtain an absolute 0.6 k -approximation algorithm for k -MCIP when k is even (when k is odd, the approximation ratio is 0.6 k + 0.4). [ABSTRACT FROM AUTHOR]

In the generalized budgeted submodular set function maximization problem, we are given a ground set of elements and a set of bins. Each bin has its own cost and the cost of each element depends on its associated bin. The goal is to find a subset of elements along with an associated set of bins such that the overall costs of both is at most a given budget, and the profit is maximized. We present an algorithm that guarantees a 1 2 (1 − 1 e α ) -approximation, where α ≤ 1 is the approximation factor of an algorithm for a sub-problem. If the costs satisfy a specific condition, we provide a polynomial-time algorithm that gives us α = 1 − ϵ , while for the general case we design an algorithm with α = 1 − 1 e − ϵ. We extend our results providing a bi-criterion approximation algorithm where we can spend an extra budget up to a factor β ≥ 1 to guarantee a 1 2 (1 − 1 e α β ) -approximation. [ABSTRACT FROM AUTHOR]

Abstract: We study several network design problems with degree constraints. For the minimum-cost Degree-Constrained 2-Node-Connected Subgraph problem, we obtain the first non-trivial bicriteria approximation algorithm, with violation for the degrees and a 4-approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k terminals and with minimum maximum outdegree. We show that the natural LP-relaxation has a gap of or with respect to the multiplicative degree bound violation. We overcome this hurdle by a combinatorial -approximation algorithm, where denotes the maximum degree in the optimum solution. We also give an lower bound on approximating this problem. Then we consider the undirected version of this problem, however, with an extra diameter constraint, and give an lower bound on the approximability of this version. We also consider a closely related Prize-Collecting Degree-Constrained Edge-Connectivity Survivable Network problem, and obtain several results in this direction by reducing the prize-collecting variant to the regular one. Finally, we consider the Terminal Steiner Tree problem, which is a simple variant of the Degree-Constrained Steiner Tree problem, when some terminals are required to be leaves. We show that this seemingly simple problem is equivalent to the Group Steiner Tree problem. [Copyright &y& Elsevier]

Abstract: We present a dictionary learning algorithm which is tailored to the block-based image prediction problem. More precisely, we learn two related sub-dictionaries and , the first one () for approximating known samples in a causal neighborhood of the block to be predicted and the other one () to approximate the block to be predicted. These two dictionaries are learned so that representation vectors computed by approximating the known samples using will lead to a good approximation of the block to be predicted when used together with . Because of its simplicity, this method can be used for on-the-fly learning of dictionaries. The proposed method has first been evaluated for intra prediction. It has then been applied in a complete image compression algorithm. Experimental results show gains up to 3dB in terms of prediction compared to the H.264/AVC intra modes and up to 2dB in terms of rate-distortion performance. [Copyright &y& Elsevier]

Abstract: A computational approach for obtaining a similarity measure between qualitative descriptions of shape, colour and size of objects within digital images is presented. According to the definition of the qualitative features, the similarity values determined are based on conceptual neighbourhood diagrams or interval distances. An approximate matching algorithm between object descriptions is defined and applied to tile mosaic assembling and results of previous approaches are improved. [Copyright &y& Elsevier]

Abstract: Given a graph with a cost function and a vertex subset , an internal Steiner tree is a Steiner tree that contains all the vertices in , and such that each vertex in must be an internal vertex. The internal Steiner tree problem involves finding an internal Steiner tree whose total cost is the minimum. In this paper, we first show that the internal Steiner tree problem is MAX SNP-hard. We then present a -approximation algorithm for solving the problem on complete graphs, where is an approximation ratio for the Steiner tree problem. Currently, the best-known is . Moreover, for the case where the cost of each edge is restricted to being either 1 or 2, we present a -approximation algorithm for the problem. [Copyright &y& Elsevier]

Abstract: Consider -hulls, , from a dictionary of functions in space for . Their precise metric entropy orders are derived. Sparse linear approximation bounds are obtained to characterize the number of terms needed to achieve accurate approximation of the best function in a -hull that is closest to a target function. Furthermore, in the special case of , it is shown that a weak orthogonal greedy algorithm achieves the optimal approximation under an additional condition. [Copyright &y& Elsevier]

Abstract: Given a graph of interactions, a module (also called a community or cluster) is a subset of nodes whose fitness is a function of the statistical significance of the pairwise interactions of nodes in the module. The topic of this paper is a model-based community finding approach, commonly referred to as modularity clustering, that was originally proposed by Newman (Leicht and Newman, 2008 [25]) and has subsequently been extremely popular in practice (e.g., see Agarwal and Kempe, 2008 [1], Guimer‘a et al., 2007 [20], Newman, 2006 [28], Newman and Girvan, 2004 [30], Ravasz et al., 2002 [32]). Various heuristic methods are currently employed for finding the optimal solution. However, as observed in Agarwal and Kempe (2008) [1], the exact computational complexity of this approach is still largely unknown. To this end, we initiate a systematic study of the computational complexity of modularity clustering. Due to the specific quadratic nature of the modularity function, it is necessary to study its value on sparse graphs and dense graphs separately. Our main results include a -inapproximability for dense graphs and a logarithmic approximation for sparse graphs. We make use of several combinatorial properties of modularity to get these results. These are the first non-trivial approximability results beyond the NP-hardness results in Brandes et al. (2007) [10]. [Copyright &y& Elsevier]

Abstract: In this paper modified variants of the sparse Fourier transform algorithms from Iwen (2010) [32] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings are developed. As a consequence, approximate Fourier transforms are obtained which will identify a near-optimal k-term Fourier series for any given input function, , in time (neglecting logarithmic factors). Faster randomized Fourier algorithm variants with runtime complexities that scale linearly in the sparsity parameter k are also presented. [Copyright &y& Elsevier]

Abstract: The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. [Copyright &y& Elsevier]

Abstract: Node-Weighted Steiner Forest is the following problem: Given an undirected graph, a set of pairs of terminal vertices, a weight function on the vertices, find a minimum weight set of vertices that includes and connects each pair of terminals. We consider the restriction to planar graphs where the problem remains NP-complete. Demaine et al. showed that the generic primal-dual algorithm of Goemans and Williamson is a 6-approximation on planar graphs. We present (1) two different analyses to prove an approximation factor of 3, (2) show that our analysis is best possible for the chosen proof strategy, and (3) generalize this result to feedback problems on planar graphs. We give a simple proof for the first result using contraction techniques and following a standard proof strategy for the generic primal-dual algorithm. Given this proof strategy our analysis is best possible which implies that proving a better upper bound for this algorithm, if possible, would require different proof methods. Then, we give a reduction on planar graphs of Feedback Vertex Set to Node-Weighted Steiner Tree, and Subset Feedback Vertex Set to Node-Weighted Steiner Forest. This generalizes our result to the feedback problems studied by Goemans and Williamson. For the opposite direction, we show how our constructions can be combined with the proof idea for the feedback problems to yield an alternative proof of the same approximation guarantee for Node-Weighted Steiner Forest. [Copyright &y& Elsevier]

Abstract: A cut-and-paste operation can be a reversal, a transposition, or a transreversal on circular or linear permutations. There are several approximation algorithms for sorting signed permutations by combinations of these operations. For sorting unsigned permutations, we only know an algorithm with performance ratio 3 and its improved version with performance ratio allowing reversals and transpositions. In this paper, we present a 2.25-approximation algorithm for sorting unsigned circular permutations by cut-and-paste operations. A structure called tie is proposed to represent the alternating path of length 5. We can classify the ties into 6 types and find ways to remove the breakpoints for each type of ties, so that every cut-and-paste operation can reduce at least breakpoints averagely. Our algorithm can be used to sort unsigned linear permutations and achieve the performance ratio 2.25 if another operation named revrev is allowed. [Copyright &y& Elsevier]

Abstract: The Malleable Parallel Task Scheduling problem (MPTS) is an extension of one of the most classic scheduling problems (P∥Cmax). The only difference is that for MPTS, each task can be processed simultaneously by more than one processor. Such flexibility could dramatically reduce the makespan, but greatly increase the difficulty for solving the problem. By carefully analyzing some existing algorithms for MPTS, we find each of them suitable for some specific cases, but none is effective enough for all cases. Based on such observations, we introduce some optimization algorithms and improving techniques for MPTS, with their performance analyzed in theory. Combining these optimization algorithms and improving techniques gives rise to our novel scheduling algorithm OCM (Optimizations Combined for MPTS), a 2-approximation algorithm for MPTS. Extensive simulations on random datasets and SPLASH-2 benchmark reveal that for all cases, schedules produced by OCM have smaller makespans, compared with other existing algorithms. [Copyright &y& Elsevier]

Abstract: The problem Constrained Longest Common Subsequence is a natural extension to the classical problem Longest Common Subsequence, and has important applications to bioinformatics. Given k input sequences and l constraint sequences , is the problem of finding a longest common subsequence of that is also a common supersequence of . Gotthilf et al. gave a polynomial-time algorithm that approximates within a factor , where is the length of the shortest input sequence and is the alphabet size. They asked whether there are better approximation algorithms and whether there exists a lower bound. In this paper, we answer their questions by showing that their approximation factor is in fact already very close to optimal although a small improvement is still possible: [1.] For any computable function f and any , there is no polynomial-time algorithm that approximates within a factor unless . Moreover, this holds even if the constraint sequence is unary. [2.] There is a polynomial-time randomized algorithm that approximates within a factor with high probability, where OPT is the length of the optimal solution, . For the problem over an alphabet of arbitrary size, we show that [3.] For any , there is no polynomial-time algorithm that approximates within a factor unless . [4.] There is a polynomial-time algorithm that approximates within a factor . We also present some complementary results on exact and parameterized algorithms for . [Copyright &y& Elsevier]

Abstract: Given two genomic maps and each represented as a sequence of n gene markers, the maximal strip recovery (MSR) problem is to retain the maximum number of markers in both and such that the resultant subsequences, denoted as and , can be partitioned into the same set of maximal strips, which are common substrings of length greater than or equal to two. The complementary maximal strip recovery (CMSR) problem has the complementary goal to delete the minimum number of markers. Both MSR and CMSR have been shown to be NP-hard and APX-complete, and they admit a 4-approximation and a 3-approximation respectively. In this paper, we present an improved -approximation algorithm for the CMSR problem, with its worst-case performance analysis done through a local amortization with a re-weighting scheme. [Copyright &y& Elsevier]

Abstract: In this paper, we report on internal conversion coefficients for to superheavy elements obtained from relativistic Dirac–Fock calculations. The effect of the atomic vacancy created during the conversion process has been taken into account using the so called “Frozen Orbital” approximation. The selection of this atomic model is supported by our recent comparison of experimental and theoretical conversion coefficients across a wide range of nuclei. The atomic masses, valence shell electron configurations, and theoretical atomic binding energies required for the calculations were adopted from a critical evaluation of the published data. The new conversion coefficient data tables presented here cover all atomic shells, transition energies from 1 keV up to 6000 keV, and multipole orders of 1–5. A similar approach was used in our previous calculations [T. Kibédi, T.W. Burrows, M.B. Trzhaskovskaya, P.M. Davidson, C.W. Nestor Jr., Nucl. Instrum. Methods Phys. Res. A 589 (2008) 202] for . [Copyright &y& Elsevier]

Abstract: We present a short proof of a generalization of a result of Cheriyan and Thurimella: a simple graph of minimum degree k can be augmented to a k-edge connected simple graph by adding edges, where n is the number of nodes. One application (from the previous paper) is an approximation algorithm with a guarantee of for the following NP-hard problem: given a simple undirected graph, find a minimum-size k-edge connected spanning subgraph. For the special cases of , this is the best approximation guarantee known. [Copyright &y& Elsevier]

Abstract: We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph with edge costs, a collection of ordered node pairs, and an integer , find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs . When , we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: for k-DSF by Charikar et al. (1999) , and for DSF by Chekuri et al. (2008) . Our main result is achieving the first sub-linear in terms of approximation ratio for DSF. Specifically, we give an -approximation scheme for DSF. For k-DSF we give a simple greedy -approximation algorithm. This improves upon the best known ratio by Charikar et al. (1999) , and (almost) matches, in terms of k, the best ratio known for the undirected variant (Gupta et al., 2010 ). This algorithm uses a new structure called start-junction tree which may be of independent interest. [Copyright &y& Elsevier]

Abstract: In this paper we propose an approximation algorithm for scheduling malleable tasks with precedence constraints. Based on an interesting model for malleable tasks with continuous processor allotments by Prasanna and Musicus (1991, 1994, 1996) , we define two natural assumptions for malleable tasks: the processing time of any malleable task is non-increasing in the number of processors allotted, and the speedup is concave in the number of processors. We show that under these assumptions the work function of any malleable task is non-decreasing in the number of processors and is convex in the processing time. Furthermore, we propose a two-phase approximation algorithm for the scheduling problem. In the first phase we solve a linear program to obtain a fractional allotment for all tasks. By rounding the fractional solution, each malleable task is assigned a number of processors. In the second phase a variant of the list scheduling algorithm is employed. By choosing appropriate values of the parameters, we show (via a nonlinear program) that the approximation ratio of our algorithm is at most . We also show that our result is asymptotically tight. [Copyright &y& Elsevier]

Abstract: We present a new framework for the design of computationally-efficient and incentive-compatible mechanisms for combinatorial auctions. The mechanisms obtained via this framework are randomized, and obtain incentive compatibility in the universal sense (in contrast to the substantially weaker notion of incentive compatibility in expectation). We demonstrate the usefulness of our techniques by exhibiting two mechanisms for combinatorial auctions with general bidder preferences. The first mechanism obtains an optimal -approximation to the optimal social welfare for arbitrary bidder valuations. The second mechanism obtains an -approximation for a class of bidder valuations that contains the important class of submodular bidders. These approximation ratios greatly improve over the best (known) deterministic incentive-compatible mechanisms for these classes. [Copyright &y& Elsevier]

Abstract: Magnetic insulators can be characterized by a gap separating the singlet ground state from the lowest-energy triplet, excitation. If the gap can be closed by the Zeeman interaction in applied magnetic field, the resulting quasiparticles, triplons, can have concentrations sufficient to undergo the Bose–Einstein condensates transition. We consider macroscopic properties of the triplon Bose–Einstein condensates in the Hartree–Fock–Bogoliubov approximation taking into account the anomalous averages. We prove that these averages play the qualitative role in the condensate properties. As a result, we show that with the increase in the external magnetic field at a given temperature, the condensate demonstrates an instability related to the appearance of nonzero phonon damping and a change in the characteristic dependence of the speed of sound on the magnetic field. The calculated magnetic susceptibility diverges when the external magnetic field approaches this instability threshold, providing a tool for the experimental verification of this approach. [Copyright &y& Elsevier]

Abstract: Ground-state properties are evaluated for the finite nucleus 4He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N3LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones. [Copyright &y& Elsevier]

Abstract: We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires time for each input character, where is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the and norms. For these examples, the resulting online algorithms take , , , , and time per character, respectively. The space overhead is linear in the pattern size, which we show is optimal for any deterministic algorithm. [Copyright &y& Elsevier]

Abstract: The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained). [ABSTRACT FROM AUTHOR]

Abstract: We consider the following vertex coloring problem. We are given an undirected graph , where each vertex v is associated with a penalty rejection cost . We need to choose a subset of vertices, , and to find a proper coloring of the induced subgraph of G over . We are interested in both the number of colors used to color the vertices of , and in the total rejection cost of all other vertices. The goal is to minimize the sum of these two amounts. In this paper we consider both the online and the offline versions of this problem. In the online version, vertices arrive one at a time, revealing the rejection cost of the current vertex and the set of edges connecting it to previously revealed vertices. We also consider the classical online coloring problem on bounded degree graphs and on -claw free graphs. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of computing the permanent of a n by n matrix. For a class of matrices corresponding to constant degree expanders we construct a deterministic polynomial time approximation algorithm to within a multiplicative factor , for arbitrary . This is an improvement over the best known approximation factor obtained in Linial, Samorodnitsky and Wigderson (2000) , though the latter result was established for arbitrary non-negative matrices. Our results use a recently developed deterministic approximation algorithm for counting partial matchings of a graph (Bayati, Gamarnik, Katz, Nair and Tetali (2007) ) and Jerrum–Vazirani method (Jerrum and Vazirani (1996) ) of approximating permanent by near perfect matchings. [ABSTRACT FROM AUTHOR]

Abstract: We present a simple randomized algorithmic framework for connected facility location problems. The basic idea is as follows: We run a black-box approximation algorithm for the unconnected facility location problem, randomly sample the clients, and open the facilities serving sampled clients in the approximate solution. Via a novel analytical tool, which we term core detouring, we show that this approach significantly improves over the previously best known approximation ratios for several NP-hard network design problems. For example, we reduce the approximation ratio for the connected facility location problem from 8.55 to 4.00 and for the single-sink rent-or-buy problem from 3.55 to 2.92. The mentioned results can be derandomized at the expense of a slightly worse approximation ratio. The versatility of our framework is demonstrated by devising improved approximation algorithms also for other related problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper is composed of two parts. In the first part, an improved algorithm is presented for the problem of finding length-bounded two vertex-disjoint paths in an undirected planar graph. The presented algorithm requires time and space, where is the smaller of the two given length bounds. In the second part of this paper, we consider the minmax k vertex-disjoint paths problem on a directed acyclic graph, where is a constant. An improved algorithm and a faster approximation scheme are presented. The presented algorithm requires time and space, and the presented approximation scheme requires time and space, where ϵ is the given approximation parameter and M is the length of the longest path in an optimal solution. [ABSTRACT FROM AUTHOR]

Abstract: A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao (2005) . If is the RIP constant with support size k for an measurement matrix, we investigate the trend of reducing the support size of the RIP constants for qualitative comparisons between sufficient conditions. For example, which condition is easier to satisfy, or ? Using a quantitative comparison via phase transitions for Gaussian measurement matrices, three examples from the literature of such support size reduction are considered. In each case, utilizing a larger support size for the RIP constants results in a sufficient condition for exact sparse recovery that is satisfied by a significantly larger subset of Gaussian matrices. [ABSTRACT FROM AUTHOR]