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A max-log-MAP soft demapping algorithm with logarithmic complexity is proposed for M-PAM signals. Its algorithm complexity is only Θ(logM) for M-PAM signals, in contrast to Θ(MlogM) as achieved by the conventional max-log-MAP algorithm using exhaustive search. The algorithm applies to both Gray-coded and natural-coded signals. The max-log-MAP algorithm with logarithmic complexity may be straightforwardly extended to rectangular QAM signals when the rectangular QAM signal can be decomposed into two independent PAM signals. [ABSTRACT FROM AUTHOR]

The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete dictionary from training data sets of certain signal classes for use in sparse representations has turned out to be of particular importance regarding practical signal processing applications. Most popular dictionary learning algorithms involve NP-hard sparse recovery problems in each iteration, which may give some indication about the complexity of dictionary learning but does not constitute an actual proof of computational intractability. In this technical note, we show that learning a dictionary with which a given set of training signals can be represented as sparsely as possible is indeed \ssb NP-hard. Moreover, we also establish hardness of approximating the solution to within large factors of the optimal sparsity level. Furthermore, we give \ssb NP-hardness and non-approximability results for a recent dictionary learning variation called the sensor permutation problem. Along the way, we also obtain a new non-approximability result for the classical sparse recovery problem from compressed sensing. [ABSTRACT FROM AUTHOR]

We consider the problem of survivability in multilayer networks. In single-layer networks, a pair of disjoint paths can be used to provide protection for a source-destination pair. However, this approach cannot be directly applied to layered networks where risk-disjoint paths may not always exist. In this paper, we take a new approach, which is based on finding a set of paths that may not be disjoint but together will survive any single risk. We start with two-layered communication networks, where the risks are fiber failures. We prove that in general, finding the minimum survivable path set (MSPS) is NP-hard, whereas if we restrict the length of paths the problem can be solved in polynomial time. We formulate the problem as an integer linear program (ILP), and use this formulation to develop heuristics and approximation algorithms. Moreover, we study the minimum cost survivable path set problem, where the cost is the number of fibers used, and thus, nonadditive. Finally, we generalize the survivability problem to the networks with more than two layers. By applying our algorithms for survivable path set, we assess the survivability of communication networks that operate relying on power from a power grid. [ABSTRACT FROM PUBLISHER]

In this article, we address the problem of approximating data points by C-smooth polynomial spline curves or surfaces using L-norm. The use of this norm helps to preserve the data shape and it reduces extraneous oscillations. In our approach, we introduce a new functional which enables to control directly the distance between the data points and the resulting spline solution. The computational complexity of the minimization algorithm is nonlinear. A local minimization method using sliding windows allows to compute approximation splines within a linear complexity. This strategy seems to be more robust than a global method when applied on large data sets. When the data are noisy, we iteratively apply this method to globally smooth the solution while preserving the data shape. This method is applied to image denoising. [ABSTRACT FROM AUTHOR]

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values’ Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules $w.r.t.$ AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM PUBLISHER]

Let P be a d-dimensional n-point set. A partition of P is called a Tverberg partition if the convex hulls of all sets in intersect in at least one point. We say that is t- tolerant if it remains a Tverberg partition after deleting any t points from P. Soberón and Strausz proved that there is always a t-tolerant Tverberg partition with ⌈n/(d + 1)(t + 1)⌉ sets. However, no nontrivial algorithms for computing or approximating such partitions have been presented so far. For d ≤ 2, we show that the Soberón-Strausz bound can be improved, and we show how the corresponding partitions can be found in polynomial time. For d ≥ 3, we give the first polynomial-time approximation algorithm by presenting a reduction to the regular Tverberg problem (with no tolerance). Finally, we show that it is coNP-complete to determine whether a given Tverberg partition is t-tolerant. [ABSTRACT FROM AUTHOR]

Nonbinary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in some cases, but their high decoding complexity is a significant hurdle to their applications. In this paper, we propose a decoding algorithm with reduced computational complexities and smaller memory requirements for NB-LDPC codes. First, a simplified algorithm is proposed to reduce the computational complexity of variable node processing. To reduce the memory requirements, existing NB-LDPC decoders often truncate the message vectors to a limited number nm of values. However, the memory requirements of these decoders remain high when the field size is large. In this paper, an improved trellis-based check node processing algorithm is proposed to significantly reduce the memory requirement. The number of elements in a variable-to-check message is reduced to nv~(nv

Given a graph G( N, A) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subject to an end-to-end delay constraint. The problem (with a single constraint) is NP-hard, and has been studied by many researchers who found fully polynomial approximation schemes (FPAS) for this problem. The current paper focuses on a generalized CRP version, CRP with hop-wise constraints (CRPH). In the generalized version, instead of one constraint there are up to n−1 special-type constraints, where n is the number of nodes. An FPAS based on interval partitioning is proposed for both the minimization and the maximization versions of CRPH. For G( N, A) with n nodes and m arcs, the complexity of the algorithm is O( mn/ ε). [ABSTRACT FROM AUTHOR]

Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework developed for this purpose left open the questions of computational efficiency and of providing direct bounds on generalization error. We design a new algorithm for classification in general metric spaces, whose runtime and accuracy depend on the doubling dimension of the data points, and can thus achieve superior classification performance in many common scenarios. The algorithmic core of our approach is an approximate (rather than exact) solution to the classical problems of Lipschitz extension and of nearest neighbor search. The algorithm’s generalization performance is guaranteed via the fat-shattering dimension of Lipschitz classifiers, and we present experimental evidence of its superiority to some common kernel methods. As a by-product, we offer a new perspective on the nearest neighbor classifier, which yields significantly sharper risk asymptotics than the classic analysis. [ABSTRACT FROM AUTHOR]

Abstract: We study vertex selection in the presence of multiple graphs associated with a vertex set V representing an online community. First, we formulate a collection of Markov chains on the graph ensemble and describe the characteristics of the associated mean hitting times on V. Then, we design a branch and bound optimisation technique for computing the subset of vertices A that exhibits the smallest hitting time cost across the multi-graph, given a constraint on the volume of A. The complexity of the branch and bound technique limits its application to medium-size graphs. Thus, we formulate a greedy optimisation method for computing a close approximation to the optimal subset at lower complexity, which can be implemented in a decentralised way, for further complexity reduction. We prove that the objective function under consideration is supermodular and monotonic, which guarantees near-optimal solutions for the greedy method. This is verified in our numerical experiments that compare its performance to that of the branch and bound technique, on smaller size graphs. The experiments also examine the hitting-time trade-off across the multi-graph that our optimisation exhibits, governed by the sampling cost factors λ j associated with each graph layer G j . Relative to conventional community graph centrality methods for vertex selection, we demonstrate a substantially lower sampling (network) cost and higher data dissemination rate, on actual Facebook and Internet topology data. The generality of our framework allows for its application to information retrieval, from a collection of items represented by a multi-graph. Here, we demonstrate higher semantic consistency over state-of-the-art single-graph methods, on the popular DBLP data set. [Copyright &y& Elsevier]

We present a novel method for the design of finite impulse response (FIR) filters with discrete coefficients that belong in the sum of powers-of-two (POT) space. The importance of this class of filters cannot be overstated, given the ever-increasing number of applications for which a specific hardware implementation is needed. Filters that have coefficients that belong to such a class are also referred to as multiplierless filters, given that the operations performed by the filter can all be implemented by using appropriately designed shifts of the input data, making them a perfect choice whenever implementation simplicity and processing speed are the ultimate goal. To produce such a design, we employ a vector successive approximation technique successfully used in data compression that has a very low computational complexity, the Matching Pursuits Generalized BitPlanes algorithm (MPGBP). We derive optimality conditions for the approximation dictionary. We compare filters obtained with the proposed method with those derived in previous works. Based on this comparative analysis, we show that this new and powerful way of producing the filters' coefficients is also among the simplest available in the literature. [ABSTRACT FROM PUBLISHER]

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MILPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MILPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generating a valid inequality violated by a given real vector, usually arising as the solution to a relaxation of the original problem. We show that the problem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program. In some cases, this bilevel program can be easily reformulated as a simple single-level mathematical program, yielding a standard mathematical programming formulation for the separation problem. In other cases, no such polynomial-size single-level reformulation exists unless the polynomial hierarchy collapses to its first level (an event considered extremely unlikely in computational complexity theory). We illustrate our insights by considering the separation problem for two well-known classes of valid inequalities. [ABSTRACT FROM AUTHOR]

This article presents algorithms that convert multiple precision integer or floating-point numbers from radix $2$ to radix $10$ (or to any radix $b > 2$). Those algorithms, based on the “scaled remainder tree” technique, use multiplications instead of divisions in their critical part. Both quadratic and subquadratic algorithms are detailed, with proofs of correctness. Experimental results show that our implementation of those algorithms outperforms the GMP library by up to 50 percent (using the same low-level routines). [ABSTRACT FROM AUTHOR]

We study the hardness of approximation of clause minimum and literal minimum representations of pure Horn functions in n Boolean variables. We show that unless P=NP, it is not possible to approximate in polynomial time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within a factor of $2^{\log^{1-o(1)} n}$. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O( n) clauses, for some small positive constant ε. Furthermore, we show that even allowing sub-exponential time computation, it is still not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false. [ABSTRACT FROM AUTHOR]

We consider the scheduling of simple linear deteriorating jobs on parallel machines from a new perspective based on game theory. In scheduling, jobs are often controlled by independent and selfish agents, in which each agent tries to select a machine for processing that optimizes its own payoff while ignoring the others. We formalize this situation as a game in which the players are job owners, the strategies are machines, and a player's utility is inversely proportional to the total completion time of the machine selected by the agent. The price of anarchy is the ratio between the worst-case equilibrium makespan and the optimal makespan. In this paper, we design a game theoretic approximation algorithm A and prove that it converges to a pure-strategy Nash equilibrium in a linear number of rounds. We also derive the upper bound on the price of anarchy of A and further show that the ratio obtained by A is tight. Finally, we analyze the time complexity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Matching is widely used in the estimation of treatment effects in observational studies. However, the matching paradigm may be too restrictive in many cases because exact matches often do not exist in the available data. One mechanism for overcoming this issue is to relax the requirement of exact matching on some or all of the covariates (attributes that may affect the response to treatment) to a requirement of balance on the covariate distributions for the treatment and control groups. The balance optimization subset selection (BOSS) model can be used to identify a control group featuring optimal covariate balance. This paper explores the relationship between the matching and BOSS models and shows how BOSS subsumes matching. Complexity and approximation results are presented for the resulting models. Computational results demonstrate some of the important trade-offs between matching and BOSS. [ABSTRACT FROM AUTHOR]

This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the belief propagation (BP) algorithm of artificial intelligence. The Bethe approximation and the BP algorithm are heuristic methods for estimating the partition function and marginal probabilities in graphical models, respectively. The computational complexity of the Bethe approximation is decided by the number of operations required to solve a set of nonlinear equations, the so-called Bethe equation. Although the BP algorithm was inspired and developed independently, Yedidia, Freeman, and Weiss showed that the BP algorithm solves the Bethe equation if it converges (however, it often does not). This naturally motivates the following question to understand limitations and empirical successes of the Bethe and BP methods: is the Bethe equation computationally easy to solve? We present a message-passing algorithm solving the Bethe equation in a polynomial number of operations for general binary graphical models of \(n\) variables, where the maximum degree in the underlying graph is \(O(\log n)\) . Equivalently, it finds a stationary point of the Bethe free energy function. Our algorithm can be used as an alternative to BP fixing its convergence issue and is the first fully polynomial-time approximation scheme for the BP fixed-point computation in such a large class of graphical models, whereas the approximate fixed-point computation is known to be polynomial parity arguments on directed graphs (PPAD-)hard in general. We believe that our technique is of broader interest to understand the computational complexity of the cavity method in statistical physics. [ABSTRACT FROM AUTHOR]

In a classic optimization problem, the complete input data is assumed to be known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In the case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multiobjective optimization problems. In this setting we are given a main objective function and a set of secondary objectives which are modeled via budget constraints. Multiobjective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting goals. The main contribution of this paper is showing that two of the main tools for the design of approximation algorithms for multiobjective optimization problems, namely, approximate Pareto sets and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto sets, we devise truthful deterministic and randomized multicriteria fully polynomial-time approximation schemes (FPTASs) for multiobjective optimization problems whose exact version admits a pseudopolynomial-time algorithm, as, for instance, the multibudgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching,and matroid intersection. Our construction also applies to multidimensional knapsack and multiunit combinatorial auctions. Our FPTASs compute a (1+ε)-approximate solution violating each budget constraint by a factor (1+ ε). When feasible solutions induce an independence system, i.e., when subsets of feasible solutions are feasible as well, we present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally, we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint, where one wants to compute a minimum cost spanning tree whose length is at most a given value L. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and with a random perturbation step (ensuring low expected running time). This result can be derandomized in the case of integral lengths. All the mentioned results match the best known approximation ratios, which are, however, obtained by nontruthful algorithms. [ABSTRACT FROM AUTHOR]

As an imperative channel for fast information propagation, online social networks (OSNs) also have their defects. One of them is the information leakage, i.e., information could be spread via OSNs to the users whom we are not willing to share with. Thus the problem of constructing a circle of trust to share information with as many friends as possible without further spreading it to unwanted targets has become a challenging research topic but still remained open. Our work is the first attempt to study the Maximum Circle of Trust problem seeking to share the information with the maximum expected number of poster's friends such that the information spread to the unwanted targets is brought to its knees. First, we consider a special and more practical case with the two-hop information propagation and a single unwanted target. In this case, we show that this problem is NP-hard, which denies the existence of an exact polynomial-time algorithm. We thus propose a Fully Polynomial-Time Approximation Scheme (FPTAS), which can not only adjust any allowable performance error bound but also run in polynomial time with both the input size and allowed error. FPTAS is the best approximation solution one can ever wish for an NP-hard problem. We next consider the number of unwanted targets is bounded and prove that there does not exist an FPTAS in this case. Instead, we design a Polynomial-Time Approximation Scheme (PTAS) in which the allowable error can also be controlled. When the number of unwanted targets are not bounded, we provide a randomized algorithm, along with the analytical theoretical bound and inapproximaibility result. Finally, we consider a general case with many hops information propagation and further show its #P-hardness and propose an effective Iterative Circle of Trust Detection (ICTD) algorithm based on a novel greedy function. An extensive experiment on various real-world OSNs has validated the effectiveness of our proposed approximation and ICTD algorithms. Such an extensive experiment also highlights several important observations on information leakage which help to sharpen the security of OSNs in the future. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the selective graph coloring problem. Given an integer and a graph with a partition of V, it consists in deciding whether there exists a set in G such that for all , and such that the graph induced by is k-colorable. We investigate the complexity status of this problem in various classes of graphs. [Copyright &y& Elsevier]

Abstract: The reload cost concept refers to the cost that occurs at a vertex along a path on an edge-colored graph when it traverses an internal vertex between two edges of different colors. This cost depends only on the colors of the traversed edges. Reload costs arise in various applications such as transportation networks, energy distribution networks, and telecommunications. Previous work on reload costs focuses on two problems of finding a spanning tree with minimum cost with respect to two different cost measures. In both problems the cost is associated with a set of paths from a given vertex r to all the leaves of the constructed tree. The first cost measure is the sum of the reload costs of all paths from r to the leaves. The second cost measure is the changeover cost, in which the cost of traversing a vertex by using two specific incident edges is paid only once regardless of the number of paths traversing it. The first problem is inapproximable within any polynomial time computable function of the input size [1], and the second problem is inapproximable within for any [2]. In this paper we show that the first hardness result holds also for the second problem. Given this strong inapproximability result, we study the complexity and approximability properties of numerous special cases of this second problem. We mainly focus on bounded costs, and consider both directed and undirected graphs, bounded and unbounded number of colors, and both bounded and unbounded degree graphs. We also present polynomial time exact algorithms and an approximation algorithm for some special case. To the best of our knowledge, these are the first algorithms with a provable performance guarantee for the problem. Moreover, our approximation algorithm shows a tight bound on the approximability of the problem for a specific family of instances. [Copyright &y& Elsevier]

In a communication network one often needs to combine several communication requests into a path in a physical layer of the network. In these cases the cost is measured in terms of the total length of these paths or the total hardware cost of maintaining these paths. In this paper we consider a problem belonging to this general family of optimization problems. We consider the problem of minimizing the number of regenerators in optical networks with traffic grooming. In this problem we are given a network with an underlying topology of a graph G, a set of requests that correspond to paths in G and two positive integers g and d. There is a need to put a regenerator every d edges of every path, because of a degradation in the quality of the signal. Each regenerator can be shared by at most g paths, g being the grooming factor. On the one hand, we show that even in the case of d=1 the problem is APX- hard, i.e. a polynomial time approximation scheme for it does not exist (unless P=NP). On the other hand, we solve such a problem for general G and any d and g, by providing an O(log g)-approximation algorithm and thus extending previous results holding only for specific topologies and specific values of d or g. [ABSTRACT FROM AUTHOR]

In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks such that, for each edge e of P, the total demand of selected tasks that use e does not exceed the capacity of e. This is a well-studied problem that has been described under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack, and interval packing. We present a polynomial time constant-factor approximation algorithm for this problem. This improves on the previous best known approximation ratio of O(log n). The approximation ratio of our algorithm is 7 + ∈ for any ∈ > 0. We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves to optimality a special case of the problem of finding a maximum weight independent set of rectangles. In the setting of resource augmentation, wherein the capacities can be slightly violated, we give a (2 + ∈)-approximation algorithm. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either 1, 2, or 3. [ABSTRACT FROM AUTHOR]

In this article, we consider k-way vertex cut: the problem of finding a graph separator of a given size that decomposes the graph into the maximum number of components. Our main contribution is the derivation of an efficient polynomial-time approximation scheme for the problem on planar graphs. Also, we show that k-way vertex cut is polynomially solvable on graphs of bounded treewidth and fixed-parameter tractable on planar graphs with the size of the separator as the parameter. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 170-178 2014 [ABSTRACT FROM AUTHOR]

Abstract: This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine maximum lateness minimization problem when jobs have different release dates and tails (or delivery times) under the no idle time assumption (i.e., the schedule cannot contain any idle time between two consecutive jobs on the machine). Our work is motivated by interesting industrial applications to the production area (Chrétienne (2008) [3]). Our analysis shows that modifications of the classical algorithms of Potts and Schrage can lead to the same worst-case performance ratios obtained for the relaxed problem without the no idle time constraint. Then, we extend the result developed by Mastrolilli (2003) [13] for such a relaxed problem and we propose a polynomial time approximation scheme with efficient time complexity. [Copyright &y& Elsevier]

Abstract: Matching problems on bipartite graphs where the entities on one side may have different sizes are intimately related to scheduling problems with processing set restrictions. We survey the close relationship between these two problems, and give new approximation algorithms for the (NP-hard) variations of the problems in which the sizes of the jobs are restricted. Specifically, we give an approximation algorithm with an additive error of one when the sizes of the jobs are either 1 or 2, and generalise this to an approximation algorithm with an additive error of for the case where each job has a size taken from the set (for any constant integer ). We show that the above two problems become polynomial-time solvable if the processing sets are nested. [Copyright &y& Elsevier]

In heterogeneous networks, devices communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available ones, each device might establish several connections. A connection may be established when the devices at its endpoints share at least one active interface. In this paper, we consider two fundamental optimization problems. In the first one (Maximum Flow in Multi-Interface Networks, MFMI), we aim to establish the maximal bandwidth that can be guaranteed between two given nodes of the input network. In the second problem (Minimum-Cost Flow in Multi-Interface Networks, (MCFMI)), we look for activating the cheapest set of interfaces among a network to guarantee a minimum bandwidth $(B)$ of communication between two specified nodes. We show that MFMI is polynomially solvable while MCFMI is $(NP)$-hard even for a bounded number of different interfaces and bounded degree networks. Moreover, we provide polynomial approximation algorithms for MCFMI and exact algorithms for relevant subproblems. Finally, we experimentally analyze the proposed approximation algorithm, showing that in practical cases it guarantees a low approximation ratio. [ABSTRACT FROM PUBLISHER]

In complex scenes with many objects, collision detection plays a key role in the simulation performance. This is particularly true in fracture simulation for two main reasons. One is that fracture fragments tend to exhibit very intensive contact, and the other is that collision detection data structures for new fragments need to be computed on the fly. In this paper, we present novel collision detection algorithms and data structures for real-time simulation of fracturing rigid bodies. We build on a combination of well-known efficient data structures, namely, distance fields and sphere trees, making our algorithm easy to integrate on existing simulation engines. We propose novel methods to construct these data structures, such that they can be efficiently updated upon fracture events and integrated in a simple yet effective self-adapting contact selection algorithm. Altogether, we drastically reduce the cost of both collision detection and collision response. We have evaluated our global solution for collision detection on challenging scenarios, achieving high frame rates suited for hard real-time applications such as video games or haptics. Our solution opens promising perspectives for complex fracture simulations involving many dynamically created rigid objects. [ABSTRACT FROM AUTHOR]

A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows exponentially with the code length. Thus, the core problem that needs to be solved is that of faithfully approximating a bit-channel with an intractably large alphabet by another channel having a manageable alphabet size. We devise two approximation methods which “sandwich” the original bit-channel between a degraded and an upgraded version thereof. Both approximations can be efficiently computed and turn out to be extremely close in practice. We also provide theoretical analysis of our construction algorithms, proving that for any fixed \varepsilon > 0 and all sufficiently large code lengths n, polar codes whose rate is within \varepsilon of channel capacity can be constructed in time and space that are both linear in n. [ABSTRACT FROM AUTHOR]

With the growing application of wireless networks, there are increasing security issues. The forecasting technologies for network traffic are effectively used to deal with these emerging problems. However, because the wireless network traffic has several characteristics such as nonlinearity and bursty, the classical methods could be scarcely applied to the increasingly complicated wireless network traffic problems. Minimax Probability Machine (MPM) is a recently intelligent algorithm used to deal with model for wireless network traffic. Like global SVM, global MPM has the same shortcomings on the forecast accuracy and computational complexity. Therefore, a local MPM algorithm, LMPM, is proposed in this paper, and experimental results show that forecasting accuracy and real-time computing capability of LMPM are much better than that ofglobal MPM. [ABSTRACT FROM AUTHOR]

We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which may depend on the arc. This problem has recently been shown to be weakly NP -complete even on series-parallel graphs. In this article, we provide further complexity and approximability results for MFPMQ and several special cases. We first show that it is strongly NP -hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor. On series-parallel graphs, however, we present a pseudo-polynomial time dynamic programming algorithm for the problem. We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still weakly NP -complete on general graphs, but can be solved in strongly polynomial time on series-parallel graphs. On general graphs, we present a \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}(2-\frac{1}{\lambda})\end{align*}\end{document} -approximation algorithm for this case, where λ denotes the common minimum quantity of all arcs. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013 [ABSTRACT FROM AUTHOR]

In this letter, a fast backprojection algorithm (FBPA) is proposed for bistatic synthetic aperture radar imaging. For range compression, the signal recorded by the synchronization channel of the receiver on the ground is used as a matched filter to compress the echo signal. This method can reduce the requirements of satellite-orbit measurement and synchronization precision. For azimuth compression, a secondary phase correction is implemented to reduce the effect caused by the approximation involved in the FBPA. The computational complexity of the proposed algorithm is \O(\N^2.5). The proposed algorithm is applied in a graphics processing unit and verified by simulation and real raw data. [ABSTRACT FROM PUBLISHER]

Preintegrated volume rendering produces high-quality renderings without increased sampling rates. However, a look-up table of a conventional preintegrated volume rendering requires a dimensionality of two, which disturbs interactive renderings when the transfer function is changed. Furthermore, as the resolution of the volume data set increases, the memory space required is impractical or inefficient, especially on GPUs. In the past, several approximation methods have been proposed to reduce the complexity of both the time and memory requirement, but most of them do not correctly present thin opaque structures within slabs and ignore the self-attenuation. We propose an advanced interactive preintegrated volume rendering algorithm that achieves not only high-quality renderings comparable to the conventional ones, but also $(O(n))$ time and memory space requirements even with the self-attenuation within the slabs applied. The algorithm proposed in this paper decomposes the exponential term of the ray integration equation into a power series of a finite order in the form of a linear combination to build a one-dimensional look-up table. Moreover, the proposed algorithm effectively applies the self-attenuation that is caused by fully opaque isosurfaces, by introducing an opaque prediction table. Experimental results demonstrate that the proposed algorithm offers renderings visibly identical to existing preintegrated volume renderings without degrading rendering speed. [ABSTRACT FROM AUTHOR]

SUMMARY An improved algorithm is presented for a signal's direction of arrival estimation to reduce the computational complexity of the existing modified multiple signal classification (MMUSIC) algorithm. In this paper, FFT algorithm is introduced to narrow the searching range of the direction angle. Afterwards, a compromise approach-based SVD and orthogonal-triangular decomposition takes the place of traditional double SVDs. Then, during matrix calculation, the noise subspace is achieved for the signal's direction of arrival. Finally, the system simulation demonstrates the efficiency and reliability of this novel MMUSIC algorithm. Compared with the existing algorithm, MMUSIC effectively saves the computational complexity with the approximation estimation performance. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is OPT for a rectilinear polygon, our algorithm produces a guard set of size O( OPT). [ABSTRACT FROM AUTHOR]

Abstract: Shortest common supersequence and longest common subsequence are two widely used measures to compare sequences in different fields, from AI planning to Bioinformatics. Inspired by recently proposed variants of these two measures, we introduce a new version of the shortest common supersequence problem, where the solution is required to satisfy a given constraint on the number of occurrences of each symbol. First, we investigate the computational and approximation complexity of the problem, then we give a -approximation algorithm. Finally, we investigate the parameterized complexity of the problem, and we present a fixed-parameter algorithm. [Copyright &y& Elsevier]

Discrete Fourier transform (DFT) is widespread used in many fields of science and engineering. DFT is implemented with efficient algorithms categorized as fast Fourier transform. A fast algorithm is proposed for computing a length-N=6^m DFT. The proposed algorithm is a blend of radix-3 and radix-6 FFT. It is a variant of split radix and can be flexibly implemented a length 2^r\times 3^m DFT. Novel order permutation of sub-DFTs and reduction of the number of arithmetic operations enhance the practicability of the proposed algorithm. It inherently provides a wider choice of accessible FFT's lengths. [ABSTRACT FROM AUTHOR]