Algorithm Of Polynomial Complexity Research Articles

Complexity-Improved Sphere Decoder for MIMO Systems Using PSK Modulations

It has been shown in recent years that the iterative decoding techniques, improve performance (e.g., bit error rate) of various digital communication systems. Techniques of Multiple-Input Multiple-Output (MIMO) are a key technology to promote and achieve high-speed wireless communications. They demand only a low complexity system for detection since a high CPU processing involves more energy consumption and therefore less flexibility in mobility terms. The sphere decoding (SD) technique has been proposed as an effcient algorithm to solve this problem. SD is known to be an algorithm of polynomial complexity that has become a powerful tool to achieve a high performance close to that given by the maximum likelihood (ML) (which is considered ideal), but with less complexity. This paper proposes a modification to the SD technique in order to reduce its complexity named: improved Less Complexity SD (iLSD).

Algorithm for calculating the analytic solution for economic dispatch with multiple fuel units

The problem of economic dispatch with multiple fuel units has been widely addressed via different techniques using approximate methods due to the exponential complexity of full enumeration in the underlying combinatory problem. A method has recently been outlined by Min et al. (2008) [12], that allows the problem to be solved in an exact way in polynomial time. In this paper, we present an alternative technique and take this idea further, studying and comparing two algorithms of polynomial complexity: basic recurrence and divide-and-conquer. Moreover, we provide the exact solution to the problem by Lin and Viviani (1984) [1], that constitutes the traditional test for all approximate methods and present a comprehensive survey of several heuristic approaches.

Reply to Farina and Enoka: The Reconstruct-and-Test Approach Is the Most Appropriate Validation for Surface EMG Signal Decomposition to Date

reply: We thank Drs. Farina and Enoka for recognizing our surface electromyographic (sEMG) signal decomposition technology as being “impressive” and for appreciating that “the approach is far superior to even the most optimistic expectations in the field.” We will use this opportunity to assuage doubts they and others might have, to correct their misunderstanding, and to expand on the advantages of our accuracy verification approach. They begin by casting doubt on our algorithm's ability to resolve N overlapping action potentials in complex signal segments by relying on the notion that “global optimization of overlapping action potentials is a…NP-hard problem that cannot be solved by polynomial complexity algorithms.” To those not versed in complexity theory, the jargon of NP-hard (nondeterministic polynomial time-hard) can create the mistaken impression that such problems are impossible to solve in any practical way unless N is small (say N 95.2% on average) is an empirical validation that for relatively large values of N, a great preponderance of segments in real sEMG signals can be resolved correctly. They proceed to question the accuracy assessments we reported for our algorithm. They make four claims, each of which shows a major misunderstanding of our reconstruct-and-test approach.

Cross-Layer Design for Multihop Wireless Relaying Networks

Employing channel state information at the network layer, efficient routing protocols for equal-power and optimal-power allocation in a multihop network in fading are proposed. The end-to-end outage probability from source to destination is used as the optimization criterion. The problem of finding the optimal route is investigated under either known mean channel state information (CSI) or known instantaneous CSI. The analysis shows that the proposed routing strategy achieves full diversity order, equal to the total number of nodes in the network excluding the destination, only when instantaneous CSI is known and used. The optimal routing algorithm requires a centralized exhaustive search which leads to an exponential complexity, which is infeasible for large networks. An algorithm of polynomial complexity for a centralized environment is developed by reducing the search space. A distributed approach based on the Bellman-Ford routing algorithm is proposed which achieves a good implementation complexity-performance trade-off.

Cross-Layer Design for Multihop Wireless Relaying Networks

Employing channel state information at the network layer, efficient routing protocols for equal-power and optimal-power allocation in a multihop network in fading are proposed. The end-to-end outage probability from source to destination is used as the optimization criterion. The problem of finding the optimal route is investigated under either known mean channel state information (CSI) or known instantaneous CSI. The analysis shows that the proposed routing strategy achieves full diversity order, equal to the total number of nodes in the network excluding the destination, only when instantaneous CSI is known and used. The optimal routing algorithm requires a centralized exhaustive search which leads to an exponential complexity, which is infeasible for large networks. An algorithm of polynomial complexity for a centralized environment is developed by reducing the search space. A distributed approach based on the Bellman-Ford routing algorithm is proposed which achieves a good implementation complexity-performance trade-off.

Solution of some convex separable resource allocation and production planning problems with bounds on the variables

In this paper, we consider the problems of minimizing convex separable functions of two specific forms over a feasible region defined by a linear inequality or linear equality constraint, and two-sided bounds on the variables (box constraints). These problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems and in various practical problems, for example, resource allocation and production planning problems. Necessary and sufficient condition is proved for a feasible solution to be an optimal solution to a more general convex separable problem consisting in minimizing a strictly convex separable function subject to a linear inequality constraint and box constraints. Necessary and sufficient conditions for a feasible solution to be an optimal solution to the two problems under consideration are obtained as corollaries of this more general result. Iterative algorithms of polynomial complexity for solving such problems are proposed and their convergence is proved. Some examples and results of numerical experiments are also presented.

Integrated Power Controlled Rate Adaptation and Medium Access Control in Wireless Mesh Networks

In this paper, a new mathematical programming model and assignment algorithms are developed for minimizing the schedule length in adaptive power and adaptive rate link scheduling in spatial-TDMA wireless networks. The underlying problem entails the optimal joint scheduling of transmissions across multi-access communication links combined with the simultaneous allocation of transmit power levels and data rates across active links, while meeting required Signal-to-Interference-plus-Noise Ratio (SINR) levels at intended receivers. We prove that the problem can be modeled as a Mixed Integer-Linear Programming (MILP) and show that the latter yields a solution that consists of transmit power levels that are strongly Pareto Optimal. We note this problem to be NP-complete. For comparison purposes, we employ the MILP formulation for computing the optimal schedule for networks with small number of designated links and limited number of data rate levels. We proceed to develop and investigate a heuristic algorithm of polynomial complexity for solving the problem in a computationally effective manner. The algorithm is based on the construction of a Power Controlled Rate adaptation Interference Graph. The desired schedule is then derived by using a greedy algorithm to construct an independence set from this graph. Based on system analyses, we show, for smaller illustrative networks, the performance behavior realized by the heuristic algorithms to generally be in the 75 percentile of those attained by the optimal schedule. We also show that performance of our heuristic algorithm is on average 20% better than that attained under prior algorithms that were developed for use under fixed transmit power and fixed rate link scheduling.

Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints

A minimization problem with strictly convex separable objective function subject to a convex separable inequality constraint of the form “less than or equal to” and bounds on the variables is considered. Necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. An iterative algorithm of polynomial complexity for solving such problems is suggested and its convergence is proved. Modifications of this algorithm are proposed in connection with some extensions of the considered problem as well as in order to avoid some computational difficulties. Examples of important convex functions for the problem under consideration and computational results are presented.

Decentralized Diagnosis of Event-Driven Systems for Safely Reacting to Failures

We introduce the notion of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safe-codiagnosability</i> , extending the notion of safe-diagnosability (Paoli and Lafortune, 2005) to the decentralized setting. For a system, a certain subbehavior is deemed safe (captured via a safety specification), and a further subbehavior is deemed nonfaulty (captured via a nonfault specification). Safe-codiagnosability requires that when the system executes a trace that is faulty, there exists at least one diagnoser that can detect this within bounded delay and also before the safety specification is violated. The above notion of safe-codiagnosability may also be viewed as an extension of the notion of codiagnosability (Qiu and Kumar, 2006), where the latter did not have any safety requirement. We show that safe-codiagnosability is equivalent to codiagnosability together with ldquozero-delay codiagnosabilityrdquo of ldquoboundary safe tracesrdquo. (A safe trace is a boundary safe trace if there exists a single-event extension that is unsafe.) We give an algorithm of polynomial complexity for verifying safe-codiagnosability. For a safe-codiagnosable system, the same methods as those proposed in (Qiu and Kumar, 2006) can be applied for offline synthesis of individual diagnosers, as well as for online diagnosis using them.

Directed Control of Discrete Event Systems for Safety and Nonblocking

We introduce the notion of directed control, where a directed controller is one that selects at most one controllable event to be enabled at any instant. This is in contrast to supervisory control, where a supervisory controller enables a maximum allowable set of controllable events at any instant, i.e., no specific selection for executing an enabled event is made. While the design of a supervisory controller is meaningful for plants that are generator of controllable events, a directed controller design makes more sense for plants that are executor of controllable events. The control goal is the same as that in a supervisory control setting, namely, safety and nonblockingness. A safe and nonblocking directed controller exists if and only if a safe and nonblocking supervisory controller exists, thereby proving the polynomiality of verifying existence. We also develop a set of algorithms of polynomial complexity to compute a safe and nonblocking directed controller (whenever one exists).

Multi-cost job routing and scheduling in Grid networks

A key problem in Grid networks is how to efficiently manage the available infrastructure, in order to satisfy user requirements and maximize resource utilization. This is in large part influenced by the algorithms responsible for the routing of data and the scheduling of tasks. In this paper, we present several multi-cost algorithms for the joint scheduling of the communication and computation resources that will be used by a Grid task. We propose a multi-cost scheme of polynomial complexity that performs immediate reservations and selects the computation resource to execute the task and determines the path to route the input data. Furthermore, we introduce multi-cost algorithms that perform advance reservations and thus also find the starting times for the data transmission and the task execution. We initially present an optimal scheme of non-polynomial complexity and by appropriately pruning the set of candidate paths we also give a heuristic algorithm of polynomial complexity. Our performance results indicate that in a Grid network in which tasks are either CPU- or data-intensive (or both), it is beneficial for the scheduling algorithm to jointly consider the computational and communication problems. A comparison between immediate and advance reservation schemes shows the trade-offs with respect to task blocking probability, end-to-end delay and the complexity of the algorithms.

Routing and scheduling connections in networks that support advance reservations

A key problem in networks that support advance reservations is the routing and time scheduling of connections with flexible starting time and known data transfer size. In this paper we present a multicost routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the data should start and end transmission at each link so as to minimize the reception time at the destination, or optimize some other performance criterion. The utilization profiles of the network links, the link propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm. We initially present a scheme of non-polynomial complexity to compute a set of so-called non-dominated candidate paths, from which the optimal path can be found. We then propose two mechanisms to appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of polynomial complexity. We examine the performance of the algorithms in the special case of an Optical Burst Switched network. Our results indicate that the proposed polynomial-time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network propagation delays and link-state update policies have on performance.

On the numerical evaluation of one-loop amplitudes: the gluonic case

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules, tree amplitudes are constructed using recursive relations. The tree amplitudes are then used to build one-loop amplitudes using an integer dimension on-shell cut method. As a first application we considered only three and four gluon vertices calculating the pure gluonic one-loop amplitudes for arbitrary external helicity or polarization states. We compare our numerical results to analytical results in the literature, analyze the time behavior of the algorithm and the accuracy of the results, and give explicit results for fixed phase space points for up to twenty external gluons.

Convex separable minimization with box constraints

AbstractA minimization problem with convex separable objective function subject to a convex separable inequality constraint of the form “less than or equal to” and bounds on the variables (box constraints) is considered. Necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. An iterative algorithm of polynomial complexity for solving problems of the considered form is suggested and its convergence is proved. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

An Optimal Directed Control Framework for Discrete Event Systems

In an earlier paper, we introduced the notion of directed control, where a directed controller, which is simply referred to as a director, is one that selects at most one controllable event to be enabled at any instant. In this paper, we develop an optimization-based approach for the design of a director: starting from any state, the worst cost to the nearest reachable marked state is minimized. The motivation is that a pending task can be completed in the least possible cost. A necessary and sufficient condition for the existence of an optimal director is obtained. Furthermore, for systems that are cycle-free, we provide an algorithm of polynomial complexity to compute an optimal director.

Optimum Integrated Link Scheduling and Power Control for Multihop Wireless Networks

In this paper, a new mathematical programming formulation is developed for minimizing the schedule length in multihop wireless networks based on the optimal joint scheduling of transmissions across multi-access communication links and the allocation of transmit power levels while meeting the requirements on the signal-to-interference-plus-noise ratio at intended receivers. The authors prove that the problem can be represented as a mixed-integer linear programming (MILP) and show that the latter yields a solution that consists of transmit power levels that are strongly Pareto optimal. It was demonstrated that the MILP formulation can be used effectively to derive optimal scheduling and power levels for networks with as many as 30 designated communication links. The authors show that the MILP formulation can also be effectively solved to provide upper and lower bounds (corresponding to an approximation factor Delta) for the optimum schedule length of networks with as many as 100 designated links. It is proved that the integrated link scheduling and power control problem (ILSP) is NP-complete. Consequently, a heuristic algorithm of polynomial complexity is developed and investigated for solving the problem in a timely and practical manner. The algorithm is based on the properties of a novel interference i.e., the generalized power-based interference graph, whose chromatic and independence numbers provide fundamental bounds for the ILSP. It is demonstrated that the frame length of schedules realized by the heuristic scheme resides in the 25th percentile of those attained by the optimal mechanism for randomly generated topologies with as many as 30 designated communication links. Furthermore, it is shown that the algorithm significantly outperforms a corresponding algorithm presented in the literature

Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pentagrid Ising model and on overlapping unit cells in three dimensions and how these works can be utilized once more detailed results for pair correlations in, e.g., the eight-vertex model or the chiral Potts model or even threedimensional Yang-Baxter integrable models become available.

Branching bisimulation for probabilistic systems: Characteristics and decidability

We address the concept of abstraction in the setting of probabilistic reactive systems, and study its formal underpinnings for the strictly alternating model of Hansson. In particular, we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations, viz. coloured trace equivalence and branching bisimilarity using maximal probabilities. We show that both alternatives coincide with branching bisimilarity. The alternative characterisations have their own merits and focus on different aspects of branching bisimilarity. Coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler. Branching bisimilarity, rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence. Together they give a better understanding of branching bisimilarity. Furthermore, we show that the notions of branching bisimilarity in the alternating model of Hansson and in the non-alternating model of Segala differ: branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar.

Diagnosability of Semiconductor Manufacturing Equipment

Diagnosis of discrete event systems such as complex semiconductor manufacturing equipment has become more and more difficult such that it cannot be performed based on experience. Systematic approaches for the diagnosis problem are urgently needed. In this paper, we present an algorithm of polynomial complexity in the number of nodes for computing a sufficient condition of diagnosability of semiconductor manufacturing equipment modeled by Petri nets. Our algorithm is more efficient than previous ones since no state enumeration is necessary. This gives us an advantage to solve large real-world problems. Our algorithm is formulated as a linear programming problem, which is well-known to be of polynomial complexity in the worst case. We use a Metal-Organic Vapor Phase Epitaxy system that is simplified from real-world semiconductor manufacturing equipment applications to illustrate our proposed approach.

Amplitude quanta in multiparticle-system simulation

An algorithmic approach to theoretical quantum physics is described postulating that any multiparticle quantum evolution can be simulated by classical algorithms of polynomial complexity. Its implementation is presented that is based on the concept of an amplitude quantum, i.e., the smallest carrier of amplitude. As a consequence, the Born rule for quantum probability is derived within the classical urn scheme. Decoherence is treated as stemming from the inherently limited amount of computational resources available for multiparticle simulation. The algorithmic approach denies the possibility of creating a scalable quantum computer. It is therefore refutable by construction of such a computer.