Algorithms for quadratic forms

We present algorithms for square classes, quadratic forms and Witt classes of quadratic forms over the field of rational functions of one variable over the reals. The algorithms are capable of: finding the unique representative of a square class, deciding if a given function is a square or a sum of squares and deciding if a quadratic form is isotropic or hyperbolic. Moreover we propose a representation for Witt classes of quadratic forms. With this representation one can manipulate Witt classes without operating directly on their coefficients. We present algorithms both for computing this representation and manipulating Witt classes.     

Detection of global predicates: Techniques and their limitations

Summary. We show that the problem of predicate detection in distributed systems is NP-complete. In the past, efficient algorithms have been developed for special classes of predicates such as stable predicates, observer independent predicates, and conjunctive predicates. We introduce a class of predicates, semi-linear predicates, which properly contains all of the above classes. We first discuss stable, observer independent and semi-linear classes of predicates and their relationships with each other. We also study closure properties of these classes with respect to conjunction and disjunction. Finally, we discuss algorithms for detection of predicates in these classes. We provide a non-deterministic detection algorithm for each class of predicate. We show that each class can be equivalently characterized by the degree of non-determinism present in the algorithm. Stable predicates are defined as those that can be detected by an algorithm with the most non-determinism. All other classes can be derived by appropriately constraining the non-determinism in this algorithm.     

A performance study of uplink scheduling algorithms in point-to-multipoint WiMAX networks

The IEEE 802.16 standard defines the specifications for medium access control (MAC) and physical (PHY) layers of WiMAX networks. A critical part of the MAC layer specification is packet scheduling, which resolves contention for bandwidth and determines the transmission order of users. Evaluating the performance packet scheduling algorithms is of utmost importance towards realizing large-scale WiMAX deployment. In this paper, we conduct a comprehensive performance study of scheduling algorithms in point-to-multipoint mode of OFDM-based WiMAX networks. We first make a classification of WiMAX scheduling algorithms, then simulate a representative number of algorithms in each class taking into account that vital characteristics of the IEEE 802.16 MAC layer and OFDM physical layer. We evaluate the algorithms with respect to their abilities to support multiple classes of service, providing quality of service (QoS) guarantees, fairness amongst service classes and bandwidth utilization. To the best of our knowledge, no such comprehensive performance study has been reported in the literature. Simulation results indicate that none of the current algorithms is capable of effectively supporting all WiMAX classes of service. We demonstrate that an efficient, fair and robust scheduler for WiMAX is still an open research area. We conclude our study by making recommendations that can be used by WiMax protocol designers.     

On the Vapnik-Chervonenkis dimension of computer programs which use transcendental elementary operations

We exhibit upper bounds for the Vapnik-Chervonenkis (VC) dimension of a wide family of concept classes that are defined by algorithms using analytic Pfaffian functions. We give upper bounds on the VC dimension of concept classes in which the membership test for whether an input belongs to a concept in the class can be performed either by a computation tree or by a circuit with sign gates containing Pfaffian functions as operators. These new bounds are polynomial both in the height of the tree and in the depth of the circuit. As consequence we obtain polynomial VC dimension not also for classes of concepts whose membership test can be defined by polynomial time algorithms but also for those defined by well-parallelizable sequential exponential time algorithms.     

Elastic threshold-based admission control for QoS satisfaction with reward optimization for servicing multiple priority classes in wireless networks

We analyze performance characteristics of a class of call admission control (CAC) algorithms designed for servicing multiple priority classes in wireless networks with the goal of quality of service (QoS) satisfaction and reward optimization. By reward, we mean some sort of “value” obtained by the system as a result of servicing multiple priority classes. In this paper we design and evaluate the performance of a new algorithm, elastic threshold-based CAC, in terms of the maximum reward obtainable with QoS satisfaction from servicing multiple priority classes with distinct QoS requirements, and compare it with existing partitioning, threshold, and spillover CAC algorithms. We also develop a heuristic-based search method to determine the best threshold-value sets used for multiple service classes by sequentially adjusting these thresholds based on the reward and rejection rate obtainable vs. QoS constraints of each service class. We demonstrate through test cases and simulation that elastic threshold-based CAC outperforms existing CAC algorithms for QoS satisfaction and reward optimization in solution optimality for serving multiple QoS service classes in wireless networks.     

Optimal reconfiguration algorithms for real-time fault-tolerantprocessor arrays

In this paper we consider the problem of reconfiguring processor arrays subject to computational loads that alternate between two modes. A strict mode is characterized by a heavy computational load and severe constraints on response time while a relaxed mode is characterized by a relatively light computational load and relaxed constraints on response time. In the strict mode, reconfiguration is performed by a distributed local algorithm in order to achieve fast recovery from faults. In the relaxed mode, a global reconfiguration algorithm is used to restore the system to a state that maximizes the probability that future faults occurring in subsequent strict modes will be repairable. Several new results are given for this problem. Efficient reconfiguration algorithms are described for a number of general classes of architectures. These general algorithms obviate the need for architecture-specific algorithms for architectures in these classes. We show that it is unlikely that similar algorithms can be obtained for related classes of architectures since the reconfiguration problem for these classes is NP-complete. Finally, a general approximation algorithm is described that can be used for any architecture. Experimental results are given, suggesting that our algorithms are very effective     

Optimal and Efficient Algorithms for Summing and Prefix Summing on Parallel Machines

The problem of designing efficient parallel algorithms for summing and prefix summing for certain classes of the LogP model is studied. We present optimal algorithms for summing and show that any optimal summing algorithm must have a certain inherent structure. Moreover, we present optimal or near-optimal algorithms for prefix summing for both non-commutative and commutative binary operators. Furthermore, we show that the optimal algorithms for prefix summing for these two types of operators are not equivalent.     

Symbolic computation with sequences

We present several classes of univariate sequences and sketch some algorithms for computing with sequences from these classes. The text was submitted by the author in English.     

Computing minimum distortion embeddings into a path for bipartite permutation graphs and threshold graphs

The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent stoc and soda conferences. So far, all such results concern approximation algorithms or exponential-time exact algorithms. We give the first polynomial-time algorithms for computing minimum distortion embeddings of graphs into a path when the input graphs belong to specific graph classes. In particular, we solve this problem in polynomial time for bipartite permutation graphs and threshold graphs. For both graph classes, the distortion can be arbitrarily large. The graphs that we consider are unweighted.     

Detecting moving shadows: algorithms and evaluation

Moving shadows need careful consideration in the development of robust dynamic scene analysis systems. Moving shadow detection is critical for accurate object detection in video streams since shadow points are often misclassified as object points, causing errors in segmentation and tracking. Many algorithms have been proposed in the literature that deal with shadows. However, a comparative evaluation of the existing approaches is still lacking. In this paper, we present a comprehensive survey of moving shadow detection approaches. We organize contributions reported in the literature in four classes two of them are statistical and two are deterministic. We also present a comparative empirical evaluation of representative algorithms selected from these four classes. Novel quantitative (detection and discrimination rate) and qualitative metrics (scene and object independence, flexibility to shadow situations, and robustness to noise) are proposed to evaluate these classes of algorithms on a benchmark suite of indoor and outdoor video sequences. These video sequences and associated "ground-truth" data are made available at http://cvrr.ucsd.edu/aton/shadow to allow for others in the community to experiment with new algorithms and metrics.     

Empirical analysis of search based algorithms to identify change prone classes of open source software

There are numerous reasons leading to change in software such as changing requirements, changing technology, increasing customer demands, fixing of defects etc. Thus, identifying and analyzing the change-prone classes of the software during software evolution is gaining wide importance in the field of software engineering. This would help software developers to judiciously allocate the resources used for testing and maintenance. Software metrics can be used for constructing various classification models which can be used for timely identification of change prone classes. Search based algorithms which form a subset of machine learning algorithms can be utilized for constructing prediction models to identify change prone classes of software. Search based algorithms use a fitness function to find the best optimal solution among all the possible solutions. In this work, we analyze the effectiveness of hybridized search based algorithms for change prediction. In other words, the aim of this work is to find whether search based algorithms are capable for accurate model construction to predict change prone classes. We have also constructed models using machine learning techniques and compared the performance of these models with the models constructed using Search Based Algorithms. The validation is carried out on two open source Apache projects, Rave and Commons Math. The results prove the effectiveness of hybridized search based algorithms in predicting change prone classes of software. Thus, they can be utilized by the software developers to produce an efficient and better developed software.     

Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows

We examine the performance in terms of computing time of different parallel AMG algorithms that are applied within the context of industrial computational fluid dynamics (CFD) problems. We give an overview over the most important classes of algorithms described in literature, pick out four fundamentally different algorithms and perform numerical experiments on up to 16 processors with two benchmarks representing an important class of CFD-problems. The results indicate that aggregation-based algorithms have advantages compared to algorithms based on the concept of C–F-splitting.     

Learning algorithms for feedforward networks based on finitesamples

We present two classes of convergent algorithms for learning continuous functions and regressions that are approximated by feedforward networks. The first class of algorithms, applicable to networks with unknown weights located only in the output layer, is obtained by utilizing the potential function methods of Aizerman et al. (1970). The second class, applicable to general feedforward networks, is obtained by utilizing the classical Robbins-Monro style stochastic approximation methods (1951). Conditions relating the sample sizes to the error bounds are derived for both classes of algorithms using martingale-type inequalities. For concreteness, the discussion is presented in terms of neural networks, but the results are applicable to general feedforward networks, in particular to wavelet networks. The algorithms can be directly adapted to concept learning problems.     

On the correspondence between AVL trees and brother trees

We discuss the relationships of the classes of height-balanced (search) trees and the classes of brother (search) trees. In particular we characterize each class of height-balanced trees in terms of the class of “corresponding” brother trees and vice versa. Secondly, we show how this characterization leads to the notion of nonstandard updating algorithms. We derive a nonstandard insertion algorithm for height-balanced search trees to illustrate the notion. Finally we consider something of the similarities and differences between the standard and nonstandard insertion algorithms for height-balanced search rees.     

Interval arithmetic block cyclic reduction on vector computers

We introduce several algorithms for interval arithmetic block cyclic reduction for efficient application to vector computers under the condition that interval arithmetic inclusion properties be preserved. Interval arithmetic block cyclic reduction is used as part of almost globally convergent Newton-like methods for some classes of large nonlinear systems of equations. We further introduce truncated variants of the above algorithms and discuss their integration into nonlinear methods. We report numerical results carried out on a CRAY-1/M.     

Self-protected quantum algorithms based on quantum state tomography

Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new quantum algorithms are given which are based on quantum state tomography. These include an algorithm for the calculation of several quantum mechanical expectation values and an algorithm for the determination of polynomial factors. These quantum algorithms are important in their own right. However, it is remarkable that these quantum algorithms are immune to a large class of errors. We describe these algorithms and provide conditions for immunity.      

A Case Study in Real-Time Parallel Computation: Correcting Algorithms

A correcting algorithm is one that receives an endless stream of correc- tions to its initial input data and terminates when all the corrections received have been taken into account. We give a characterization of correcting algorithms based on the theory of data-accumulating algorithms. In particular, it is shown that any correcting algorithm exhibits superunitary behavior in a parallel computation setting if and only if the static counterpart of that correcting algorithm manifests a strictly superunitary speedup. Since both classes of correcting and data-accumulating algorithms are included in the more general class of real-time algorithms, we show in fact that many problems from this class manifest superunitary behavior. Moreover, we give an example of a real-time parallel computation that pertains to neither of the two classes studied (namely, correcting and data-accumulating algorithms), but still manifests superunitary behavior. Because of the aforementioned results, the usual measures of performance for parallel algorithms (that is, speedup and efficiency) lose much of their ability to convey effectively the nature of the phenomenon taking place in the real-time case. We propose therefore a more expressive measure that captures all the relevant parameters of the computation. Our proposal is made in terms of a graphical representation. We state as an open problem the investigation of such a measure, including finding an analytical form for it.     

New Tractable Classes From Old

The constraint satisfaction problem is known to be NP-hard in general, but a number of restrictions of the problem have been identified over the years which ensure tractability. This paper introduces two simple methods of combining two or more tractable classes over disjoint domains, in order to synthesise larger, more expressive tractable classes. We demonstrate that the classes so obtained are genuinely novel, and have not been previously identified. In addition, we use algebraic techniques to extend the tractable classes which we identify, and to show that the algorithms for solving these extended classes can be less than obvious.     

Simple On-Line Algorithms for the Maximum Disjoint Paths Problem

In this paper we study the classical problem of finding disjoint paths in graphs. This problem has been studied by a number of authors both for specific graphs and general classes of graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of on-line algorithms, not much is known about how well on-line algorithms can perform in the general setting. The best results obtained so far use the expansion of a network to measure the algorithms performance. We use a different parameter called the routing number that, as we will show, allows more precise results than the expansion. It enables us to prove tight upper and lower bounds for deterministic on-line algorithms. The upper bound is obtained by surprisingly simple greedy-like algorithms. Interestingly, our upper bound on the competitive ratio is even better than the best previous approximation ratio for off-line algorithms. Furthermore, we introduce a refined variant of the routing number and show that this variant allows us, for some classes of graphs, to construct on-line algorithms with a competitive ratio significantly below the best possible upper bound that could be obtained using the routing number or the expansion of a network only. We also show that our on-line algorithms can be transformed into efficient algorithms for the more general unsplittable flow problem.     

Parsers for indexed grammars

Three classes of parsable indexed grammars are defined. The new parsing mechanisms are derived by extending those that have been most successful for contextfree grammars, the LR and LL algorithms. Design criteria for the new grammar classes include membership decidability and unambiguity. We show that all three parsers operate in linear time for at least some grammars in our new classes. One of our new classes generates all the deterministic contextfree languages, along with some noncontextfree languages. We also show that the flag strings generated by indexed grammars are regular sets. This is done by showing that they can be generated by regular canonical systems.