A parameterized view on matroid optimization problems

Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial n^O(k)$n^{O\left(k\right)}$ time brute force algorithm for finding a k$k$-element solution, we try to give algorithms with uniformly polynomial (i.e., f(k)⋅n^O(1)$f\left(k\right)\cdot n^{O\left(1\right)}$) running time. The main result is that if the ground set of a represented linear matroid is partitioned into blocks of size ?$?$, then we can determine in randomized time f(k,?)⋅n^O(1)$f(k,?)\cdot n^{O\left(1\right)}$ whether there is an independent set that is the union of k$k$ blocks. As a consequence, algorithms with similar running time are obtained for other problems such as finding a k$k$-element set in the intersection of ?$?$ matroids, or finding k$k$ terminals in a network such that each of them can be connected simultaneously to the source by ?$?$ disjoint paths.     

Compositional analysis for verification of parameterized systems

Many safety-critical systems that have been considered by the verification community are parameterized by the number of concurrent components in the system, and hence describe an infinite family of systems. Traditional model checking techniques can only be used to verify specific instances of this family. In this paper, we present a technique based on compositional model checking and program analysis for automatic verification of infinite families of systems. The technique views a parameterized system as an expression in a process algebra (CCS) and interprets this expression over a domain of formulas (modal mu-calculus), considering a process as a property transformer. The transformers are constructed using partial model checking techniques. At its core, our technique solves the verification problem by finding the limit of a chain of formulas. We present a widening operation to find such a limit for properties expressible in a subset of modal mu-calculus. We describe the verification of a number of parameterized systems using our technique to demonstrate its utility.     

A unified approach to analyzing models of cellular communication networks with data call buffering

A unified approach to the analysis of models of cellular communication networks with queues of data calls was developed. Consideration was given to the models with two types of strategies for admission to the cell channels and the buffer. In one strategy, admission to the voice call channels is based on reservation of channels for handover of calls of the given type, and in the other strategy, on the scheme of truncating the calls of the given type. In both models, the strategy of buffer admission by the data calls relies on the scheme of place reservation for handover of the calls of the given type. The models with finite and infinite data call queues were studied. For different admission strategies, algorithms to calculate the servicing performance indices were given, and the results of their comparative analysis were presented.     

A unified view of class-selection with probabilistic classifiers

The possibility of selecting a subset of classes instead of one unique class for assignation is of great interest in many decision making systems. Selecting a subset of classes instead of singleton allows to reduce the error rate and to propose a reduced set to another classifier or an expert. This second step provides additional information, and therefore increases the quality of the result. In this paper, a unified view of the problem of class-selection with probabilistic classifiers is presented. The proposed framework, based on the evaluation of the probabilistic equivalence, allows to retrieve class-selective frameworks that have been proposed in the literature. We also describe an approach in which the decision rules are compared by the help of a normalized area under the error/selection curve. It allows to get a relative independence of the performance of a classifier without reject option, and thus a reliable class-selection decision rule evaluation. The power of this generic proposition is demonstrated by evaluating and comparing it to several state of the art methods on nine real world datasets, and four different probabilistic classifiers.     

Approximated parameterized verification of infinite-state processes with global conditions

We present a simple and effective approximated backward reachability procedure for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. The procedure operates on an over-approximation of the transition system induced by the parameterized system. We verify mutual exclusion for complex protocols such as atomic, non-atomic and distributed versions of Lamport’s bakery algorithm.     

A unified presentation of some urn models

For a sequence ofm urns we investigate how the number of urns satisfying a certain condition (e.g., being empty) evolves in time when after each time unit a ball is thrown. We show for a variety of urn models that this process (suitably normalized) converges weakly to a Gaussian process. The first and third authors’ work was supported by the Austrian Science Foundation FWF, Grant P10187-MAT. The second author was also supported by the Austrian-French project AMADEUS No. 97049. Online publication September 22, 2000.     

A unified formalization of four shared-memory models

The authors present a data-race-free-1, shared-memory model that unifies four earlier models: weak ordering, release consistency (with sequentially consistent special operations), the VAX memory model, and data-race-free-0. Data-race-free-1 unifies the models of weak ordering, release consistency, the VAX, and data-race-free-0 by formalizing the intuition that if programs synchronize explicitly and correctly, then sequential consistency can be guaranteed with high performance in a manner that retains the advantages of each of the four models. Data-race-free-1 expresses the programmer's interface more explicitly and formally than weak ordering and the VAX, and allows an implementation not allowed by weak ordering, release consistency, or data-race-free-0. The implementation proposal for data-race-free-1 differs from earlier implementations by permitting the execution of all synchronization operations of a processor even while previous data operations of the processor are in progress. To ensure sequential consistency, two sychronizing processors exchange information to delay later operations of the second processor that conflict with an incomplete data operation of the first processor     

A unified view of the complexity of evaluation and interpolation

Summary Four problems are considered: 1) from an n-precision integer compute its residues modulo n single precision primes; 2) from an n-degree polynomial compute its values at n points; 3) from n residues compute the unique n-precision integer congruent to the residues; 4) from n points compute the unique interpolating polynomial through those points. If M (n) is the time for n-precision integer multiplication, then the time for problems 1 and 2 is shown to be M (n) log n and for problems 3 and 4 to be M (n) (log n) ². Moreover it is shown that each of the four algorithms are really all instances of the same general algorithm. Finally it is shown how preconditioning or a change of domain will reduce the time for problems 3 and 4 to M (n) (log n).This research was supported by the National Science Foundation under grant GJ-33169.     

A logic of argumentation for specification and verification of abstract argumentation frameworks

In this paper, we propose a logic of argumentation for the specification and verification (LA4SV) of requirements on Dung??s abstract argumentation frameworks. We distinguish three kinds of decision problems for argumentation verification, called extension verification, framework verification, and specification verification respectively. For example, given a political requirement like ??if the argument to increase taxes is accepted, then the argument to increase services must be accepted too,?? we can either verify an extension of acceptable arguments, or all extensions of an argumentation framework, or all extensions of all argumentation frameworks satisfying a framework specification. We introduce the logic of argumentation verification to specify such requirements, and we represent the three verification problems of argumentation as model checking and theorem proving properties of the logic. Moreover, we recast the logic of argumentation verification in a modal framework, in order to express multiple extensions, and properties like transitivity and reflexivity of the attack relation. Finally, we introduce a logic of meta-argumentation where abstract argumentation is used to reason about abstract argumentation itself. We define the logic of meta-argumentation using the fibring methodology in such a way to represent attack relations not only among arguments but also among attacks. We show how to use this logic to verify the requirements of argumentation frameworks where higher-order attacks are allowed [A preliminary version of the logic of argumentation compliance was called the logic of abstract argumentation?(2005).]     

A unified view on lifetime distributions arising from selection mechanisms

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In constructing this model, we assume that the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. This function has an important role in the selection procedure as well as in computing the conditional personal cure rate. Finally, we illustrate how various models can be deduced as special cases of the proposed model.     

Formal specification and compositional verification of an atomic broadcast protocol

We apply a formal method based on assertions to specify and verify an atomic broadcast protocol. The protocol is implemented by replicating a server process on all processors in a network. We show that the verification of the protocol can be done compositionally by using specifications in which timing is expressed by local clock values. First the requirements of the protocol are formally described. Next the underlying communication mechanism, the assumptions about local clocks, and the failure assumptions are axiomatized. Also the server process is represented by a formal specification. Then we verify that parallel execution of the server processes leads to the desired properties by proving that the conjunction of all server specifications and the axioms about the system implies the requirements of the protocol.     

Probabilistic verification of communication protocols

Complete behavior of a communication protocol can be very large. It is worth investigating whether partial exploration of the behavior generates reasonable results. We present such a procedure which performs partial exploration using most-probable-first search. Some of the ideas used in this procedure are based on a convolutional decoding procedure due to Jelinek and a performance evaluation procedure due to Rudin. Multiple trees of protocol behavior are constructed. Some results on estimating the probability of encountering an unexplored state in a finite run of a protocol are also presented. Nicholas F. Maxemchuk received the B.S.E.E. degree from the City College of New York, NY, and the M.S.E.E. and Ph.D. degrees from the University of Pennsylvania, Philadelphia. He is the Head of the Distributed Systems Research Department at AT & T Bell Laboratories, Murray Hill, NJ, and has been at AT & T Bell Laboratories since 1976. Prior to joining Bell Laboratories he was at the RCA David Sarnoff Research Center in Princeton, NJ for eight years. Dr. Maxemchuk has been on the adjunct faculties of Columbia University and the University of Pennsylvania. He has been an advisor to the United Nations on data networking and has been on networking panels for the US Air Force and DARPA. He has served as the Editor for Data Communications for the IEEE Transactions on Communications, as a Guest Editor for the IEEE Journal on Selected Areas in Communications, and has been on the program committee for numerous conferences and workshops. He was awarded the RCA Laboratories Outstanding Achievement Award, the Bell Laboratories Distinguished Technical Staff Award, and the IEEE's 1985 and 1987 Leonard G. Abraham Prize Paper Award. Krishan Sabnani received a BSEE degree from Indian Institute of Technology, New Delhi, India and a PhD degree from Columbia University, New York, NY. In 1981, he joined AT & T Bell Laboratories after graduating from Columbia University. He is currently working in the Distributed Systems Research Department of AT & T Bell Laboratories. His major area of interest is communication protocols. Dr. Sabnani was a co-chairman of the Eighth International Symposium on Protocol Specification, Testing, and Verification held in Atlantic City, NJ during June 1988. He is currently an editor of the IEEE Transactions on Communications and of the IEEE Transactions on Computers. He has served on the program committees of several conferences. He is also a guest editor of two special issues of the Journal on Selected Areas in Communications (JSAC) and the Computer Networks and ISDN Systems Journal, respectively.     

Designing energy efficient communication runtime systems: a view from PGAS models

As the march to the exascale computing gains momentum, energy consumption of supercomputers has emerged to be the critical roadblock. While architectural innovations are imperative in achieving computing of this scale, it is largely dependent on the systems software to leverage the architectural innovations. Parallel applications in many computationally intensive domains have been designed to leverage these supercomputers, with legacy two-sided communication semantics using Message Passing Interface. At the same time, Partitioned Global Address Space Models are being designed which provide global address space abstractions and one-sided communication for exploiting data locality and communication optimizations. PGAS models rely on one-sided communication runtime systems for leveraging high-speed networks to achieve best possible performance. In this paper, we present a design for Power Aware One-Sided Communication Llibrary – PASCoL. The proposed design detects communication slack, leverages Dynamic Voltage and Frequency Scaling (DVFS), and Interrupt driven execution to exploit the detected slack for energy efficiency. We implement our design and evaluate it using synthetic benchmarks for one-sided communication primitives, Put, Get, and Accumulate and uniformly noncontiguous data transfers. Our performance evaluation indicates that we can achieve significant reduction in energy consumption without performance loss on multiple one-sided communication primitives. The achieved results are close to the theoretical peak available with the experimental test bed.     

A unified view of the apriori-based algorithms for frequent episode discovery

Frequent episode discovery framework is a popular framework in temporal data mining with many applications. Over the years, many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper, we present a unified view of all the apriori-based discovery methods for serial episodes under these different notions of frequencies. Specifically, we present a unified view of the various frequency counting algorithms. We propose a generic counting algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies, and we present quantitative relationships among different frequencies. Our unified view also helps in obtaining correctness proofs for various counting algorithms as we show here. It also aids in understanding and obtaining the anti-monotonicity properties satisfied by the various frequencies, the properties exploited by the candidate generation step of any apriori-based method. We also point out how our unified view of counting helps to consider generalization of the algorithm to count episodes with general partial orders.     

A truncated Levenberg-Marquardt algorithm for the calibration of highly parameterized nonlinear models

We propose a modification to the Levenberg-Marquardt minimization algorithm for a more robust and more efficient calibration of highly parameterized, strongly nonlinear models of multiphase flow through porous media. The new method combines the advantages of truncated singular value decomposition with those of the classical Levenberg-Marquardt algorithm, thus enabling a more robust solution of underdetermined inverse problems with complex relations between the parameters to be estimated and the observable state variables used for calibration. The truncation limit separating the solution space from the calibration null space is re-evaluated during the iterative calibration process. In between these re-evaluations, fewer forward simulations are required, compared to the standard approach, to calculate the approximate sensitivity matrix. Truncated singular values are used to calculate the Levenberg-Marquardt parameter updates, ensuring that safe small steps along the steepest-descent direction are taken for highly correlated parameters of low sensitivity, whereas efficient quasi-Gauss-Newton steps are taken for independent parameters with high impact. The performance of the proposed scheme is demonstrated for a synthetic data set representing infiltration into a partially saturated, heterogeneous soil, where hydrogeological, petrophysical, and geostatistical parameters are estimated based on the joint inversion of hydrological and geophysical data.     

Fault tolerant computing and reliable communication: A unified approach

We define and study varying-structure linear systems (VLS) over finite Abelian groups. All the VLS computational procedures are very fast with upper bounds on the number of computer operations similar to that of fast Fourier transform algorithms over groups. Specially designed VLS process n-vectors in linear (in n) number of computer operations. These systems are used in problems related to information channels (optimal estimation of noise-corrupted signals) and computation channels (error detection). We consider problems of optimal synthesis procedures of such systems relative to two easily computed criteria. The best approximation problem of classical systems by VLS also is studied. It is shown that the VLS constitute a class of suboptimal systems from which approximations can be found to a given information and/or computation channel. The approach chosen for these two channel types is unified. Information channel problems are usually solved in Euclidean type norms, whereas computation channel problems are dealt with via the generalized Hamming distance.     

A unified view of product-form approximation techniques for general closed queueing networks

Two major approximate techniques have been proposed for the analysis of general closed queueing networks, namely the aggregation method and Marie's method. The idea of the aggregation technique is to replace a subsystem (a subnetwork) by a flow equivalent single-server with load-dependent service rates. The parameters of the equivalent server are obtained by analyzing the subsystem in isolation as a closed system with different populations. The idea of Marie's method is also to replace a subsystem by an equivalent exponential service station with load-dependent service rates. However, in this case, the parameters of the equivalent server are obtained by analyzing the subsystem in isolation under a load-dependent Poisson arrival process. Moreover, in Marie's case, the procedure is iterative.

In this paper we provide a general and unified view of these two methods. The contributions of this paper are the following. We first show that their common principle is to partition the network into a set of subsystems and then to define an equivalent product-form network. To each subsystem is associated a load-dependent exponential station in the equivalent network. We define a set of rules in order to partition any general closed network with various features such as general service time distributions, pupulation constraints, finite buffers, state-dependent routing. We then show that the aggregation method and Marie's method are two ways of obtaining the parameters of the equivalent network associated with a given partition. Finally, we provide a discussion pertaining to the comparison of the two methods with respect to their accuracy and computational complexity.