Auction algorithms for network flow problems: A tutorial introduction

This paper surveys a new and comprehensive class of algorithms for solving the classical linear network flow problem and its various special cases such as shortest path, max-flow, assignment, transportation, and transhipment problems. The prototype method, from which the other algorithms can be derived, is the auction algorithm for the assignment problem. This is an intuitive method that operates like a rel auction where persons compete for objects by raising their prices through competitive bidding; the prices can be viewed as dual variables. Conceptually, auction algorithms represent a significant departure from the cost improvement idea that underlies primal simplex and dual ascent methods; at any one iteration, they may deteriorate both the primal and the dual cost. Auction algorithms perform very well for several important types of problems, both in theory and in practice, and they are also well suited for parallel computation.     

On the Distribution of Activity Time in PERT

In PERT analysis the activity-time distribution is assumed to be a beta distribution, and the mean and variance of the activity time are estimated on the basis of the ‘pessimistic’, ‘most likely’ and ‘optimistic’ completion times, which are subjectively determined by an analyst. In this paper, on the basis of the study of the PERT assumptions, we present an improvement of these estimates. It is also shown that, by means of additional reasonable assumptions, the activity-time distribution in PERT analysis may be essentially simplified.     

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas—Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special cases of the proximal point algorithm. This observation allows the unification and generalization of a variety of convex programming algorithms. By introducing a modified version of the proximal point algorithm, we derive a new,generalized alternating direction method of multipliers for convex programming. Advances of this sort illustrate the power and generality gained by adopting monotone operator theory as a conceptual framework.This paper is drawn largely from the dissertation research of the first author. The dissertation was performed at M.I.T. under the supervision of the second author, and was supported in part by the Army Research Office under grant number DAAL03-86-K-0171, and by the National Science Foundation under grant number ECS-8519058.     

Dual coordinate step methods for linear network flow problems

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of-complementary slackness, and most do not explicitly manipulate any global objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of newserial computational complexity results. We develop the basic theory of these methods and present two specific methods, the-relaxation algorithm for the minimum-cost flow problem, and theauction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N ³ logNC) and O(NA logNC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement-relaxation in a completely asynchronous, chaotic environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.Supported by Grant NSF-ECS-8217668 and by the Army Research Office under grant DAAL03-86-K-0171. Thanks are due to David Castañon, Paul Tseng, and Jim Orlin for their helpful comments.     

Development and validation of a liquid chromatographic/tandem mass spectrometric assay for the quantitation of nucleoside HIV reverse transcriptase inhibitors in biological matrices

Besides liquid chromatographic (LC)/UV methods adapted to therapeutic drug monitoring, there is still a need for more powerful techniques that can be used for pharmacological research and clinical purposes. We developed an LC method coupled with tandem mass spectrometry (MS/MS) to separate, detect and quantify with high sensitivity the nucleoside analogues used in multitherapies (zidovudine, stavudine, zalcitabine, didanosine, lamivudine and abacavir) in plasma and in the intracellular medium. We worked on two essential issues: (i) the need to use two ionization modes in order to achieve the best sensitivity, which leads to the optimization of the chromatographic separation of drugs detected in the positive ionization mode and drugs detected in the negative ionization mode, and (ii) the need to optimize the extraction step in order to enhance sample recovery. The peripheral blood mononuclear cells were lysed in Tris buffer-MeOH. A clean-up procedure was performed by solid-phase extraction only for plasma samples. The LC separation was carried out on a Zorbax Stable Bond C(18) column followed by MS/MS analysis after electrospray ionization in either the negative or positive mode. The positive ionization mode was applied at the beginning of the run to detect zalcitabine and lamivudine, then the ionization mode was changed to negative for the detection of didanosine, stavudine, internal standard and zidovudine. The calibration range for all the analytes was 0.5-200 ng ml(-1). The recoveries were between 64 and 90%, with coefficients of variation (CVs) lower than 15%. The inaccuracy (bias) was +/-15% with CVs always lower than 12%. The analytes were stable at room temperature and in the extraction solvent for at least 24 h, after storage at -80 degrees C for 3 months, after three freeze-thaw cycles and in the injection solvent after 48 h at 4 degrees C. Together with the measurement of intracellular triphosphorylated metabolites thanks to the powerful plasma and intracellular assay method for intact drugs, it is possible to describe the behaviour of nucleoside analogues against HIV through plasma pharmacokinetics, cell membrane diffusion including drug transport involvement, and also the intracellular metabolism.     

A generic auction algorithm for the minimum cost network flow problem

In this paper we broadly generalize the assignment auction algorithm to solve linear minimum cost network flow problems. We introduce a generic algorithm, which contains as special cases a number of known algorithms, including the -relaxation method, and the auction algorithm for assignment and for transportation problems. The generic algorithm can serve as a broadly useful framework for the development and the complexity analysis of specialized auction algorithms that exploit the structure of particular network problems. Using this framework, we develop and analyze two new algorithms, an algorithm for general minimum cost flow problems, called network auction, and an algorithm for thek node-disjoint shortest path problem.     

Two-electron transfer for Tl(aq)(3+)/Tl(aq)(+) revisited. Common virtual [Tl(II)-Tl(II)](4+) intermediate for homogeneous (superexchange) and electrode (sequential) mechanisms

Homogeneous and electrochemical two-electron transfers within the Tl(aq)(3+)/Tl(aq)(+) couple are considered on a common conceptual basis. For the 2 equiv electrochemical reduction of Tl(aq)(3+) to Tl(aq)(+), the intermediate state with a formal reduction potential, E(1) = 1.04 +/- 0.10 V vs the normal hydrogen electrode, was detected, different from the established value of 0.33 V for a Tl(3+)/Tl(2+) couple. Examination of obtained electrochemical (cyclic voltammetry (CV) and rotating disk electrode techniques, along with the CV-curve computer simulation procedure) and literature data indicate that the detected formal potential cannot be the property of electrode-adsorbed species, but rather of the covalently interacting dithallium intermediate [Tl(II)-Tl(II)](4+) located at the outer Helmholtz plane. The analysis of microscopic mechanisms, based on the recent hypothesis of H. Taube and the Marcus-Hush theory extended by Zusman and Beratan, and Koper and Schmickler, revealed that the homogeneous process most probably takes place through the superexchange inner-sphere two-electron-transfer mechanism, via an essentially virtual (undetectable) dithallium intermediate. In contrast, the electrochemical process occurs through a sequential mechanism, via the rate-determining step of Tl(aq)(2+) ion formation immediately followed by activationless formation of the metastable (CV-active) dithallium state. The second electrochemical electron-transfer step is fast, and shows up only in the peak height (but not in the shape) of the observed CV cathodic wave. The anodic wave for a microscopically reverse process of the oxidation of Tl(aq)(+) to Tl(aq)(3+) cannot be observed within the considered potential range due to the blocking of through-space electron transfer by the competitor process of ion transfer to the electrode.     

Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition

We show the incompleteness of a usually used version of the generalized Ambrosetti?CRabinowitz condition in superlinear problems, also used in the paper cited in the title, and we propose a complete one.