Preface

ACM SIGOPS ChinaSys conference is organized twice a year by ChinaSys, which is an active community forresearchers and practitioners on computer systems in China. Since August 2015, ChinaSys has become an ACMSIGOPS chapter. The first ChinaSys conference happened in November 2011 in Shenzhen. Now it has become anew leading international forum for academia, industry, and government to present novel research results in theprinciple and practice of computer systems. All topic areas related to design and implementation of computersystems are of interest and in scope.     

Computational performances of a simple interchange heuristic for a scheduling problem with an availability constraint

This paper deals with a scheduling problem on a single machine with an availability constraint. The problem is known to be NP-complete and admits several approximation algorithms. In this paper we study the approximation scheme described in He et al. [Y. He, W. Zhong, H. Gu, Improved algorithms for two single machine scheduling problems, Theoretical Computer Science 363 (2006) 257–265]. We provide the computation of an improved relative error of this heuristic, as well as a proof that this new bound is tight. We also present some computational experiments to test this heuristic on random instances. These experiments include an implementation of the fully-polynomial time approximation scheme given in Kacem and Ridha Mahjoub [I. Kacem, A. Ridha Mahjoub, Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers and Industrial Engineering 56 (2009) 1708–1712].     

Physarum can compute shortest paths: A short proof

The purpose of this note is to give a short proof that a standard model for the Physarum polycephalum slime mold correctly computes the shortest path in an undirected weighted graph [V. Bonifaci, K. Mehlhorn, G. Varma, Physarum can compute shortest paths, in: Proc. of the 23rd ACM–SIAM Symposium on Discrete Algorithms, SIAM, 2012, pp. 233–240].     

A test of “reason-based” and “reluctance-to-think” accounts of the disjunction effect

The disjunction effect violates Savage’s sure-thing principle: that is, if a is preferred over b regardless of whether relevant outcome x occurs, then a should always be preferred over b [L.J. Savage, The Foundations of Statistics, New York, Wiley, 1954]. We tested “reason-based” and “reluctance-to-think” accounts of the disjunction effect. According to the former account, the disjunction effect occurs when different reasons underlie the preference for a under x versus the preference for a under not x. According to the latter account, the disjunction effect is due to the failure to consider preferences when x is unknown. We tested these accounts by varying the number of reasons underlying choices in the x and not x conditions. Consistent with the reason-based account, when only one reason was available, the disjunction effect was reduced. In addition, we propose a new method of measuring the disjunction effect under different conditions based on the logic proposed by Lambdin and Burdsal (2007) [C. Lambdin, C. Burdsal, The disjunction effect reexamined: relevant methodological issues and the fallacy of unspecified percentage comparisons, Organizational Behavior and Human Decision Processes 103 (2007) 268–276].     

Low Angle Estimation: Models,Methods, and Bounds

Boman, K. and Stoica, P., Low Angle Estimation: Models, Methods, and Bounds. Digital Signal Processing11 (2001), 35–79.In this work we study the performance of elevation estimators and lower bounds of the estimation error variance for a low angle target in a smooth sea scenario using an antenna array. The article is structured around some key assumptions on multipath knowledge, signal parameterization and noise covariance. We prove that the Cramér–Rao bound is highly dependent on the multipath model, while it is the same for the different signal parameterizations, and that it is independent of the noise covariance. The Cramér–Rao bound is sometimes too optimistic and not achievable. The tighter Barankin bound is derived to predict the threshold behavior seen at low SNR. Simulations show that the maximum likelihood methods are statistically efficient and achieve the theoretical lower bound on error variance, in the case of high enough SNR. Finally we show that the bounds can be used to design an improved array structure and study the influence of multiple frequencies.     

Partial evaluation technique for distributed image processing

In this paper, a partial evaluation technique to reduce communication costs of distributed image processing is presented. It combines application of incomplete structures and partial evaluation together with classical program optimization such as constant-propagation, loop unrolling and dead-code elimination. Through a detailed performance analysis, we establish conditions under which the technique is beneficial. Andrei Tchernykh received his Ph.D. degree in computer science from the Institute of Precise Mechanics and Computer Technology of the Russian Academy of Sciences (RAS), Russia in 1986. From 1975 to 1995 he was with the Institute of Precise Mechanics and Computer Technology of the RAS, Scientific Computer Center of the RAS, and at Institute for High Performance Computer Systems of the RAS, Moscow, Russia. Since 1995 he has been working at Computer Science Department at the CICESE Research Center, Ensenada, Baja California, Mexico. His main interests include cluster and Grid computing, incomplete information processing, and on-line scheduling. Vitaly Kober obtained his MS degree in Applied Mathematics from the Air-Space University of Samara (Russia) in 1984, and his PhD degree in 1992 and Doctoral degree in 2004 in Image Processing from the Institute of Information Transmission Problems, Russian Academy of Sciences. Now he is a titular researcher at the Centro de Investigation Cientifica y de Educatión Superior de Ensenada (Cicese), México. His research interests include signal and image processing, pattern recognition. Alfredo Cristóbal-Salas received his Ph.D. degree in computer science from the Computer Science Department at the CICESE Research Center, Ensenada, Baja California, México. Now he is a researcher at School of Chemistry Sciences and Engineering, University of Baja California, Tijuana, B.C. Mexico His main interests include cluster and Grid computing, incomplete information processing, and online scheduling. Iosif A. Ovseevich graduated from the Moscow Electrotechnical Institute of Telecommunications. Received candidate’s degree in 1953 and doctoral degree in information theory in 1972. At present he is Emeritus Professor at the Institute of Information Transmission Problems of the Russian Academy of Sciences. His research interests include information theory, signal processing, and expert systems. He is a Member of IEEE, Popov Radio Society.     

A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.     

Multi-hop all-to-all optical routings in Cartesian product networks

This paper considers the wavelength assignment problem for Cartesian product networks with multi-hops. An upper bound of the (uniform) wavelength index for Cartesian product networks with single-hop is established. This result leads to a consequence for the nth power of an arbitrary network with k-hops. In particular, if k=1, this bound partially generalizes the results of Pankaj [R.K. Pankaj, Architectures for linear lightwave networks, PhD thesis, Dept. of Electrical Engineering and Computer Science, MIT, Cambridge, MA, 1992], Bermond et al. [J.-C. Bermond, L. Gargano, S. Perennes, A.A. Rescigno, U. Vaccaro, Efficient collective communication in optical networks, Theoret. Comput. Sci. 233 (2000) 165-189] and Beauquier [B. Beauquier, All-to-all communication for some wavelength-routed all-optical networks, Networks 33 (1999) 179-187] for hypercubes and Hamming graphs. As an application, a tight upper bound for Hamming graph with k hops is established and a corresponding open problem is also proposed.     

Security flaw of Hölbl et al.’s protocol

Recently, Hölbl et al. [M. Hölbl, T. Welzer, B. Brumen, Improvement of the Peyravian–Jeffries’s user authentication protocol and password change protocol, Computer Communications 31 (2008) 1945–1951] have proposed an improvement of Peyravian–Jeffries’s user authentication protocol and password change protocol [M. Peyravian, C. Jeffries, Secure remote user access over insecure networks, Computer Communications 29 (5–6) (2006) 660–667]. Peyravian–Jeffries’s scheme suffers from an active off-line password-guessing attack [J. Munilla, A. Peinado, Off-line password-guessing attack to Peyravian–Jeffries’s remote user authentication protocol, Computer Communications 30 (1) (2006) 52–54], and Hölbl et al. state that their improved protocol overcomes this weakness. However, we show in this paper that although this proposed protocol prevents this active attack, it remains vulnerable to a passive (simpler) off-line password-guessing attack.     

Executability of scenarios in Petri nets

In this paper, we show that it can be tested in polynomial time as to whether a scenario is an execution of a Petri net. This holds for a wide variety of Petri net classes, ranging from elementary nets to general inhibitor nets. Scenarios are given by causal structures expressing causal dependencies and concurrency among events. In the case of elementary nets and of place/transition nets, such causal structures are partial orders among transition occurrences. For several extended Petri net classes, the extension of partial orders to stratified order structures is considered.The algorithms are based on the representation of the non-sequential behavior of Petri nets by so-called token flow functions and a characterization of Petri net executions called token flow property. This property allows nontrivial transformations into flow optimization problems, which can be solved in polynomial time. The paper is a revised, consolidated and extended version of the conference papers [G. Juhás, R. Lorenz, J. Desel, Can I execute my scenario in your net?, in: G. Ciardo, P. Darondeau (Eds.), ICATPN, in: Lecture Notes in Computer Science, Springer, 2005, pp. 289–308; R. Lorenz, S. Mauser, R. Bergenthum, Testing the Executability of Scenarios in General Inhibitor Nets, in: ACSD, IEEE Computer Society, 2007, pp. 167–176] and includes parts of the habilitation thesis [R. Lorenz, Szenario-basierte Verifikation und Synthese von Perinetzen: Theorie und Anwendungen, Habilitation, 2006].     

Intrinsic Parameterizations of Surface Meshes

Parameterization of discrete surfaces is a fundamental and widely‐used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least‐distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two‐dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least‐distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.     

On a simple randomized algorithm for finding a 2-factor in sparse graphs

We analyze the performance of a simple randomized algorithm for finding 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O(n²) expected time. The analysis of our algorithm is based on random walks on the line and interestingly resembles the analysis of a randomized algorithm for the 2-SAT problem given by Papadimitriou [On selecting a satisfying truth assignment, in: Proc. 32nd Annual IEEE Symp. on the Foundations of Computer Science (FOCS), 1991, p. 163]. For the undirected case, the algorithm finds a 2-factor in O(n³) expected time. We also analyze random versions of these graphs and show that cycles of length Ω(n/logn) can be found with high probability in polynomial time. This partially answers an open question of Broder et al. [Finding hidden Hamilton cycles, Random Structures Algorithms 5 (1994) 395] on finding hidden Hamiltonian cycles in sparse random graphs and improves on a result of Karger et al. [On approximating the longest path in a graph, Algorithmica 18 (1997) 82].     

A monitoring system for detecting repeated packets with applications to computer worms

We present a monitoring system which detects repeated packets in network traffic, and has applications including detecting computer worms. It uses Bloom filters with counters. The system analyzes traffic in routers of a network. Our preliminary evaluation of the system involved traffic from our internal lab and a well known historical data set. After appropriate configuration, no false alarms are obtained under these data sets and we expect low false alarm rates are possible in many network environments. We also conduct simulations using real Internet Service Provider topologies with realistic link delays and simulated traffic. These simulations confirm that this approach can detect worms at early stages of propagation. We believe our approach, with minor adaptations, is of independent interest for use in a number of network applications which benefit from detecting repeated packets, beyond detecting worm propagation. These include detecting network anomalies such as dangerous traffic fluctuations, abusive use of certain services, and some distributed denial-of-service attacks. P. van Oorschot(Ph.D. Waterloo, 1988) is a Professor in the School of Computer Science at Carleton University, and Canada Research Chair in Network and Software Security. He is the founding director of Carleton's Digital Security Group. He has worked in research and development in cryptography and network security, including at Bell-Northern Research (Ottawa), and Entrust Technologies (Ottawa) as VP and Chief Scientist. He is coauthor of the standard reference Handbook of Applied Cryptography. His current research interests include authentication and identity management, network security, software protection, and security infrastructures. J.-M. Robertis a Principal Security Researcher at Alcatel in Ottawa, Ontario. His research interests are network and telecom infrastructure security, focusing mainly on denial-of-service attacks and worm propagation. Previously, Dr. Robert worked as Security Director for the North American Development Center of Gemplus International as well as Professor at the Université du Québec à Chicoutimi. Dr. Robert received a Ph.D. in Computer Science from McGill University. M. Vargas Martinis an Assistant Professor at the University of Ontario Institute of Technology (Oshawa, Canada), with faculty appointments in Business and Information Technology, as well as Engineering and Applied Science. He was previously a post-doctoral researcher at Carleton University supported in part by Alcatel Canada. He holds a Ph.D. in Computer Science (Carleton University, 2002), a Masters degree in Electrical Engineering (Cinvestav, Mexico, 1998), and a Bachelor of Computer Science (Universidad Autónoma de Aguascalientes, Mexico, 1996). His current research interests include network and host-based intrusion detection and reaction, mitigation of denial-of-service (DoS) and distributed DoS attacks, Web modeling and optimization, Internet connectivity, and interconnection protocols.     

Numerical study of a nonlinear heat equation for plasma physics

This paper is devoted to the numerical approximation of a nonlinear parabolic balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical difficulties, in particular for the long-time behaviour approximation, when solved with standard methods. An efficient numerical scheme is presented in this paper, based on a combination of a directional splitting scheme and the implicit–explicit scheme introduced in Filbet and Jin [A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comput. Phys. 229 (2010), pp. 7625–7648].     

A new model for selfish routing

In this work, we introduce and study a new, potentially rich model for selfish routing over non-cooperative networks, as an interesting hybridization of the two prevailing such models, namely the KPmodel [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404–413] and the Wmodel [J.G. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the of the Institute of Civil Engineers 1 (Pt. II) (1952) 325–378].     

Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2

A crucial problem in Bayesian posterior computation is efficient sampling from a univariate distribution, e.g. a full conditional distribution in applications of the Gibbs sampler. This full conditional distribution is usually non-conjugate, algebraically complex and computationally expensive to evaluate. We propose an alternative algorithm, called ARMS2, to the widely used adaptive rejection sampling technique ARS [Gilks, W.R., Wild, P., 1992. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41 (2), 337-348; Gilks, W.R., 1992. Derivative-free adaptive rejection sampling for Gibbs sampling. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Clarendon, Oxford, pp. 641-649] for generating a sample from univariate log-concave densities. Whereas ARS is based on sampling from piecewise exponentials, the new algorithm uses truncated normal distributions and makes use of a clever auxiliary variable technique [Damien, P., Walker, S.G., 2001. Sampling truncated normal, beta, and gamma densities. Journal of Computational and Graphical Statistics 10 (2) 206-215]. Furthermore, we extend this algorithm to deal with non-log-concave densities to provide an enhanced alternative to adaptive rejection Metropolis sampling, ARMS [Gilks, W.R., Best, N.G., Tan, K.K.C., 1995. Adaptive rejection Metropolis sampling within Gibbs sampling. Applied Statistics 44, 455-472]. The performance of ARMS and ARMS2 is compared in simulations of standard univariate distributions as well as in Gibbs sampling of a Bayesian hierarchical state-space model used for fisheries stock assessment.     

Iterative Toeplitz solvers with local quadratic convergence

We study an iterative, locally quadratically convergent algorithm for solving Toeplitz systems of equations from [R. P. Brent, F. G. Gustavson and D. Y. Y. Yun. “Fast solution of Toeplitz systems of equations and computation of Padé approximations”,J. Algorithms, 1:259–295, 1980]. We introduce a new iterative algorithm that is locally quadratically convergent when used to solve symmetric positive definite Toeplitz systems. We present a set of numerical experiments on randomly generated symmetric positive definite Toeplitz matrices. In these experiments, our algorithm performed significantly better than the previously proposed algorithm.     

Automated support for deriving test requirements from UML statecharts

Many statechart-based testing strategies result in specifying a set of paths to be executed through a (flattened) statechart. These techniques can usually be easily automated so that the tester does not have to go through the tedious procedure of deriving paths manually to comply with a coverage criterion. The next step is then to take each test path individually and derive test requirements leading to fully specified test cases. This requires that we determine the system state required for each event/transition that is part of the path to be tested and the input parameter values for all events and actions associated with the transitions. We propose here a methodology towards the automation of this procedure, which is based on a careful normalization and analysis of operation contracts and transition guards written with the Object Constraint Language (OCL). It is illustrated by one case study that exemplifies the steps of our methodology and provides a first evaluation of its applicability. The scope of the testing activity depends on what is modeled by the statechart. If the statechart models the behavior of a single class, then it can be used to support unit testing. If the behavior of a class-cluster, a subsystem or a component is modeled, then we are concerned with integration testing. If the whole system is modeled, then the focus of statechart-based testing is system testing. Lionel C. Briand is on the faculty of the Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada, where he founded and leads the Software Quality Engineering Laboratory (http://www.sce.carleton.ca/Squall/ Squall.htm). He has been granted the Canada Research Chair in Software Quality Engineering and is also a visiting professor at the Simula laboratories, University of Oslo, Norway. Before that he was the software quality engineering department head at the Fraunhofer Institute for Experimental Software Engineering, Germany. Dr. Lionel also worked as a research scientist for the Software Engineering Laboratory, a consortium of the NASA Goddard Space Flight Center, CSC, and the University of Maryland. He has been on the program, steering, or organization committees of many international, IEEE conferences such as ICSE, ICSM, ISSRE, and METRICS. He is the coeditor-in-chief of Empirical Software Engineering (Springer) and is a member of the editorial board of Systems and Software Modeling (Springer). He was on the board of IEEE Transactions on Software Engineering from 2000 to 2004. His research interests include: object-oriented analysis and design, inspections and testing in the context of object-oriented development, quality assurance and control, project planning and risk analysis, and technology evaluation. Lionel received the BSc and MSc degrees in geophysics and computer systems engineering from the University of Paris VI, France. He received the PhD degree in computer science, with high honors, from the University of Paris XI, France. Yvan Labiche received the BSc in Computer System Engineering, from the graduate school of engineering: CUST (Centre Universitaire des Science et Techniques, Clermont-Ferrand), France. He completed a Master of fundamental computer science and production systems in 1995 (Université Blaise Pascal, Clermont Ferrand, France). While doing his Ph.D. in Software Engineering, completed in 2000 at LAAS/CNRS in Toulouse, France, Yvan worked with Aerospatiale Matra Airbus (now EADS Airbus) on the definition of testing strategies for safety-critical, on-board software, developed using object-oriented technologies. In January 2001, Dr. Yvan Labiche joined the Department of Systems and Computer Engineering at Carleton University, as an Assistant Professor. His research interests include: object-oriented analysis and design, software testing in the context of object-oriented development, and technology evaluation. He is a member of the IEEE. Jim (Jingfeng) Cui completed his BSc in Industrial Automation Control, from the School of Information and Engineering, Northeastern University, China. He received a Master of Applied Science (specialization in Software Engineering) in 2004 from the Ottawa-Carleton Institute of Electrical and Computer Engineering, Ottawa, Canada. While in his graduate study, he was awarded the Ontario Graduate Scholarship of Science and Technology. He is now a senior Software Architect in Sunyard System & Engineering Co.Ltd., China. His interest includes Object-Oriented Software Development, Quality Assurance, and Content Management System.     

Simplicialization of digital volumes in 26-adjacency: Application to topological analysis

In this paper, we introduce a simple and original algorithm to compute a three-dimensional simplicial complex topologically equivalent to a 3D digital object V, according to the 26-adjacency. The use of this adjacency generates issues like auto-intersecting triangles that unnecessarily increase the dimensionality of the associated simplicial complex. To avoid these problems, we present an approach based on a modified Delaunay tetrahedralization of the digital object, that preserves its topological characteristics. Considering the resulting complex as an input in algebraic-topological format (fixing a ground ring for the coefficients), we develop propositions regardless of the adjacency considered. These potential applications are related to topological analysis like thinning, homology computation, topological characterization and control. Moreover, our technique is susceptible to be extended to higher dimensions. The article is published in the original. Jean-Luc Mari received his PhD degree in 2002. He has been an Associate Professor since 2003 in the Department of Computer Science at the Faculté des Sciences de Luminy (University of Marseilles). He is also a member of the Information and System Science Laboratory (LSIS), in the team “Image and Models” (Computer Graphics group). His research interests include geometrical modeling, model representation, implicit and subdivision surfaces, meshes, multiresolution, skeleton based objects and reconstruction. Pedro Real received his PhD degree in 1993. He has been an Associate Professor since 1995 in the Department of Applied Mathematics I at Higher Technical School of Computer Engineering (University of Seville, Spain). He is the main responsible of the andalusian research group “Computational Topology and Applied Mathematics.” His research interests include computational algebraic topology, topological analysis of digital images, algebraic pattern recognition and computational algebra.     

A note on “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo,Yinzhen Li,Mitsuo Gen,Computers & Industrial Engineering (2007)

In 2007, a spanning tree-based genetic algorithm approach for solving nonlinear fixed charge transportation problem proposed by Jo et al. [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022] was published in Computers & Industrial Engineering journal. In 2008, comments like calculation of total cost, indication of problem size were given by Kannan et al. [Kannan, G., Kumar, P. S., Vinay V. P. (2008). Comments on ‘‘Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007). Computers & Industrial Engineering. doi:10.1016/j.cie.2007.12.019] for the published model of [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering.doi:10.1016/j.cie.2007.06.022]. In this note, as a response to the comments of Kannan et al., the formula for calculating the total cost of nonlinear fixed charge transportation problem is illustrated with examples, to which the near-optimal solutions are given.