approximation algorithms for the test cover problem in the test cover problem a set of m items is given together with a collection of subsets called tests a smallest subcollection of tests is to be selected such that for each pair of items there is a test in the selection that contains exactly one of the two items it is known that the problem is np hard and that the greedy algorithm has a performance ratio o log m we observe that unless p np no polynomial time algorithm can do essentially better for the case that each test contains at most k items we give an o log k approximation algorithm we pay special attention to the case that each test contains at most two items a strong relation with a problem of packing paths in a graph is established which implies that even this special case is np hard we prove apx hardness of both problems derive performance guarantees for greedy algorithms and discuss the performance of a series of local improvement heuristics

an efficient algorithm for computing bisimulation equivalence we propose an efficient algorithmic solution to the problem of determining a bisimulation relation on a finite structure working both on the explicit and on the implicit symbolic representation as far as the explicit case is concerned starting from a set theoretic point of view we propose an algorithm that optimizes the solution to the relational coarsest partition problem given by paige and tarjan siam j comput 16 6 1987 973 its use in model checking packages is also discussed and tested for well structured graphs our algorithm reaches a linear worst case behaviour the proposed algorithm is then re elaborated to produce a symbolic version

a chebyshev approximation for solving nonlinear integral equations of hammerstein type abstract a numerical method for solving fredholm volterra hammerstein integral equations is presented this method is based on replacement of the unknown function by truncated series of well known chebyshev expansion of functions the quadrature formula which we use to calculate integral terms can be estimated by fast fourier transform fft the numerical examples and the number of operations show the advantages of this method to some other usual methods

an approximation method for the solution of nonlinear integral equations a chebyshev collocation method has been presented to solve nonlinear integral equations in terms of chebyshev polynomials this method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown chebyshev coefficients finally some examples are presented to illustrate the method and results discussed

gauge equivalence theory of the noncompact ishimori model and the davey stewartson equation the gauge equivalence between a noncompact version of the ishimori spin model and the davey stewartson equation is established explicit relationships connecting the corresponding two sets of fields involved in these systems are obtained via any pair of complex functions satisfying an equation of the schrodinger type for a free particle using these formulas two examples of classes of nontrivial exact singular solutions to the davey stewartson equation are given one of them is of the closed stringlike type while the other is doubly periodic and is expressed in terms of riemann theta functions the role played by the symmetry group associated with the gauge equivalent equations under consideration is also clarified

the gauge equivalence of the davey stewartson equation and 2 1 dimensional continuous heisenberg ferromagnetic model the gauge equivalence between the davey stewartson ds equation and the 2 1 dimensional continuous heisenberg ferromagnetic model is shown explicitly through the gauge transformation solutions of the dsii are obtained from the vortex type solutions of the former equation

the gauge equivalence of the nls and the schrodinger flow of maps in 2 1 dimensions the gauge equivalence of the analogues of the nonlinear schrodinger equation nls and those of the schrodinger flow of maps into h2 the minkowski hf model in 2 1 dimensions are proved respectively combining these with the already known results we obtain a complete understanding of the gauge equivalence of the analogous models of the nonlinear schrodinger equation for 1 or 1 and those of the heisenberg ferromagnet model for euclidean or minkowski in 2 1 dimensions

a different approach for solving the nonlinear fredholm integral equations of the second kind in this paper we proposed a method for finding a approximate solution for the nonlinear fredholm integral equations of the second kind in this approach the nonlinearity of the kernel has no serious effect on the convergence of the solution first we convert the problem to an optimal control problem by introducing an artificial control function then by using some concepts of measure theory we make a metamorphosis in the space of the problem and finally we will get a linear programming whose solution gives rise to the approximate solution of the integral equation

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

solution of nonlinear volterra fredholm hammerstein integral equations via rationalized haar functions abstract rationalized haar functions are developed to approximate of the nonlinear volterra fredholm hammerstein integral equations the properties of rationalized haar functions are first presented and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations into some algebraic equations the method is computationally attractive and applications are demonstrated through illustrative examples

numerical computation method in solving integral equations by using chebyshev wavelet operational matrix of integration a direct method for solving integral equations whose solutions are continuous or discontinuous by using chebyshev wavelet basis in galerkin equations is presented another method for solving volterra type integral equations which use operational matrix of integration omi for chebyshev wavelets is introduced and used to reduce this type of integral equations to a system of algebraic equations some quadrature formula for calculating inner products have presented which can be operated by fast fourier transform fft the numerical examples and the number of operations show the advantages of chebyshev wavelet galerkin method to some other usual methods and usual chebyshev basis

variable transformations in the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels extensions to fredholm integral equations abstract a number of techniques that use variable transformations in numerical integration have been developed recently cf sidi numerical integration iv h brass g hammerlin eds birkhauser basel 1993 pp 359 373 laurie j comput appl math 66 1996 337 344 the use of these transformations resulted in increasing the order of convergence of the trapezoidal and the midpoint quadrature rule in this paper the application of variable transformation techniques of sidi and laurie type to the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels is considered since the transformations are such that the end points of integration need not be used as mesh points the methods introduced can be used for vie with both continuous and weakly singular kernel in a uniform way the methods have also the advantages of simplicity of application and of achieving high order of convergence the application of the idea to fredholm integral equations with continuous and weakly singular equations is also considered numerical results are included and they verify the expected increased order of convergence they were obtained by using the trapezoidal formula for the evaluation of the transformed integrals

a collocation method to find solutions of linear complex differential equations in circular domains in this study we introduce a collocation approach for solving high order linear complex differential equations in circular domain by using collocation points defined in a circular domain and bessel functions of the first kind this method transforms the linear complex differential equations into a matrix equation the matrix equation corresponds to a system of linear equations with the unknown bessel coefficients proposed method gives the analytic solution when the exact solutions are polynomials numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results the results obtained from the examples demonstrate the efficiency and accuracy of the present work all of the numerical computations have been computed on computer using a code written in matlab

approximately counting hamilton paths and cycles in dense graphs we describe fully polynomial randomized approximation schemes for the problems of determining the number of hamilton paths and cycles in an n vertex graph with minimum degree frac 1 2 a n for any fixed a 0 we show that the exact counting problems are p complete we also describe fully polynomial randomized approximation schemes for counting paths and cycles of all sizes in such graphs

identifying and locating dominating codes np completeness results for directed graphs let g v a be a directed asymmetric graph and c a subset of vertices and let b sub r sup v denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs if the sets b sub r sup v spl cap c v spl isin v respectively v spl isin v spl bsol c are all nonempty and different we call c an r identifying code respectively an r locating dominating code of g in other words if c is an r identifying code then one can uniquely identify a vertex v spl isin v only by knowing which codewords belong to b sub r sup v and if c is r locating dominating the same is true for the vertices v in v spl bsol c we prove that given a directed asymmetric graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r spl ges 1 and remains so even when restricted to strongly connected directed asymmetric bipartite graphs or to directed asymmetric bipartite graphs without directed cycles

set graphs ii complexity of set graph recognition and similar problems a graph g is said to be a set graph if it admits an acyclic orientation that is also extensional in the sense that the out neighborhoods of its vertices are pairwise distinct equivalently a set graph is the underlying graph of the digraph representation of a hereditarily finite set in this paper we continue the study of set graphs and related topics focusing on computational complexity aspects we prove that set graph recognition is np complete even when the input is restricted to bipartite graphs with exactly two leaves the problem remains np complete if in addition we require that the extensional acyclic orientation be also slim that is that the digraph obtained by removing any arc from it is not extensional our approach in fact allows us to also show that the counting variants of the above problems are p complete and prove similar complexity results for problems related to a generalization of extensional acyclic digraphs the so called hyper extensional digraphs which were proposed by aczel to describe hypersets our proofs are based on reductions from variants of the hamiltonian path problem we also consider a variant of the well known notion of a separating code in a digraph the so called open out separating code and show that it is np complete to determine whether an input extensional acyclic digraph contains an open out separating code of given size

bessel polynomial solutions of high order linear volterra integro differential equations abstract in this study a practical matrix method which is based on collocation points is presented to find approximate solutions of high order linear volterra integro differential equations vides under the mixed conditions in terms of bessel polynomials numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with the existing results the results show the efficiency and accuracy of the present work all of the numerical computations have been performed on the computer using a program written in matlab v7 6 0 r2008a

interaction of lumps with a line soliton for the dsii equation abstract exact solutions of the focussing davey stewartson ii equation are presented which describe the interaction of n lumps with a line soliton these solutions are constructed by analysing the inverse spectral problem of the associated lax pair the dynamical properties of these solutions are also discussed

numerical solution of nonlinear volterra fredholm hammerstein integral equations via collocation method based on radial basis functions abstract a numerical technique based on the spectral method is presented for the solution of nonlinear volterra fredholm hammerstein integral equations this method is a combination of collocation method and radial basis functions rbfs with the differentiation process drbf using zeros of the shifted legendre polynomial as the collocation points different applications of rbfs are used for this purpose the integral involved in the formulation of the problems are approximated based on legendre gauss lobatto integration rule the results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme

solutions of convolution integral and fredholm integral equations via double fourier series double fourier series are developed to approximate the solutions of the convolution integral and fredholm integral equations properties of fourier series are first briefly presented and the operational matrix of integration together with the product operational matrix is utilized to reduce the computation of integral equations to a set of simultaneous linear algebraic equations the method is computationally very attractive and applications are demonstrated through illustrative examples

numerical solution of differential equations by using chebyshev wavelet operational matrix of integration in this paper we present operational matrix of integration omi of chebyshev wavelets basis and the product operation matrix pom of it some comparative examples are included to demonstrate the superiority of operational matrix of chebyshev wavelets to those of legendre wavelets

on the solutions of a system of linear retarded and advanced differential equations by the bessel collocation approximation in this study we present a numerical approximation for the solutions of the system of high order linear retarded and advanced differential equations with variable coefficients under the mixed conditions this method is based on taking the truncated bessel expansion of the functions in the retarded and advanced differential equation system by the aid of the matrix operations and the collocation points the problem is transformed into a matrix equation with the unknown bessel coefficients by solving this matrix equation the unknown coefficients of the approximate solutions are computed in addition examples that illustrate the pertinent features of the method are presented and the results of this investigation are discussed

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

collocation method for linear and nonlinear fredholm and volterra integral equations a collocation procedure is developed for the linear and nonlinear fredholm and volterra integral equations using the globally defined b spline and auxiliary basis functions the solution is collocated by cubic b spline and then the integral equation is approximated by the 5 points gauss turan quadrature formula with respect to the legendre weight function combination of these two approaches is the main idea of this paper to reduce the cost of computation and complexity the error analysis of proposed numerical method is studied theoretically numerical results are given to illustrate the efficiency of the proposed method the results are compared with the results obtained by other methods to verify that this method is accurate and efficient

a new collocation type method for hammerstein integral equations on presente une methode du type de collocation pour la resolution numerique des equations integrales d hammerstein on etablit la convergence de l approximation desiree vers la solution exacte

taylor polynomial solutions of nonlinear volterra fredholm integral equations the kanwal and liu method for the solution of fredholm integral equations is applied to certain nonlinear volterra fredholm integral equations in addition examples that illustrate the pertinent features of the method are presented and the results of study are discussed

on a new class of codes for identifying vertices in graphs we investigate a new class of codes for the optimal covering of vertices in an undirected graph g such that any vertex in g can be uniquely identified by examining the vertices that cover it we define a ball of radius t centered on a vertex spl upsi to be the set of vertices in g that are at distance at most t from spl upsi the vertex spl upsi is then said to cover itself and every other vertex in the ball with center spl upsi our formal problem statement is as follows given an undirected graph g and an integer t spl ges 1 find a minimal set c of vertices such that every vertex in g belongs to a unique set of balls of radius t centered at the vertices in c the set of vertices thus obtained constitutes a code for vertex identification we first develop topology independent bounds on the size of c we then develop methods for constructing c for several specific topologies such as binary cubes nonbinary cubes and trees we also describe the identification of sets of vertices using covering codes that uniquely identify single vertices we develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords finally we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems

an application of rationalized haar functions for variational problems a direct method for solving variational problems using rationalized haar is presented an operational matrix of integration and the cross product of two rationalized haar function vectors are utilized to reduce a variational problem to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique

double shifted chebyshev series for convolution integral and integral equations double shifted chebyshev polynomials are developed in this study to approximate the solutions of the convolution integral volterra integral equation and fredholm integral equation this method simplifies the computations of integral equations to the successive solutions of a linear algebraic equation in matrix form in addition the computational complexity can be reduced remarkably three examples are illustrated it is seen that the proposed approach is straightforward and convenient and converges faster in finding approximations than other existing orthogonal function methods

bicomplex formulation and moyal deformation of 2 1 dimensional fordy kulish systems using bicomplex formalism we construct generalizations of fordy kulish systems of matrix nonlinear schrodinger equations on two dimensional space time in two respects firstly we obtain corresponding equations in three space time dimensions secondly a moyal deformation is applied to the space time coordinates and the ordinary product of functions replaced by the moyal product in a suitable way both generalizations preserve the existence of an infinite set of conservation laws

minimizing the size of an identifying or locating dominating code in a graph is np hard let g v e be an undirected graph and c a subset of vertices if the sets br v c v v respectively v v c are all nonempty and different where br v denotes the set of all points within distance r from v we call c an r identifying code respectively an r locating dominating code we prove that given a graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r

generation of higher order pseudospectral integration matrices a new explicit expression of the higher order pseudospectral integration matrices is presented using an explicit formula for computing iterated integrals of chebyshev polynomials applications to initial value problems boundary value problems linear integral and integro differential equations are presented the present numerical results are in satisfactory agreement with the exact solutions and show the advantages of this method to some other known methods

derivative free iterative methods for nonlinear systems in this work we introduce a new operator of divided differences that preserves the convergence order when it is used for approximating the jacobian matrix in iterative method for solving nonlinear systems we obtain derivative free iterative methods with lower computational cost than the corresponding ones with different operators of divided differences we also study the global convergence of these methods by analyzing their dynamical behavior

numerical solution of volterra integral algebraic equations using block pulse functions this paper presents a method for computing numerical solutions for linear volterra integral algebraic equations using block pulse functions the problem is transformed to a linear lower triangular system of algebraic equations using the operational matrix associated with block pulse functions convergence result and numerical examples are presented to illustrate the efficiency and applicability of the method