translation of the problem of complete test set generation to pseudo boolean programming an attempt is made to demonstrate that the problem of complete test set generation is amenable to the problem of pseudo boolean programming for this purpose various types of faults viz single faults multiple faults and bridging faults are considered the key issue is to obtain logical expressions for the primary output line in terms of different faulty internal nodes to find real transforms using standard rules the real transforms of a boolean function can be obtained directly without any algebraic manipulation

cellular automata for weighted random pattern generation fault testing random pattern resistant circuits requires that bist built in self test techniques generate large numbers of pseudorandom patterns to shorten these long test lengths this study describes a cellular automata based method that efficiently generates weighted pseudorandom bist patterns this structure called a weighted cellular automaton wca uses no external weighting logic the design algorithm mwcargo combines generation of the necessary weight sets and design of the wca in this study wca pattern generators designed by mwcargo achieved 100 percent coverage of testable stuck at faults for benchmark circuits with random pattern resistant faults the wca applies complete tests much faster than existing test per scan techniques at the same time the hardware overhead of wca proves to be competitive with that of current test per clock schemes

a cutting plane approach to the sequential ordering problem with applications to job scheduling in manufacturing the sequential ordering problem sop finds a minimum cost hamiltonian path subject to certain precedence constraints the sop has a number of practical applications and arises for instance in production planning for flexible manufacturing systems this paper presents several 0 1 models of the sop and reports the authors computational experience in finding lower bounds of the optimal solution value of several real life instances of sop one of the most successful approaches is a cutting plane procedure that is based on polynomial time separation algorithms for large classes of valid inequalities for the associated polyhedron

halin graphs and the travelling salesman problem a halin graphh t c is obtained by embedding a treet having no nodes of degree 2 in the plane and then adding a cyclec to join the leaves oft in such a way that the resulting graph is planar these graphs are edge minimal 3 connected hamiltonian and in general have large numbers of hamilton cycles we show that for arbitrary real edge costs the travelling salesman problem can be polynomially solved for such a graph and we give an explicit linear description of the travelling salesman polytope the convex hull of the incidence vectors of the hamilton cycles for such a graph

positivity preserving property for a class of biharmonic elliptic problems the lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds we show that this property holds in general domains for suitable linear combinations of dirichlet and navier boundary conditions the spectrum of this operator exhibits some unexpected features radial data may generate nonradial solutions these boundary conditions are also of some interest in semilinear equations since they enable us to give explicit radial singular solutions to fourth order gelfand type problems

a multi start dynasearch algorithm for the time dependent single machine total weighted tardiness scheduling problem we extend the dynasearch technique recently proposed by congram et al in the context of time dependent combinatorial optimization problems as an application we consider a general time dependent idleness version of the well known single machine total weighted tardiness scheduling problem in which the processing time of a job depends on its starting time of execution we develop a multi start local search algorithm and present experimental results on several types of instances showing the superiority of the dynasearch neighborhood over the traditional one

green function and martin kernel for higher order fractional laplacians in balls abstract we give the explicit formulas for the green function and the martin kernel for all integer and fractional powers of the laplacian s 1 in balls as consequences we deduce interior and boundary regularity estimates for solutions to linear problems and positivity preserving properties our proofs rely on a characterization of suitable s harmonic functions and on a differential recurrence equation

on polynomial time testable combinational circuits the problems of identifying several nontrivial classes of polynomial time testable ptt circuits are shown to be np complete or harder first ptt classes obtained by using circuit decompositions proposed by fujiwara 1988 and chakradhar et al 1990 are considered another type of decompositions based on fanout reconvergent f r pairs which also lead to ptt classes are proposed the problems of obtaining these decompositions and also some structurally similar general graph decompositions are shown to be np complete or harder then the problems of recognizing ptt classes formed by the boolean formulae belonging to the weakly positive weakly negative bijunctive and affine classes are shown to be np complete

positivity for equations involving polyharmonic operators with dirichlet boundary conditions cranston fabes and zhao 26 5 established the uniform bound sup x y 2 x 6 y r g1 n x z g1 n z y dz g1 n x y m 1 1 where g1 n x y is the green function for the laplacian with dirichlet boundary conditions on a lipschitz domain rn with n 3 see 27 for n 2 this estimate was used in 23 and 18 to obtain positivity uniformly with respect to f 0 for noncooperative elliptic systems as

confidence intervals for expected coverage from a beta testability model abstract the testability distribution of a vlsi circuit can be used to predict the fault coverage of a set of test patterns by restricting the standard test pattern generation process to a sample of faults when testability of a vlsi circuit is modeled as a beta distribution the random detection counts obtained have a beta binomial distribution this paper includes a three confidence intervals for the parameters of the beta binomial distribution b a determination of the proper sample size needed such that the theoretical confidence intervals agree with the actual ones and c a determination of the effect of the number of generated tests on confidence interval widths restricting the test generation process to a sample of faults results in major savings in the overall costs of test generation experimental results are given on three of the large combinational benchmark circuits presented at the 1985 international symposium on circuits and systems

an implicit enumeration algorithm to generate tests for combinational logic circuits the d algorithm dalg is shown to be ineffective for the class of combinational logic circuits that is used to implement error correction and translation ecat functions podem path oriented decision making is a new test generation algorithm for combinational logic circuits podem uses an implicit enumeration approach analogous to that used for solving 0 1 integer programming problems it is shown that podem is very efficient for ecat circuits and is significantly more efficient than dalg over the general spectrum of combinational logic circuits a distinctive feature of podem is its simplicity when compared to the d algorithm podem is a complete algorithm in that it will generate a test if one exists heuristics are used to achieve an efficient implicit search of the space of all possible primary input patterns until either a test is found or the space is exhausted

an efficient genetic algorithm for the traveling salesman problem with precedence constraints abstract the traveling salesman problem with precedence constraints tsppc is one of the most difficult combinatorial optimization problems in this paper an efficient genetic algorithm ga to solve the tsppc is presented the key concept of the proposed ga is a topological sort ts which is defined as an ordering of vertices in a directed graph also a new crossover operation is developed for the proposed ga the results of numerical experiments show that the proposed ga produces an optimal solution and shows superior performance compared to the traditional algorithms

strong unique continuation for products of elliptic operators of second order we study strong unique continuation for products of elliptic operators the main tools are carleman inequalities for second order elliptic operators we obtain strong unique continuation assuming either gevrey regularity of the coefficients or some pointwise conditions on the coefficients

solving the asymmetric travelling salesman problem with time windows by branch and cut many optimization problems have several equivalent mathematical models it is often not apparent which of these models is most suitable for practical computation in particular when a certain application with a specific range of instance sizes is in focus our paper addresses the asymmetric travelling salesman problem with time windows atsp tw from such a point of view the real world application we aim at is the control of a stacker crane in a warehouse we have implemented codes based on three alternative integer programming formulations of the atsp tw and more than ten heuristics computational results for real world instances with up to 233 nodes are reported showing that a new model presented in a companion paper outperforms the other two models we considered at least for our special application and that the heuristics provide acceptable solutions

a quantitative carleman estimate for second order elliptic operators we prove a carleman estimate for elliptic second order partial differential expressions with lipschitz continuous coefficients the carleman estimate is valid for any complex valued function u w2 2 with support in a punctured ball of arbitrary radius the novelty of this carleman estimate is that we establish an explicit dependence on the lipschitz and ellipticity constants the dimension of the space and the radius of the ball in particular we provide a uniform and quantitative bound on the weight function for a class of elliptic operators given explicitly in terms of ellipticity and lipschitz constant

an inexact algorithm for the sequential ordering problem abstract given the directed g n a and the penalty matrix c the sequential ordering problem hereafter sop consists of finding the permutation of the nodes from the set n such that it minimizes a c based function and does not violate the precedence relationships given by the set a strong sufficient conditions for the infeasibility of a sop s instance are embedded in a procedure for the sop s pre processing note that it is one of the key steps in any algorithm that attempts to solve sop by dropping the constraints related to the precedence relationships sop can be converted in the classical asymmetric traveling salesman problem hereafter astp the algorithm obtains hopefully satisfactory solutions by modifying the optimal solution to the related assignment problem hereafter ap if it is not a feasible sequential ordering hereafter fso the new solution patches the subtours if any giving preference to the patches with zero reduced cost in the linking arcs the ap based lower bound on the optimal solution to atsp is tightened by using some of the procedures given in 1 in any case a local search for improving the initial fso is performed it uses 3 and 4 changed based procedures computational results on a broad set of cases are reported

atpg for heat dissipation minimization during test application a automatic test pattern generator atpg algorithm is proposed that reduces switching activity between successive test vectors during test application the main objective is to permit safe and inexpensive testing of low power circuits and bare die that might otherwise require expensive heat removal equipment for testing at high speeds three new cost functions namely transition controllability observability and test generation costs have been defined it has been shown for a fanout free circuit under test that the transition test generation cost for a fault is the minimum number of transitions required to test a given stuck at fault the proposed algorithm has been implemented and the generated tests are compared with those generated by a standard podem implementation for the larger iscas85 benchmark circuits the results clearly demonstrate that the tests generated using the proposed atpg can decrease the average number of weighted transitions between successive test vectors by a factor of 2 to 23

the bipartite quadratic assignment problem and extensions abstract we introduce a new binary quadratic program that subsumes the well known quadratic assignment problem this problem is shown to be np hard when some associated parameters are restricted to simple values but solvable in polynomial time when some other parameter values are restricted three different neighborhood structures are introduced a best solution in all these neighborhoods can be identified in polynomial time even though two of these neighborhoods are of exponential size different local search algorithms and their enhancements using tabu search are developed using these neighborhoods experimental analysis show that two hybrid algorithms obtained by combining these neighborhoods in specific ways yield results that are superior to the algorithms that use these neighborhoods separately extensive computational results and statistical analysis of the resulting data are presented

architecture of a testable analog fuzzy logic controller the authors discuss problems of testability of analog fuzzy logic controllers implemented as vlsi chips enhancements to standard architecture of fuzzy logic controllers which facilitate testing are proposed to improve controllability and observability of internal nodes analog switching blocks are introduced together with some additional circuitry these blocks allow one to test each basic cell of a fuzzy logic controller e g membership function cell minimax cell etc separately the analog switching blocks do not contribute to the power consumption in a working chip end therefore can be used in low power analog fuzzy logic controllers

on the acceleration of test generation algorithms in order to accelerate an algorithm for test generation it is necessary to reduce the number of backtracks in the algorithm and to shorten the process time between backtracks in this paper we consider several techniques to accelerate test generation and present a new test generation algorithm called fan fan out oriented test generation algorithm it is shown that the fan algorithm is faster and more efficient than the podem algorithm reported by goel we also present an automatic test generation system composed of the fan algorithm and the concurrent fault simulation experimental results on large combinational circuits of up to 3000 gates demonstrate that the system performs test generation very fast and effectively

a threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem in real life scheduling variations of the standard traveling salesman problem are very often encountered the aim of this work is to present a new heuristic method for solving three such special instances with a common approach the proposed algorithm uses a variant of the threshold accepting method enhanced with intense local search while the candidate solutions are produced through an insertion heuristic scheme the main characteristic of the algorithm is that it does not require modifications and parameter tuning in order to cope with the three different problems computational results on a variety of real life and artificial problems are presented at the end of this work and prove the efficiency and the ascendancy of the proposed method over other algorithms found in the literature

a probabilistic analysis of the switching algorithm for the euclidean tsp the well known switching algorithm proposed by lin and kernighan for the euclidean travelling salesman problem has proved to be a simple efficient algorithm for medium size problems though it often gets trapped in local optima although its complexity status is still open it has been observed to be polynomially bounded in practice when applied to uniformly distributed points in the unit square in this paper this polynomial behaviour is derived theoretically however we will come up with a bound of o n18 with probability 1 c n whereas in practice the algorithm works slightly better

test generation for iterative logic arrays based on an n cube of cell states model the authors present a novel approach to the test generation problem for a more general class of two dimensional iterative logic arrays ilas than considered by previous researchers for certain ilas it is possible to find a test set whose size remains fixed irrespective of the size of the ila while for others it varies with array size given an arbitrary ila cell truth table and a cell interconnection structure the goal is to determine if a fixed size test can be found if not then a test set whose size grows as slowly as possible with the size of the array should be found the authors propose a new model called the n cube of cell states model for representing the cell truth table and interconnection structure the test generation problem is shown to be related to certain properties of cycles in a set of graphs obtained from this model by careful analysis of these cycles efficient testing schedules can be obtained the proposed technique can be applied to unilateral as well as regular bilateral ilas in which the bilateral direction of signal flow are restricted to lie along the horizontal axis

an elementary proof that the biharmonic green function of an eccentric ellipse changes sign p r garabedian showed in 1951 that the green function for the biharmonic boundary value problem with vanishing dirichlet data changes sign in case the domain is a sufficiently eccentric ellipse this refuted a conjecture made by j hadamard in 1908 the proof of garabedian was based on kernel functions the present note gives an elementary proof

polynomial time testability of circuits generated by input decomposition considers polynomial time testability of combinational circuits generated by input decomposition especially those generated by the logic synthesis tool factor first the complexity of the fault detection problem in this class of circuits is explored using a stuck at fault model an o 2 sup k m algorithm for detecting a single stuck at fault is given that is faster than the o 16 sup k m previously reported best algorithm proposed by fujiwara 1990 where k is the number of inputs in a subcircuit and m the number of signal lines in the circuit efficient polynomial time algorithms are described for generating a test set for all single stuck at faults in the circuit the basic strategy is to eliminate backtracks during line justification by constructing tables or vector sets in each subcircuit which makes the fault propagation procedure very simple and eventually results in an efficient test generation procedure this presentation of efficient polynomial time test generation algorithms for factor generated circuits is important since it shows that it is possible to synthesize circuits that are optimized for area and are polynomial time testable at the same time

polynomially solvable cases of the bipartite traveling salesman problem abstract given two sets r and b consisting of n cities each in the bipartite traveling salesman problem one looks for the shortest way of visiting alternately the cities of r and b returning to the city of origin this problem is known to be np hard for arbitrary sets r and b in this paper we provide an o n 6 algorithm to solve the bipartite traveling salesman problem if the quadrangle property holds in particular this algorithm can be applied to solve in o n 6 time the bipartite traveling salesman problem in the following cases s r b is a convex point set in the plane s r b is the set of vertices of a simple polygon and v r b is the set of vertices of a circular graph for this last case we also describe another algorithm which runs in o n 2 time

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

a polyhedral approach to the asymmetric traveling salesman problem several branch and bound algorithms for the exact solution of the asymmetric traveling salesman problem atsp based on the assignment problem ap relaxation have been proposed in the literature these algorithms perform very well for some instances e g those with uniformly random integer costs but very poorly for others the aim of this paper is to evaluate the effectiveness of a branch and cut algorithm exploiting atsp specific facet defining cuts to be used to attack hard instances that cannot be solved by the ap based procedures from the literature we present new separation algorithms for some classes of facet defining cuts and a new variable pricing technique for dealing with highly degenerate primal lp problems a branch and cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real world instances the outcome of the research is that on hard instances the branch and cut algorithm clearly outperforms the best ap based algorithms from the literature

sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the cauchy problem for the anisotropic plate equation abstract we prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients then we derive various kinds of quantitative estimates of unique continuation for the anisotropic plate equation among these we prove a stability estimate for the cauchy problem for such an equation and we illustrate some applications to the size estimates of an unknown inclusion made of different material that might be present in the plate the paper is self contained and the carleman estimate from which the sharp three sphere inequality is derived is proved in an elementary and direct way based on standard integration by parts

a study of exponential neighborhoods for the travelling salesman problem and for the quadratic assignment problem this paper deals with exponential neighborhoods for combinatorial optimization problems exponential neighborhoods are large sets of feasible solutions whose size grows exponentially with the input length we are especially interested in exponential neighborhoods over which the tsp respectively the qap can be solved in polynomial time and we investigate combinatorial and algorithmical questions related to such neighborhoods first we perform a careful study of exponential neighborhoods for the tsp we investigate neighborhoods that can be defined in a simple way via assignments matchings in bipartite graphs partial orders trees and other combinatorial structures we identify several properties of these combinatorial structures that lead to polynomial time optimization algorithms and we also provide variants that slightly violate these properties and lead to np complete optimization problems whereas it is relatively easy to find exponential neighborhoods over which the tsp can be solved in polynomial time the corresponding situation for the qap looks pretty hopeless every exponential neighborhood that is considered in this paper provably leads to an np complete optimization problem for the qap

a duality approach in the optimization of beams and plates we introduce a class of nonlinear transformations called resizing rules which associate with optimal shape design problems certain equivalent distributed control problems while preserving the state of the system this puts into evidence the duality principle that the class of system states that can be achieved under a prescribed force via modifications of the structure shape of the system can be obtained as well via the modifications of the force action under a prescribed structure we apply such transformations to the optimization of beams and plates and in the simply supported or cantilevered cases the obtained control problems are even convex in all cases we establish existence theorems for optimal pairs by assuming only boundedness conditions moreover in the simply supported case we also prove the uniqueness of the global minimizer a general algorithm that iterates between the original transformed problems is introduced and studied the applications also include the case of variational inequalities

average value of solutions for the bipartite boolean quadratic programs and rounding algorithms we consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem bbqp with m n variables a closed form formula is developed to compute the average objective function value a of all solutions in o m n time however computing the median objective function value of the solutions is shown to be np hard also we show that any solution with objective function value no worse than a dominates at least 2 m n 2 solutions and this bound is the best possible further we show that such a solution can be identified in o m n time and hence the domination ratio of this algorithm is at least 1 4 we then show that for any fixed natural numbers a and b such that a b 1 no polynomial time approximation algorithm exists for bbqp with domination ratio larger than 1 2 1 m n unless p np it is shown that some powerful local search algorithms can get trapped at a local maximum with objective function value less than a one of our approximation algorithms has an interesting rounding property which provides a data dependent lower bound on the optimal objective function value a new integer programming formulation of bbqp is also given and computational results with our rounding algorithms are reported

constraint satisfaction using constraint logic programming abstract constraint logic programming clp is a new class of declarative programming languages whose primitive operations are based on constraints e g constraint solving and constraint entailment clp languages naturally combine constraint propagation with nondeterministic choices as a consequence they are particularly appropriate for solving a variety of combinatorial search problems using the global search paradigm with short development time and efficiency comparable to procedural tools based on the same approach in this paper we describe how the clp language cc fd a successor of chip using consistency techniques over finite domains can be used to solve two practical applications test pattern generation and car sequencing for both applications we present the cc fd program describe how constraint solving is performed report experimental results and compare the approach with existing tools

on solutions of second and fourth order elliptic equations with power type nonlinearities abstract we study second and fourth order semilinear elliptic equations with a power type nonlinearity depending on a power p and a parameter 0 for both equations we consider dirichlet boundary conditions in the unit ball b r n regularity of solutions strictly depends on the power p and the parameter we are particularly interested in the radial solutions of these two problems and many of our proofs are based on an ordinary differential equation approach

new optimization heuristics in a former paper we introduced a very effective new general purpose optimization principle we compared this method which we called threshold accepting ta with the well known simulated annealing sa method for discrete optimization the empirical results demonstrated the superiority of the ta algorithm in further experiments with the ta principle we discovered two new powerful optimization heuristics the great deluge algorithm gda and the record to record travel rrt these algorithms resemble in their structure the formerly studied ta and the sa method the differences lie in their acceptance rules for worse intermediate solutions both the gda and the rrt are essentially one parameter algorithms i e for the achievement of best possible performance a good choice is necessary only for a single parameter this is in contrast for instance to the classical as algorithm where it is necessary to choose carefully a certain sequence of parameters the so called annealing schedule the quality of the computational results obtained so far by rrt and gda shows that the new algorithms behave equally well as ta and thus a fortiori better than sa

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

regularity of solutions to the polyharmonic equation in general domains the present paper establishes boundedness of m frac n 2 frac 1 2 derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of mathbb r n 2 n 2m 1 without any restrictions on the geometry of the underlying domain it is shown that this result is sharp and cannot be improved in general domains moreover it is accompanied by sharp estimates on the polyharmonic green function

the bilinear assignment problem complexity and polynomially solvable special cases in this paper we study the bilinear assignment problem bap with size parameters m and n m le n bap is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence np hard we show that bap cannot be approximated within a constant factor unless p np even if the associated quadratic cost matrix q is diagonal further we show that bap remains np hard if m o root r of n for some fixed r but is solvable in polynomial time if m o left frac log n log log n right when the rank of q is fixed bap is observed to admit fptas and when this rank is one it is solvable in polynomial time under some additional restrictions we then provide a necessary and sufficient condition for bap to be equivalent to two linear assignment problems a closed form expression to compute the average of the objective function values of all solutions is presented whereas the median of the solution values cannot be identified in polynomial time unless p np we then provide polynomial time heuristic algorithms that find a solution with objective function value no worse than that of m 1 n 1 solutions however computing a solution whose objective function value is no worse than that of m n lceil frac m beta rceil lceil frac n beta rceil solutions is np hard for any fixed rational number beta 1

on positivity for the biharmonic operator under steklov boundary conditions the positivity preserving property for the inverse of the biharmonic operator under steklov boundary conditions is studied it is shown that this property is quite sensitive to the parameter involved in the boundary condition moreover positivity of the steklov boundary value problem is linked with positivity under boundary conditions of navier and dirichlet type

construction heuristics for the asymmetric tsp abstract non euclidean traveling salesman problem tsp construction heuristics and especially asymmetric tsp construction heuristics have been neglected in the literature by comparison with the extensive efforts devoted to studying euclidean tsp construction heuristics this state of affairs is at odds with the fact that asymmetric models are relevant to a wider range of applications and indeed are uniformly more general that symmetric models moreover common construction approaches for the euclidean tsp have been shown to produce poor quality solutions for non euclidean instances motivation for remedying this gap in the study of construction approaches is increased by the fact that such methods are a great deal faster than other tsp heuristics which can be important for real time problems requiring continuously updated response the purpose of this paper is to describe two new construction heuristics for the asymmetric tsp and a third heuristic based on combining the other two extensive computational experiments are performed for several different families of tsp instances disclosing that our combined heuristic clearly outperforms well known tsp construction methods and proves significantly more robust in obtaining relatively high quality solutions over a wide range of problems

global stability for an inverse problem in soil structure interaction we consider the inverse problem of determining the winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary the plate is loaded by a concentrated force and its transversal deflection is measured at the interior points we prove a global holder stability estimate under mild regularity assumptions on the unknown coefficient

cluster based branching for the asymmetric traveling salesman problem abstract this paper presents a new branching scheme for the asymmetric traveling salesman problem atsp based on clusters a cluster is defined as a node set with the characteristic that there exists an optimal solution in which the nodes in the node set are visited consecutively the paper considers identification of clusters implementation of a cluster based branching scheme and cluster based dominance tests the new approach is implemented in a branch and bound algorithm using a well known additive bounding procedure considerable savings in computing time are obtained compared to previously published assignment based branch and bound algorithms for the atsp

the complexity of very simple boolean formulas with applications the concepts of textbf sat hardness and textbf sat completeness modulo npolylogn time and linear size reducibility denoted by textbf sat hard npolylogn n and textbf sat complete npolylogn n respectively are introduced regardless of whether textbf p textbf np or textbf p neq textbf np it is shown that intuitivelyeach textbf sat hard npolylogn n problem requires essentially at least as much deterministic time as andeach textbf sat complete npolylogn n problem requires essentially the same deterministic time as the satisfiability problem for 3cnf formulas it is proved that the leqq satisfiability tautology unique satisfiability equivalence and minimization problems are already textbf sat complete npolylogn n for very simple boolean formulas and for very simple systems of boolean equations these completeness results are used to characterize the deterministic time complexities of a number of problems for lattices propositional calculi

a new ilp based refinement heuristic for vehicle routing problems in this paper we address the distance constrained capacitated vehicle routing problem dcvrp where k minimum cost routes through a central depot have to be constructed so as to cover all customers while satisfying for each route both a capacity and a total distance travelled limit

on the use of counters for reproducing deterministic test sets we propose a very simple and fast cad tool to check whether a binary counter can reproduce a predetermined set of test patterns in a reasonable time given a test matrix t the tool uses column merging complementation and permutation so that the distance between the starting and the finishing vector of the corresponding counter is minimized the hardware overhead of the proposed approach is by far lower than that of any other existing approach although it is computationally difficult np hard to obtain the absolute minimum distance we present an algorithm which in the absence of don t cares in the test matrix finds an appropriate column merging complementation and permutation that guarantees the distance is never more than twice as large as the best possible in the presence of don t cares the latter algorithm forms the basis of a powerful heuristic experiments on various test sets on benchmark circuits show that the exact number of clock cycles needed for a binary counter to reproduce all the patterns for the hard to detect faults compares favorably with the expected number yielded by existing weighted random lfsr based approaches which have significantly higher hardware overhead

extended neighborhood definition and characterization we consider neighborhood search defined on combinatorial optimization problems suppose that n is a neighborhood for combinatorial optimization problem x we say that n is lo equivalent locally optimal to n if for any instance of x the set of locally optimal solutions with respect to n and n are the same the union of two lo equivalent neighborhoods is itself lo equivalent to the neighborhoods the largest neighborhood that is lo equivalent to n is called the extended neighborhood of n and denoted as n we analyze some basic properties of the extended neighborhood we provide a geometric characterization of the extended neighborhood n when the instances have linear costs defined over a cone for the tsp we consider 2 opt the extended neighborhood for the 2 opt i e 2 exchange neighborhood structure we show that number of neighbors of each tour t in 2 opt is at least n 2 2 we show that finding the best tour in the 2 opt neighborhood is np hard we also show that the extended neighborhood for the graph partition problem is the same as the original neighborhood regardless of the neighborhood defined this result extends to the quadratic assignment problem as well this result on extended neighborhoods relies on a proof that the convex hull of solutions for the graph partition problem has a diameter of 1 that is every two corner points of this polytope are adjacent

static test compaction for full scan circuits based on combinational test sets and nonscan input sequences and a lower bound on the number of tests a new class of static compaction procedures is described that generate test sets with reduced test application times for scan circuits the proposed class of procedures combines the advantages of two earlier static compaction procedures one that tends to generate large numbers of tests with a short primary input sequence included in every test and one that tends to generate small numbers of tests with a long primary input sequence included in one of the tests a procedure of the proposed class starts from an initial test set that has a large number of tests and long primary input sequences and it selects a subset of the tests and subsequences of their primary input sequences it thus has the flexibility of finding an appropriate balance between the number of tests and the lengths of the primary input sequences in order to minimize the test application time several ways of computing the primary input sequences for the initial test set are considered the most compact test sets are obtained when a test sequence for the nonscan circuit is available and this sequence is used as part of every test in the initial test set however it is shown that high levels of compaction can also be achieved without the overhead of test generation for the nonscan circuit specifically we show that the industry practice of holding a primary input vector constant between scan operations can be accommodated we estimate the ability of the procedure to achieve optimum test sets by computing a lower bound on the number of tests and demonstrating that the procedure achieves or approaches this lower bound

sorting jordan sequences in linear time using level linked search trees for a jordan curve c in the plane nowhere tangent to the x axis let x1 x2 xn be the abscissas of the intersection points of c with the x axis listed in the order the points occur on c we call x1 x2 xn a jordan sequence in this paper we describe an o n time algorithm for recognizing and sorting jordan sequences the problem of sorting such sequences arises in computational geometry and computational geography our algorithm is based on a reduction of the recognition and sorting problem to a list splitting problem to solve the list splitting problem we use level linked search trees

test vector embedding into accumulator generated sequences a linear time solution the test set embedding problem is typically formed as follows given an n stage pattern generator and a test set calculate the minimum number of steps that the generator needs to operate in order to generate all vectors in the test set the cornerstone of a test set embedding technique is its embedding algorithm an embedding algorithm given an n stage pattern generator initialized to a starting value and an n bit target vector v calculates the location of v in the generated sequence in this paper a novel algorithm is presented that calculates the location of a vector into a sequence generated by an n stage accumulator accumulating a constant pattern the time complexity of the algorithm is of the order o n to the best of our knowledge this is the first embedding algorithm of the order o n that has been presented in the literature experiments performed on well known benchmark circuits reveal that complete test sets are embedded in sequences of practically acceptable length

the time dependent traveling salesman problem abstract a problem often considered in operations research and computational physics is the traveling salesman problem in which a traveling salesperson has to find the shortest closed tour between a given set of cities touching each city exactly once the distances between the single nodes are known to the traveling salesperson an extension of this problem is the time dependent traveling salesman problem in which these distances vary in time i will show how this more complex problem is treated with physical optimization algorithms like simulated annealing i will present results for the problem of the 127 beergardens in the area of augsburg in which i define a traffic zone in which traffic jams occur in the afternoon

an effective implementation of the lin kernighan traveling salesman heuristic abstract this paper describes an implementation of the lin kernighan heuristic one of the most successful methods for generating optimal or near optimal solutions for the symmetric traveling salesman problem tsp computational tests show that the implementation is highly effective it has found optimal solutions for all solved problem instances we have been able to obtain including a 13 509 city problem the largest non trivial problem instance solved to optimality today

application of threshold accepting to the evaluation of the discrepancy of a set of points efficient routines for multidimensional numerical integration are provided by quasi monte carlo methods these methods are based on evaluating the integrand at a set of representative points of the integration area a set may be called representative if it shows a low discrepancy however in dimensions higher than two and for a large number of points the evaluation of discrepancy becomes infeasible the use of the efficient multiple purpose heuristic threshold accepting offers the possibility to obtain at least good approximations to the discrepancy of a given set of points this paper presents an implementation of the threshold accepting heuristic an assessment of its performance for some small examples and results for larger sets of points with unknown discrepancy

multiobjective traveling salesperson problem on halin graphs in this paper we study traveling salesperson tsp and bottleneck traveling salesperson btsp problems on special graphs called halin graphs although both problems are np hard on general graphs they are polynomially solvable on halin graphs we address the multiobjective versions of these problems we show computational complexities of finding a single nondominated point as well as finding all nondominated points for different objective function combinations we develop algorithms for the polynomially solvable combinations

hyperneural network an efficient model for test generation in digital circuits this paper considers the problem of applying neural network for logic circuit testing and proposes an efficient method based on hyperneural network hnn the hnn uses an energy function that not only considers binary relations but also captures all higher order relations among n neurons we illustrate the hyperneural concept using two formulations first a constraint energy function is defined and the gate model is obtained second the hopfield network is reformulated to generate the gate level hyperneural model the gate level hnn are used to give a mathematical form to the digital circuit that in turn requires optimization techniques to solve the test generation problem we have used iscas 85 benchmark circuits to illustrate the method results are compared with those obtained from podem modem and fan

efficient vlsi fault simulation let c be an acyclic boolean circuit with n gates and n inputs a circuit manufacture error may result in a stuck at s a fault in a circuit identical to c except a gate v only outputs a fixed boolean value the s a fault simulation problem for c is to determine all possible s a faults which can be detected i e faults circuit and c would give distinct outputs by a given test pattern input we consider the case where c is a tree i e has fan out 1 we give a practical algorithm for fault simulation which simultaneously determines all detectable s a faults for every gate in the circuit tree c our algorithm required only the evaluation of a circuit fs c which has 7n gates and has depth 3 d 1 when d is the depth of c thus the sequential time of our algorithm is 7n and the parallel time is 3 d 1 furthermore fs c requires only a small constant factor more vlsi area than does the original circuit c we also extend our results to get efficient methods for fault simulation of oblivious vlsi circuits with feedback lines

detecting an inclusion in an elastic body by boundary measurements we consider the problem of determining within an elastic isotropic body omega the possible presence of an inclusion d made of different elastic material from boundary measurements of traction and displacement we prove that the volume size of d can be estimated from above and below by an easily expressed quantity related to work depending only on the boundary traction and displacement

positivity and almost positivity of biharmonic green s functions under dirichlet boundary conditions in general for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or equivalently a positivity preserving property is available the problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems it is shown that on the other hand for bounded smooth domains omega subset mathbb r n the negative part of the corresponding green s function is small when compared with its singular positive part provided n geqq 3 moreover the biharmonic green s function in balls b subset mathbb r n under dirichlet that is clamped boundary conditions is known explicitly and is positive it has been known for some time that positivity is preserved under small regular perturbations of the domain if n 2 in the present paper such a stability result is proved for n geqq 3