logic test pattern generation using linear codes logic testing of today s integrated circuits is a task of increasing difficulty as the number of circuits or transistors packed onto a single chip grows higher and higher exhaustive pattern testing with adequate partitioning of logic has been explored regarding its potential in solving the problems in test pattern generation and fault coverage in this paper we propose a new method of simultaneously generating exhaustive test patterns for all possible input subsets each corresponding to an output up tq a specified size the method is based on the structure of linear polynomial codes and can be easily implemented by modifying existing shift registers in an lssd or scan path design to embody additional feedback connections this is particularly attractive since the implementation is compatible with the approach of self testing using pseudorandom patterns thus a very reasonable strategy is to combine limited exhaustive pattern testing with pseudorandom pattern testing ini cases where complete exhaustive testing is not practical

the shortest path problem with two objective functions abstract we present methods to find the shortest path in a network where each path is associated with two objectives we describe how to obtain the nondominated paths and the extreme nondominated paths and compare the expected complexity of the methods an improvement in efficiency can be obtained when quasiconcave or quasiconvex utility functions are assumed in the first case we describe how to find the optimal extreme nondominated path and bounds for the optimal path value then the optimal path can be located by calculating the k th shortest path in the second case we suggest a branch and bound method to solve the problem

enhancing spl epsiv approximation algorithms with the optimal linear scaling factor finding a least cost path subject to a delay constraint in a network is an np complete problem and has been extensively studied many works reported in the literature tackle this problem by using epsiv approximation schemes and scaling techniques i e by mapping link costs into integers or at least discrete numbers a solution which satisfies the delay constraint and has a cost within a factor of the optimal one that can be computed with pseudopolynomial computational complexity in this paper having observed that the computational complexities of the epsiv approximation algorithms using the linear scaling technique are linearly proportional to the linear scaling factor we investigate the issue of finding the optimal the smallest linear scaling factor to reduce the computational complexities and propose two algorithms the optimal linear scaling algorithm olsa and the transformed olsa we analytically show that the computational complexities of our proposed algorithms are very low as compared with those of epsiv approximation algorithms therefore incorporating the two algorithms can enhance the epsiv approximation algorithms by granting them a practically important capability self adaptively picking the optimal linear scaling factors in different networks as such epsiv approximation algorithms become more flexible and efficient

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

approximation algorithms for constructing some required structures in digraphs abstract we consider a new problem of constructing some required structures in digraphs where all arcs installed in such required structures are supposed to be cut from some pieces of a specific material of length l formally we consider the model a digraph d v a w a structure s and a specific material of length l where w a r we are asked to construct a subdigraph d from d having the structure s such that each arc in d is constructed by a part of a piece or and some whole pieces of such a specific material the objective is to minimize the number of pieces of such a specific material to construct all arcs in d for the two required structures 1 a directed path from a node s to a node t and 2 a strongly connected spanning subdigraph we design four approximation algorithms with constant performance ratios to solve the both problems respectively

approximating some network design problems with node costs we study several multi criteria undirected network design problems with node costs and lengths all these problems are related to the multicommodity buy at bulk mbb problem in which we are given a graph g v e demands d s t s t v and a family c v v v of subadditive cost functions for every s t v we seek to send d s t flow units from s to t so that vc v f v is minimized where f v is the total amount of flow through v it is shown in andrews and zhang 2002 2 that with a loss of 2 e in the ratio we may assume that each st flow is unsplittable namely uses only one path in the multicommodity cost distance mcd problem we are also given lengths v v v and seek a subgraph h of g that minimizes c h s t vd s t h s t where h s t is the minimum length of an st path in h the approximability of these two problems is equivalent up to a factor 2 e 2 we give an o log 3n approximation algorithm for both problems for the case of the demands polynomial in n the previously best known approximation ratio for these problems was o log 4n chekuri et al 2006 2007 5 6 we also consider the maximum covering tree maxct problem which is closely related to mbb given a graph g v e costs c v v v profits p v v v and a bound c find a subtree t of g with c t c and p t maximum the best known approximation algorithm for maxct moss and rabani 2001 18 computes a tree t with c t 2c and p t w opt logn we provide the first nontrivial lower bound on approximation by proving that the problem admits no better than w 1 loglogn approximation assuming np quasi p this holds true even if the solution is allowed to violate the budget by a constant r as was done in 18 with r 2 our result disproves a conjecture of 18 another problem related to mbb is the shallow light steiner tree slst problem in which we are given a graph g v e costs c v v v lengths v v v a set u v of terminals and a bound l the goal is to find a subtree t of g containing u with diam t l and c t minimum we give an algorithm that computes a tree t with c t o log 2n opt and diam t o logn l previously a polylogarithmic bicriteria approximation was known only for the case of edge costs and edge lengths

complexity of single machine scheduling subject to nonnegative inventory constraints abstract this paper focuses on single machine scheduling subject to inventory constraints jobs either add items to an inventory or remove items from that inventory jobs that have to remove items cannot be processed if the required number of items is not available we consider scheduling problems on a single machine with the minimization of the total weighted completion time the maximum lateness and the number of tardy jobs respectively as objective and determine their computational complexity since the general versions of our problems turn out to be strongly np hard we consider special cases by assuming that different jobs have certain parameter values in common we determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs

linear dependencies in linear feedback shift registers linear feedback shift registers have been proposed to generate test patterns for the self test of logic networks the probability of linear dependence among k bit positions of a subset of k bits in a maximum length shift register sequence is an outstanding problem in this correspondence we derive a formula for the calculation of the probability

an fptas for minimizing the product of two non negative linear cost functions we consider a quadratic programming qp problem of the form min x t c x subject to ax b x 0 where c in mathbb r n times n rm rank c 1 and a in mathbb r m times n b in mathbb r m we present an fully polynomial time approximation scheme fptas for this problem by reformulating the qp as a parameterized lp and rounding the optimal solution furthermore our algorithm returns an extreme point solution of the polytope therefore our results apply directly to 0 1 problems for which the convex hull of feasible integer solutions is known such as spanning tree matchings and sub modular flows they also apply to problems for which the convex hull of the dominant of the feasible integer solutions is known such as s t shortest paths and s t min cuts for the above discrete problems the quadratic program models the problem of obtaining an integer solution that minimizes the product of two linear non negative cost functions

small approximate pareto sets for biobjective shortest paths and other problems we investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy epsilon the pareto curve of a multiobjective optimization problem we show that for a broad class of biobjective problems containing many important widely studied problems such as shortest paths spanning tree matching and many others we can compute in polynomial time an epsilon pareto set that contains at most twice as many solutions as the minimum set furthermore we show that the factor of 2 is tight for these problems i e it is np hard to do better we present upper and lower bounds for three or more objectives as well as for the dual problem of computing a specified number k of solutions which provide a good approximation to the pareto curve

approximation schemes for the restricted shortest path problem this note contains two fully polynomial approximation schemes for the shortest path problem with an additional constraint the main difficulty in constructing such algorithms arises since no trivial lower and upper bounds on the solution value whose ratio is polynomially bounded are known in spite of this difficulty one of the algorithms presented here is strongly polynomial applications to other problems are also discussed

formal language constrained path problems given an alphabet sigma a directed graph g whose edges are weighted and sigma labeled and a formal language l subseteq sigma the formal language constrained shortest simple path problem consists of finding a shortest simple path p in g complying with the additional constraint that l p in l here l p denotes the unique word obtained by concatenating the sigma labels of the edges along the path p the main contributions of this paper include the following we show that the formal language constrained shortest path problem is solvable efficiently in polynomial time when l is restricted to be a context free language cfl when l is specified as a regular language we provide algorithms with improved space and time bounds in contrast we show that the problem of finding a simple path between a source and a given destination is np hard even when l is restricted to fixed simple regular languages and to very simple classes of graphs e g complete grids for the class of treewidth bounded graphs we show that i the problem of finding a regular language constrained simple path between source and destination is solvable in polynomial time and ii the extension to finding cfl constrained simple paths is np complete our results extend the previous results in siam j comput 24 1995 pp 1235 1258 proceedings of the 76th annual meeting of the transportation research board 1997 and proceedings of the 9th acm sigact sigmod sigart symposium on database systems 1990 pp 230 242 several additional extensions and applications of our results in the context of transportation problems are presented for instance as a corollary of our results we obtain a polynomial time algorithm for the best k similar path problem studied in proceedings of the 76th annual meeting of the transportation reasearch board 1997 the previous best algorithm was given by proceedings of the 76th annual meeting of the transportation research board 1997 and takes exponential time in the worst case

bulk robust combinatorial optimization we commence an algorithmic study of bulk robustness a new model of robustness in combinatorial optimization unlike most existing models bulk robust combinatorial optimization features a highly nonuniform failure model instead of an interdiction budget bulk robust counterparts provide an explicit list of interdiction sets comprising the admissible set of scenarios thus allowing to model correlations between failures of different components in the system interdiction sets of variable cardinality and more the resulting model is suitable for capturing failures of complex structures in the system we provide complexity results and approximation algorithms for bulk robust counterparts of the minimum matroid basis problems and the shortest path problem our results rely on various techniques and outline the rich and heterogeneous combinatorial structure of bulk robust optimization

breakdown points of t type regression estimators summary to bound the influence of a leverage point generalised m estimators have been suggested however the usual generalised m estimator of regression has a breakdown point that is less than the inverse of its dimension this paper shows that dimension independent positive breakdown points can be attained by a class of well defined generalised mestimators with redescending scores the solution can be determined through optimisation of t type likelihood applied to properly weighted residuals the highest breakdown point of is attained by cauchy score these bounded influence and high breakdown estimators can be viewed as a fully iterated version of the one step generalised m estimates of simpson ruppert carroll 1992 with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations given the design dependent weights they can be computed via em algorithms empirical investigations show that they are highly competitive with other robust estimators of regression

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

inference and sequential design summary if an experiment is designed sequentially repeated sampling inference may not necessarily be made using distributional results that are valid for fixed designs a few simple illustrative examples and alternative approaches are given sometimes the sequential nature of design can be ignored asymptotically links are forged with inference for stochastic processes and missing data problems

novel test pattern generators for pseudoexhaustive testing pseudoexhaustive testing of a combinational circuit involves applying all possible input patterns to all its individual output cones the testing ensures detection of all detectable multiple stuck at faults in the circuit and all detectable combinational faults within individual cones test pattern generators based on coding theory principles are not tailored to a specific circuit as they do not utilize any structural information they usually generate test sets that are several orders of magnitude larger than the minimum size pseudoexhaustive test set required for a specific circuit in this paper we describe hardware efficient test pattern generators that employ knowledge of the circuit output cone structures for generating minimal test sets using our techniques we have designed generators that generate minimum size test sets for the iscas benchmark circuits

asymptotics in response adaptive designs generated by a two color randomly reinforced urn this paper illustrates asymptotic properties for a response adaptive design generated by a two color randomly reinforced urn model the design considered is optimal in the sense that it assigns patients to the best treatment with probability converging to one an approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one results on the rate of convergence of the number of patients assigned to each treatment are also obtained finally we study the asymptotic behavior of a suitable test statistic

a comparison of the efron hinkley ancillary and the likelihood ratio ancillary in a particular example two approximate ancillaries the efron hinkley ancillary and the signed likelihood ratio are compared in a specific example by means of their level curves their marginal densities and the conditional and unconditional likelihood functions it is shown that in the present model the latter of the two ancillaries is the better it is almost exactly distribution constant and has more stable conditional likelihood functions

optimal labeling of point features in rectangular labeling models we investigate the np hard label number maximization problem lnm given a set of rectangular labels each of which belongs to a point feature in the plane the task is to find a labeling for a largest subset p of a labeling is a placement such that none of the labels overlap and each p is placed according to a labeling model in the discrete models the label must be placed so that the labeled point coincides with an element of a predefined subset of corners of the rectangular label in the continuous or slider models the point must lie on a subset of boundaries of the label obviously the slider models allow a continuous movement of a label around its point feature leading to a significantly higher number of labels that can be placed we present exact algorithms for this problem that are based on a pair of so called constraint graphs that code horizontal and vertical positioning relations the key idea is to link the two graphs by a set of additional constraints thus characterizing all feasible solutions of lnm this enables us to formulate a zero one integer linear program whose solution leads to an optimal labeling we can express lnm in both the discrete and the slider labeling models to our knowledge we present the first algorithm that computes provably optimal solutions in the slider models we find it remarkable that our approach is independent of the labeling model and results in a discrete algorithm even if the problem is of continuous nature as in the slider models extensive experimental results on both real world instances and point sets created by a widely used benchmark generator show that the new approach although being an exponential time algorithm is applicable in practice

vector space theoretic analysis of additive cellular automata and its application for pseudoexhaustive test pattern generation a novel scheme for utilizing the regular structure of three neighborhood additive cellular automata cas for pseudoexhaustive test pattern generation is introduced the vector space generated by a ca can be decomposed into several cyclic subspaces a cycle corresponding to an m dimensional cyclic subspace has been shown to pseudoexhaustively test an n input circuit n or m such a cycle is shown to supply a m 1 bit exhaustive pattern including the all zeros m 1 tuple schemes have been reported specifying how one or more subsets of m 1 cell positions of an n cell ca can be identified to generate exhaustive patterns in an m dimensional cyclic subspace

fast and simple approximation schemes for generalized flow we present fast and simple fully polynomial time approximation schemes fptas for generalized versions of maximum flow multicommodity flow minimum cost maximum flow and minimum cost multicommodity flow we extend and refine fractional packing frameworks introduced in fptas s for traditional multicommodity flow and packing linear programs our fptas s dominate the previous best known complexity bounds for all of these problems some by more than a factor of n2 where n is the number of nodes this is accomplished in part by introducing an efficient method of solving a sequence of generalized shortest path problems our generalized multicommodity fptas s are now as fast as the best non generalized ones we believe our improvements make it practical to solve generalized multicommodity flow problems via combinatorial methods

design of test sequences for vlsi self testing using lfsr consider a shift register sr of length n and a collection of designated subsets of 0 1 n 1 the problem is how to add feedback to the sr such that the resulting linear feedback shift register lfsr exercises almost exhaustively each of the designated subsets and is of small period several previously known results for maximum length lfsr are extended to more general lfsr and in particular a previously known algorithm is simplified and extended applications to the problems of vlsi self testing are discussed and illustrated

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

pseudorandom arrays for built in tests parallel pseudorandom sequences for use in built in test are discussed the two dimensional nature of these sequences makes it natural to consider the resulting binary arrays some of the desired properties of such arrays are discussed as well as some of the problems generators for such arrays are described a conventional lfsr with parallel output is shown to be a poor choice for such a generator several compact generators are described which are shown to be compromises between complexity and varying degrees of implementation of the desired properties in the resulting sequences one of the compact generators produces sequences which have the desired properties for built in tests

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

on fault tolerant path optimization under qos constraint in multi channel wireless networks abstract in multi channel wireless networks a fundamental problem is to find node disjoint paths minimising global cost or the maximum individual path cost under the constraint that each path operates on a separate channel to maximise the fault tolerance and robustness against channel instability and malicious attacks meanwhile the quality of service qos requirement e g in terms of end to end delay needs to be satisfied on each path in this paper we provide a comprehensive formulation and analysis on this multi path optimization problem by casting it to the problem k disjoint path with different colours k dpdc we further formulate the restricted minsum k dpdc and restricted minmax k dpdc to denote the problems of finding multiple node and channel disjoint paths minimising the global cost and the maximum individual path cost under the qos constraint on the path end to end delay given the np hardness of both problems we focus on directed acyclic graphs and propose fully polynomial time approximation algorithms for both problems

exhaustive test pattern generation with constant weight vectors we develop in this paper a simple way of generating a test set which simultaneously provides exhaustive pattern testing with respect to all input subsets of a logic circuit up to a certain size it is shown that such a test set may be formed with vectors of a particular set of weights main theorems and examples are established and illustrated in the binary case for 2 value logic circuits and then generalized to nonbinary cases for multivalue logic circuits such test sets are simple in structure and become optimal in size in certain cases it is also shown that such a test set can be effectively implemented via a scan path type shifter

recursive pseudoexhaustive test pattern generation a recursive technique for generating exhaustive patterns is presented the method is optimal i e in one experiment it covers exhaustively every block of k adjacent inputs in the first 2 sup k vectors implementation methods based on characteristic functions of test vectors are provided they include a parallel pattern generator employing an exclusive or array and two serial generators that can be easily adopted in a scan based built in self test environment

complexity results for the linear time cost tradeoff problem with multiple milestones and completely ordered jobs abstract we consider two linear project time cost tradeoff problems with multiple milestones unless a milestone is completed on time penalty costs for tardiness may be imposed however these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs our model describes these penalty costs as the total weighted number of tardy milestone the first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs we develop a linear programming formulation for the case with a fixed number of milestones for the case with an arbitrary number of milestones we show that under completely ordered jobs the first problem is np hard in the ordinary sense while the second problem is polynomially solvable

conditional statistical inference and quantification of relevance summary we argue that it can be fruitful to take a predictive view on notions such as the precision of a point estimator and the confidence of an interval estimator in frequentist inference this predictive approach has implications for conditional inference because it immediately allows a quantification of the concept of relevance for conditional inference conditioning on an ancillary statistic makes inference more relevant in this sense provided that the ancillary is a precision index not all ancillary statistics satisfy this demand we discuss the problem of choice between alternative ancillary statistics the approach also has implications for the best choice of variance estimator taking account of correlations with the squared error of estimation itself the theory is illustrated by numerous examples many of which are classical

the constrained minimum weighted sum of job completion times problem we consider the problem of minimizing the weighted sum of job completion times on a single machine subject to certain job weights with an additional side constraint on the weighted sum of job completion times with respect to different job weights this problem is np hard and we provide a polynomial time approximation scheme for this problem our method is based on lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

exact and approximation algorithms for the min max k traveling salesmen problem on a tree abstract given k identical salesmen where k 2 is a constant independent of the input size the min max k traveling salesmen problem on a tree is to determine a set of k tours for the salesmen to serve all customers that are located on a tree shaped network so that each tour starts from and returns to the root of the tree with the maximum total edge weight of the tours minimized the problem is known to be np hard even when k 2 in this paper we have developed a pseudo polynomial time exact algorithm for this problem with any constant k 2 closing a question that has remained open for a decade along with this we have further developed a 1 approximation algorithm for any 0

an enhanced k sp algorithm with pruning strategies to solve the constrained shortest path problem a new exact algorithm for the constrained shortest path problem is presented extensive experiments comparing the behavior of the new scheme and the recent best method from the literature are provided the proposed approach solves the constrained shortest path problem in usa road networks containing millions of nodes and arcs we propose an exact method to solve the constrained shortest path csp problem the new approach takes advantage of the binary partition strategy of a recent k shortest paths k sp algorithm that allows posing numerous additional path constraints in the model without extra difficulty we adapt and incorporate several pruning strategies from the literature on the csp problem in this scheme and obtain a robust and scalable algorithm the method is compared with the current best algorithm to solve the csp problem and produces significant speedups in a wide range of network configurations an example is given where the csp problem is solved in road networks containing a million nodes and arcs

optimal data augmentation strategies for additive models abstract consider an experiment where the factors are measured on a continuous scale and suppose that the experimenter is permitted to augment the existing observations with one or more new data points bondar s universal optimality criterion u optimality suggests that the problem is best studied in the eigenvector coordinate system we proceed by showing how to construct new points that first equate and then jointly increase the smaller eigenvalues of the crossproduct of the independent variables we discuss the limitations of design augmentation strategies based solely on the crossproduct matrix our goals are to equate and minimize the variances of the estimated regression coefficients keep the new points constrained in a prespecified experimental region use as much of the information in the original points as possible and keep the number of required new points as small as possible we offer several data augmentation strategies to meet these requirements as u optimality subsumes each of the d a

on the efficiency of two stage response adaptive designs in this paper we investigate the efficiency of response adaptive locally optimum designs we focus on two stage adaptive designs where after the first stage the accrued data are used to determine a locally optimum design for the second stage on the basis of an explicit expansion of the information matrix we compare the variance of the maximum likelihood estimates obtained from a two stage adaptive design and a fixed design without adaptation for several one parameter models we provide explicit expressions for the relative efficiency of these two designs which is seen to depend sensitively on the statistical problem under investigation in particular we show that in non linear regression models with moderate or large variances the first stage sample size of an adaptive design should be chosen sufficiently large in order to address variability in the interim parameter estimates these findings support the results of recent simulation studies conducted to compare adaptive designs in more complex situations we finally present an application to a real clinical dose finding trial aiming at the estimation of the smallest dose achieving a certain percentage of the maximum treatment effect by using a three parameteremax model copyright 2012 john wiley sons ltd

the use of linear sums in exhaustive testing the increasing role of exhaustive testing techniques in vlsi has prompted a number of investigations into methods for achieving locally exhaustive testing of the components of a large digital circuit using a comparatively small number of test signals this paper examines the possibility of introducing linear sums of the test signals into this testing process it is shown that with the addition of a relatively small amount of additional circuitry significant reductions in the number of required test signals and tests can often be achieved in particular it is shown that for any specific combinational circuit the number of required test signals can be made to be independent of the number of inputs and to depend only logarithmically on the number of outputs the role of these linear sums in the generation of universal test sets is also discussed

pseudoexhaustive test pattern generator with enhanced fault coverage a method of pseudoexhaustive test pattern generation is proposed that is suitable above all for circuits using random access scan two linear feedback shift registers are used to generate scan addresses and test patterns to be scanned into these addresses it is shown that the method gives better results than random testing

computing a most probable delay constrained path np hardness and approximation schemes delay constrained path selection is concerned with finding a source to destination path so that the delay of the path is within a given delay bound when the network is modeled by a directed graph where the delay of a link is a random variable with a known mean and a known variance the problem becomes that of computing a most probable delay constrained path in this paper we present a comprehensive theoretical study of this problem first we prove that the problem is np hard next for the case where there exists a source to destination path with a delay mean no more than the given delay bound we present a fully polynomial time approximation scheme in other words for any given constant e such that 0 e 1 our algorithm computes a path whose probability of satisfying the delay constraint is at least 1 e times the probability that the optimal path satisfies the delay constraint with a time complexity bounded by a polynomial in the number of network nodes and 1 e finally for the case where any source to destination path has a delay mean larger than the given delay bound we present a simple approximation algorithm with an approximation ratio bounded by the square root of the hop count of the optimal path

conditional inference and cauchy models summary many computations associated with the two parameter cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane with this convention we show that the family is closed under m6bius transformation of the sample space there is a similar induced transformation on the parameter space the chief raison d etre of the paper however is that the two parameter cauchy model provides an example of a nonunique configuration ancillary in the sense of fisher 1934 such that the maximum likelihood estimate together with either ancillary is minimal sufficient some consequences for bayesian inference and non bayesian conditional inference are explored in particular it is shown that conditional coverage probability assessments depend on the choice of ancillary for moderate deviations the effect occurs in the op n 1 term for large deviations the relative effect is op n2

multiconstrained qos routing a norm approach a fundamental problem in quality of service qos routing is the multiconstrained path mcp problem where one seeks a source destination path satisfying k 2 additive qos constraints in a network with k additive qos parameters the mcp problem is known to be np complete one popular approach is to use the shortest path with respect to a single edge weighting function as an approximate solution to mcp in a pioneering work jaffe showed that the shortest path with respect to a scaled 1 norm of the k edge weights is a 2 approximation to mcp in the sense that the sum of the larger of the path weight and its corresponding constraint is within a factor of 2 from minimum in a recent paper xue et al showed that the shortest path with respect to a scaled oc norm of the k edge weights is a k approximation to mcp in the sense that the largest ratio of the path weight over its corresponding constraint is within a factor of k from minimum in this paper we study the relationship between these two optimization criteria and present a class of provably good approximation algorithms to mcp we first prove that a good approximation according to the second optimization criterion is also a good approximation according to the first optimization criterion but not vice versa we then present a class of very simple k approximation algorithms according to the second optimization criterion based on the computation of a shortest path with respect to a single edge weighting function

an efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection given an undirected graph g v e with v n and e m nonnegative integers ce and de for each edge e in e and a bound d the constrained minimum spanning tree problem cst is to find a spanning tree t v et such that sum e in e t d e leq d and sum e in e t c e is minimized we present an efficient polynomial time approximation scheme eptas for this problem specifically for every epsilon 0 we present a 1 epsilon approximation algorithm with time complexity o frac 1 epsilon o frac 1 epsilon n 4 our method is based on lagrangian relaxation and matroid intersection

a polynomial solvable minimum risk spanning tree problem with interval data abstract we propose and study a new model for the spanning tree problem with interval data the minimum risk spanning tree mrst problem that finds diverse applications in network design given an underlying network g v e each link e e can be established by paying a cost c e c e c e and accordingly takes a risk c e c e c e c e of link failure the mrst problem is to establish a spanning tree t in g of total cost not more than a given constant so that the risk sum over the links in t is minimized we prove that the mrst problem can be solved in polynomial time and thus has algorithmic aspect more satisfactory than the np hard robust spanning tree problem with interval data

approximating the restricted 1 center in graphs abstract this paper studies the restricted vertex 1 center problem rv1cp and restricted absolute 1 center problem ra1cp in general undirected graphs with each edge having two weights cost and delay first we devise a simple fptas for rv1cp with o m n 3 1 log log n running time based on fptas proposed by lorenz and raz 1999 11 for computing end to end restricted shortest path rsp during the computation of the fptas for rv1cp we derive a rsp distance matrix next we discuss ra1cp in such graphs where the delay is a separable e g linear function of the cost on edge we investigate an important property that the fptas for rv1cp can find a 1 approximation of ra1cp when the rsp distance matrix has a saddle point in addition we show that it is harder to find an approximation of ra1cp when the matrix has no saddle point this paper develops a scaling algorithm with at most o m n 3 k log k log log n running time where k is a step size parameter and is a given positive number to find a 1 approximation of ra1cp

multiple seed tpg structures linear feedback shift registers lfsrs are popular mechanisms for built in test pattern generation tpg they are normally used with a primitive characteristic polynomial because in that case only one initialization state seed is required we show that if the characteristic polynomial is nonprimitive irreducible the required seeds can still be efficiently generated we establish a formula that shows how the seeds of any nonprimitive irreducible polynomial relate to each other this leads to an efficient hardware implementation with small hardware overhead irrespective of the number of seeds and enhances the choices available for the design of appropriate tpg structures in the case of pseudoexhaustive tpg that were previously limited to primitive characteristic polynomials only

quickest flows over time flows over time also called dynamic flows generalize standard network flows by introducing an element of time they naturally model problems where travel and transmission are not instantaneous traditionally flows over time are solved in time expanded networks that contain one copy of the original network for each discrete time step while this method makes available the whole algorithmic toolbox developed for static flows its main and often fatal drawback is the enormous size of the time expanded network we present several approaches for coping with this difficulty first inspired by the work of ford and fulkerson on maximal s t flows over time or maximal dynamic s t flows we show that static length bounded flows lead to provably good multicommodity flows over time second we investigate condensed time expanded networks which rely on a rougher discretization of time we prove that a solution of arbitrary precision can be computed in polynomial time through an appropriate discretization leading to a condensed time expanded network of polynomial size in particular our approach yields fully polynomial time approximation schemes for the np hard quickest min cost and multicommodity flow problems for single commodity problems we show that storage of flow at intermediate nodes is unnecessary and our approximation schemes do not use any

on second order optimality of the observed fisher information the realized error of an estimate is determined not only by the efficiency of the estimator but also by chance for example suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle then intuitively the longer that vector happens to be the more accurately its angle is likely to be estimated yet this chance though its information is contained in the data cannot be accounted for by the variance of the estimate one way to capture it is by the direct estimation of the realized error in this paper we will demonstrate that the squared error of the maximum likelihood estimate to the extent to which it can be estimated can be most accurately estimated by the inverse of the observed fisher information in relation to this optimality we will also study the properties of several other estimators including the inverse of the expected fisher information the sandwich estimators the jackknife and the bootstrap estimators unlike the observed fisher information these estimators are not optimal

successive improvement of the order of ancillarity summary it is shown by an argument similar to one of welch 1947 that it is under usual regularity conditions in general possible to improve the order of ancillarity successively this means that when an asymptotic ancillary has been constructed such that its distribution is independent of the parameter apart from terms of order o n k then a new ancillary may be constructed with a distribution which depends on the parameter only through terms of order o nk22 it is shown how the new ancillary may be constructed explicitly when the expansion is of the edgeworth type more specifically when it is a normal density multiplied by linear combinations of hermite polynomials

efficient rounding of approximate designs summary discretization methods to round an approximate design into an exact design for a given sample size n are discussed there is a unique method called efficient rounding which has the smallest loss of efficiency under a wide family of optimality criteria the efficient rounding method is a multiplier method of apportionment which otherwise is known as the method of john quincy adams or the method of smallest divisors

bi objective matchings with the triangle inequality this article deals with a bi objective matching problem the input is a complete graph and two values on each edge a weight and a length which satisfy the triangle inequality it is unlikely that every instance admits a matching with maximum weight and maximum length at the same time therefore we look for a compromise solution i e a matching that simultaneously approximates the best weight and the best length for which approximation ratio can we guarantee that any instance admits a approximate matching we propose a general method which relies on the existence of an approximate matching in any graph of small size an algorithm for computing a 1 3 approximate matching in any instance is provided the algorithm uses an analytical result stating that every instance on at most 6 nodes must admit a 1 2 approximate matching we extend our analysis with a computer aided approach for larger graphs indicating that the general method may produce a 2 5 approximate matching we conjecture that a 1 2 approximate matching exists in any bi objective instance satisfying the triangle inequality

qos routing in communication networks approximation algorithms based on the primal simplex method of linear programming given a directed network with two integer weights cost and delay associated with each link quality of service qos routing requires the determination of a minimum cost path from one node to another node such that the delay of the path is bounded by a specified integer value this problem also known as the constrained shortest path problem csp admits an integer linear programming ilp formulation due to the integrality constraints the problem is np hard so approximation algorithms have been presented in the literature among these the larac algorithm based on the dual of the lp relaxation of the csp problem is very efficient in contrast to most of the currently available approaches we study this problem from a primal perspective several issues relating to efficient implementations of our approach are discussed we present two algorithms of pseudopolynomial time complexity one of these allows degenerate pivots and uses an anticycling strategy and the other called the nbs algorithm is based on a novel strategy which avoids degenerate pivots experimental results comparing the nbs algorithm the larac algorithm and general purpose lp solvers are presented in all cases the nbs algorithm compares favorably with others and beats them on dense networks

approximation schemes for a class of subset selection problems in this paper we develop an easily applicable algorithmic technique tool for developing approximation schemes for certain types of combinatorial optimization problems special cases that are covered by our result show up in many places in the literature for every such special case a particular rounding trick has been implemented in a slightly different way with slightly different arguments and with slightly different worst case estimations usually the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument our easily applied result unifies many of these results and sometimes it even leads to a simpler proof we demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems as a special case we derive the existence of an fptas for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine the approximability status of this problem has been open for some time

a polynomial approximation scheme for scheduling on uniform processors using the dual approximation approach in this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors more specifically the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible we give a family of polynomial time algorithms a such that a delivers a solution that is within a relative error of e of the optimum the technique employed is the dual approximation approach where infeasible but superoptimal solutions for a related dual problem are converted to the desired feasible but possibly suboptimal solution

a ptas for weight constrained steiner trees in series parallel graphs in this paper we study the problem of computing a minimum cost steiner tree subject to weight constraint in a series parallel graph where each edge has a nonnegative integer cost and a nonnegative integer weight we present a strongly polynomial time approximation scheme for this np complete problem

the edge recoloring cost of monochromatic and properly edge colored paths and cycles we introduce a number of problems regarding edge color modifications in edge colored graphs and digraphs consider a property a c edge colored graph g c not satisfying and an edge recoloring cost matrix r r i j c c where r i j 0 denotes the cost of changing color i of edge e to color j basically in this kind of problem the idea is to change the colors of one or more edges of g c in order to construct a new edge colored graph such that the total edge recoloring cost is minimized and property is satisfied we also consider the destruction of potentially undesirable structures with the minimum edge recoloring cost in this paper we are especially concerned with the construction and destruction of properly edge colored and monochromatic paths trails and cycles in graphs and digraphs some related problems and future directions are presented

new approaches to multi objective optimization a natural way to deal with multiple partially conflicting objectives is turning all the objectives but one into budget constraints many classical optimization problems such as maximum spanning tree and forest shortest path maximum weight perfect matching maximum weight independent set basis in a matroid or in the intersection of two matroids become np hard even with one budget constraint still for most of these problems efficient deterministic and randomized approximation schemes are known not much is known however about the case of two or more budgets filling this gap at least partially is the main goal of this paper in more detail we obtain the following main results using iterative rounding for the first time in multi objective optimization we obtain multi criteria ptass which slightly violate the budget constraints for spanning tree matroid basis and bipartite matching with k o 1 k o 1 budget constraints we present a simple mechanism to transform multi criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system this gives improved algorithms for several problems in particular this mechanism can be applied to the above bipartite matching algorithm hence obtaining a pure ptas we show that points in low dimensional faces of any matroid polytope are almost integral an interesting result on its own this gives a deterministic approximation scheme for k k budgeted matroid independent set we present a deterministic approximation scheme for k k budgeted matching in general graphs where k o 1 k o 1 interestingly to show that our procedure works we rely on a non constructive result by stromquist and woodall which is based on the ham sandwich theorem

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

three stage approaches for optimizing some variations of the resource constrained shortest path sub problem in a column generation context this paper presents a unified three stage approach tsa comprising preprocessing setup and iterative solution stages for solving several variations of the resource constrained shortest path problem rcsp tsa is designed specially for column generation applications in which sub problems must be solved repetitively the first two stages are implemented one time and only the third stage need be applied repetitively in a companion paper the authors proposed a tsa for solving rcsp on an acyclic graph with upper bound resource limitation constraints this paper shows that a tsa can be designed to solve each of several related problems shortest path with equality resource limitation constraints shortest path with resource windows resource constrained k shortest path and multiple resource multiple choice knapsack a numerical example demonstrates application of a tsa to design an international assembly system and its supply chain using branch and price with multiple choice knapsack sub problems computational results show that our tsa can solve this sub problem effectively in such a column generation environment

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated