the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

on comparability and permutation graphs this paper presents a technique for orienting a comparability graph transitively in o n 2 time the best previous algorithm for this problem required omega n 3 time when combined with a result in sp we can recognize permutation graphs in o n 2 time and determine in the same time complexity whether two permutation graphs are isomorphic the orientation algorithm can also be used to reduce the problem of recognizing comparability graphs to that of recognizing transitive graphs this gives an upper bound of o n 2 49 for comparability graph recognition while the fastest previous algorithms required omega n 3 time

swarm intelligence and evolutionary algorithms the popularity of metaheuristics especially swarm intelligence and evolutionary algorithms has increased rapidly over the last two decades numerous algorithms are proposed each year and progressively more novel applications are being found however different metaheuristics are often compared by their performance on problems with an arbitrarily fixed number of allowed function calls there are surprisingly few papers that explore the relationship between the relative performance of numerous metaheuristics on versatile numerical real world problems and the number of allowed function calls in this study the performance of 33 various metaheuristics proposed between 1960 and 2016 have been tested on 22 numerical real world problems from different fields of science with the maximum number of function calls varying between 5000 and 500 000 it is confirmed that the algorithms that succeed in comparisons when the computational budget is low are among the poorest performers when the computational budget is high and vice versa among the tested variants particle swarm optimization algorithms and some new types of metaheuristics perform relatively better when the number of allowed function calls is low whereas differential evolution and genetic algorithms perform better relative to other algorithms when the computational budget is large it is difficult to find any metaheuristic that would perform adequately over all of the numbers of function calls tested it was also found that some algorithms may become completely unreliable on specific real world problems even though they perform reasonably on others

a new evolutionary search strategy for global optimization of high dimensional problems global optimization of high dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation the weakness of randomization based evolutionary algorithms in searching high dimensional spaces is demonstrated in this paper a new strategy sp uci is developed to treat complexity caused by high dimensionalities this strategy features a slope based searching kernel and a scheme of maintaining the particle population s capability of searching over the full search space examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that sp uci surpasses two popular algorithms particle swarm optimizer pso and differential evolution de on high dimensional problems experimental results also corroborate the argument that in high dimensional optimization only problems with well formative fitness landscapes are solvable and slope based schemes are preferable to randomization based ones

delta wye transformations and the efficient reduction of two terminal planar graphs a simple o v 2 time algorithm is presented that reduces a connected two terminal undirected planar graph to a single edge by way of series and parallel reductions and delta wye transformations the method is applied to a class of optimization equilibnum problems which includes max flow shortest path and electrical resistance problems

lower bounds for the quadratic semi assignment problem abstract this paper presents a class of lower bounds for the quadratic semi assignment problem qsap these bounds are based on recent results on polynomially solvable cases in particular we will consider the qsaps whose quadratic cost coefficients define a reducible graph the idea is to decompose the problem into several subproblems each defined on a reducible subgraph lagrangean decomposition technique is used to improve the results several lower bounds are computationally compared on several types of test problems

substitutes complements and ripples in network flows we study the qualitative variation of minimum cost network flows and their associated costs with arc parameters demands are given at each node flow is conserved each arc s parameter lies in a lattice and the flow cost is real or infinity valued our main results are roughly as follows if the flow cost is arc additive the problem can be decomposed into independent problems on each biconnected component of the graph if also the flow cost is convex in the flow the magnitude of the change in the optimal flow in arc a resulting from changing arc b s parameter diminishes the less biconnected a is to b arc a is less biconnected to b than is arc d if every simple cycle containing a and b also contains d this relation is a quasi order with two distinct arcs being equivalent if and only if deleting them disconnects the graph hie hasse diagram of the partial order of the induced equivalence classes is a tree with all arcs directed towards the class containing b two arcs are complements resp substitute

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

on the o 1 t convergence rate of ye yuan s modified alternating direction method of multipliers the alternating direction method of multipliers admm is known to be a classic and efficient method for constrained optimization problem with two blocks of variables and its empirical efficiency has been well illustrated in various fields specially for improving its speed performance ye and yuan suggested to do an additional extension with an optimal step size on the variables after each iteration of the primary admm indeed the numerical experiments indicate that this modified admm improves the speed performance of the admm by around 40 without changing the algorithmic framework much recently the o 1 t convergence rate of the primary admm is established inspired by its idea in this paper we show that this improved admm also has o 1 t convergence rate the reason that larger c yields better speed performance is also investigated and explained

differential evolution with dynamic stochastic selection for constrained optimization how much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper stochastic ranking has been demonstrated as an effective technique for constrained optimization in stochastic ranking the comparison probability will affect the position of feasible solution after ranking and the quality of the final solutions in this paper the dynamic stochastic selection dss is put forward within the framework of multimember differential evolution firstly a simple version named dss mde is given where the comparison probability decreases linearly the algorithm dss mde has been compared with two state of the art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions dss mde is also evaluated on four well studied engineering design examples and the experimental results are significantly better than current available results secondly other dynamic settings of the comparison probability for dss mde are also designed and tested from the experimental results dss mde is effective for constrained optimization finally dss mde with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in cec 06 and the experimental results on most functions are competitive

multi objective particle swarm optimization with time variant inertia and acceleration coefficients in this article we describe a novel particle swarm optimization pso approach to multi objective optimization moo called time variant multi objective particle swarm optimization tv mopso tv mopso is made adaptive in nature by allowing its vital parameters viz inertia weight and acceleration coefficients to change with iterations this adaptiveness helps the algorithm to explore the search space more efficiently a new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front tv mopso has been compared with some recently developed multi objective pso techniques and evolutionary algorithms for 11 function optimization problems using different performance measures

scheduling series parallel task graphs to minimize peak memory abstract we consider a variant of the well known np complete problem of minimum cut linear arrangement for directed acyclic graphs in this variant we are given a directed acyclic graph and we are asked to find a topological ordering such that the maximum number of cut edges at any point in this ordering is minimum in our variant the vertices and edges have weights and the aim is to minimize the maximum weight of cut edges in addition to the weight of the last vertex before the cut there is a known polynomial time algorithm liu 1987 17 for the cases where the input graph is a rooted tree we focus on the instances where the input graph is a directed series parallel graph and propose a polynomial time algorithm thus expanding the class of graphs for which a polynomial time algorithm is known directed acyclic graphs are used to model scientific applications where the vertices correspond to the tasks of a given application and the edges represent the dependencies between the tasks in such models the problem we address reads as minimizing the peak memory requirement in an execution of the application our work combined with liu s work on rooted trees addresses this practical problem in two important classes of applications

calibration of rainfall runoff models application of global optimization to the sacramento soil moisture accounting model conceptual rainfall runoff models are difficult to calibrate by means of automatic methods one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters this paper investigates the consistency with which two global optimization methods the shuffled complex evolution sce ua method developed by the authors and the multistart simplex msx method are able to find the optimal parameter set during calibration of the sacramento soil moisture accounting model sac sma of the national weather service river forecast system nwsrfs in the first phase of this study error free synthetic data are used to conduct a comparative evaluation of the algorithms under ideal conditions in 10 independent trials of each algorithm in which 13 parameters of the sac sma model were optimized simultaneously the sce ua method achieved a 100 success rate in locating the precise global optimum i e the true parameter values while the msx method failed in all trials even with more than twice the number of function evaluations in the second phase historical data from the leaf river watershed are used to conduct a comparative evaluation of the algorithms under real conditions using two different estimation criteria drms and hmle the sce ua algorithm obtained consistently lower function values and more closely grouped parameter estimates while using one third fewer function evaluations than the msx algorithm

planar orientations with low out degree and compaction of adjacency matrices abstract we consider the problem of orienting the edges of a planar graph in such a way that the out degree of each vertex is minimized if for each vertex v the out degree is at most d then we say that such an orientation is d bounded we prove the following results each planar graph has a 5 bounded acyclic orientation which can be constructed in linear time each planar graph has a 3 bounded orientation which can be constructed in linear time a 6 bounded acyclic orientation and a 3 bounded orientation of each planar graph can each be constructed in parallel time o log n log n on an erew pram using o n log n log n processors as an application of these results we present a data structure such that each entry in the adjacency matrix of a planar graph can be looked up in constant time the data structure uses linear storage and can be constructed in linear time

detection and remediation of stagnation in the nelder mead algorithm using a sufficient decrease condition the nelder mead algorithm can stagnate and converge to a nonoptimal point even for very simple problems in this note we propose a test for sufficient decrease which if passed for all iterations will guarantee convergence of the nelder mead iteration to a stationary point if the objective function is smooth and the diameters of the nelder mead simplices converge to zero failure of this condition is an indicator of potential stagnation as a remedy we propose a new step which we call an oriented restart that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point we also give results that apply when the objective function is a low amplitude perturbation of a smooth function we illustrate our results with some numerical examples

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

a strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on two terminal series parallel networks we present strongly polynomial algorithms to find rational and integer flow vectors that minimize a convex separable quadratic cost function on two terminal series parallel graphs

efficient iterative solution of finite element discretized nonsmooth minimization problems abstract for the iterative solution of finite element discretized nonsmooth minimization problems the alternating direction method of multipliers admm is considered which is a flexible method to solve a large class of convex minimization problems particular features are its unconditional convergence with respect to the involved step size and its direct applicability in particular this article deals with the admm with variable step sizes and devises an adjustment rule for the step size relying on the monotonicity of the residual and discusses proper stopping criteria the proposed scheme is applied to finite element formulations of the obstacle problem and the rudin osher fatemi image denoising problem and the numerical experiments show significant improvements over established variants of the admm

solving the convex cost integer dual network flow problem in this paper 1 we consider an integer convex optimization problem where the objective function is the sum of separable convex functions that is of the form i j eq f ij w ij iep b i i the constraints are similar to those arising in the dual of a minimum cost flow problem that is of the form i j w ij i j q with lower and upper bounds on variables letn p m q andu be the largest magnitude in the lower and upper bounds of variables we call this problemthe convex cost integer dual network flow problem in this paper we describe several applications of the convex cost integer dual network flow problem arising in a dial a ride transit problem inverse spanning tree problem project management and regression analysis we develop network flow based algorithms to solve the convex cost integer dual network flow problem we show that using the lagrangian relaxation technique the convex cost integer dual network flow problem can be transformed into a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes its special structure allows the convex cost primal network flow problem to be solved ino nmlog n2 m log nu time this time bound is the same time needed to solve the minimum cost flow problem using the cost scaling algorithm and is also is best available time bound to solve the convex cost integer dual network flow problem

an algorithm for minimizing setups in precedence constrained scheduling abstract consider a set of tasks to be scheduled on a single processor subject to precedence constraints a setup occurs when a task is performed immediately after another task which is not its predecessor the general problem is to find a schedule minimizing the number of setups we present a decomposition approach for this problem this leads to new complexity results and the identification of new classes of precedence constraints for which the problem is efficiently solvable

on non ergodic convergence rate of douglas rachford alternating direction method of multipliers this note proposes a novel approach to derive a worst case o 1 k o 1 k convergence rate measured by the iteration complexity in a non ergodic sense for the douglas rachford alternating direction method of multipliers proposed by glowinski and marrocco

optimal sequencing by modular decomposition polynomial algorithms we show that the combination of dynamic programming with partial order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized the algorithm s efficiency depends on the maximum number of jobs that are not related by the precedence constraints in certain subsets of the jobs we also demonstrate how to modify this general algorithm lo take advantage of special problem characteristics

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

rationality in algebras with a series operation we consider the notion of rationality in algebras with a designated binary associative operation called the series operation or the sequential product we define automata operating in these algebras and rational expressions matching their expressive power and we show that this expressive power equals that of algebraic recognizability the framework which we consider encompasses both the free semigroup and the term algebras and the restriction of our results to these special cases coincides exactly with the classical results on recognizability kleene myhill and nerode for word languages and thatcher and wright for term languages next we consider the behavior of the automata and the rational expression which we introduce when conditions such as associativity and commutativity are imposed on the term operations we also characterize algebraically syntactically and automata theoretically the languages which have a bound on the number of nested occurrences of certain designated term operations finally we consider the applications of our results to the languages of series parallel labelled posets 2001 elsevier science

a quantum behaved particle swarm optimization with memetic algorithm and memory for continuous non linear large scale problems abstract quantum behaved particle swarm optimization qpso a novel variant of pso inspired by quantum mechanics is a global convergence guaranteed algorithm which outperforms the original pso in search ability and has fewer parameters to control but as many other psos it is easy to fall into local optimum in solving high dimensional complex optimization problems this paper proposes an improved qpso algorithm for continuous non linear large scale problems based on memetic algorithm and memory mechanism the memetic algorithm is used to make all particles each particle corresponding to a memetic gain some experience through a local search before being involved in the evolutionary process and the memory mechanism is used to introduce a so called bird kingdom with memory capacity both of which can improve the global search ability of the algorithm another difference compared to the previous qpsos is that we let each dimension of a particle update with the same random number thus increasing the speed of convergence and enhancing the ability of local search numerical experiments are conducted to compare the proposed algorithm with different variants of pso and other swarm intelligence algorithms the experimental results show the superiority of the proposed approach on benchmark test functions

robust and adaptive network flows we study network flow problems in an uncertain environment from the viewpoint of robust optimization in contrast to previous work we consider the case that the network parameters e g capacities are known and deterministic but the network structure e g nodes and arcs is subject to uncertainty in this paper we study the robust and adaptive versions of the maximum flow problem and minimum cut problems in networks with node and arc failures and establish structural and computational results the adaptive two stage model adjusts the solution after the realization of the failures in the network this leads to a more flexible model and yields less conservative solutions compared to the robust model we show that the robust maximum flow problem can be solved in polynomial time but the robust minimum cut problem is np hard we also prove that the adaptive versions are np hard we further characterize the adaptive model as a two person zero sum game and prove the existence of an equilibrium in such g

improving spanning trees by upgrading nodes we study budget constrained optimal network upgrading problems we are given an edge weighted graph g v e where node v can be upgraded at a cost of c this upgrade reduces the delay of each link emanating from the goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a good performance we consider two performance measures namely the weight of a minimum spanning tree and the bottleneck weight of a minimum bottleneck spanning tree and present approximation algorithms

m median and m center problems with mutual communication solvable special cases in this paper we consider the network version of the m median problem with mutual communication mmmc we reformulate this problem as a graph theoretic node selection problem defined on a special graph we give a polynomial time algorithm to solve the node selection problem when the flow graph graph that denotes the interaction between pairs of new facilities in mmmc has a special structure we also show that with some modification in the algorithm for mmmc the m center problem with mutual communication can also be solved when the flow graph has a special structure

convergence of the nelder mead simplex method to a nonstationary point this paper analyzes the behavior of the nelder mead simplex method for a family of examples which cause the method to converge to a nonstationary point all the examples use continuous functions of two variables the family of functions contains strictly convex functions with up to three continuous derivatives in all the examples the method repeatedly applies the inside contraction step with the best vertex remaining fixed the simplices tend to a straight line which is orthogonal to the steepest descent direction it is shown that this behavior cannot occur for functions with more than three continuous derivatives the stability of the examples is analyzed

series parallel languages and the bounded width property abstract in order to model concurrency we extend automata theory from the usual languages of words to sets of labelled series parallel posets or sp languages we use the algebraic properties of the set of series parallel posets to investigate the notion of recognizability based on finite index congruences and a notion of regularity based on a new class of branching automata the main results of the paper concern the sp languages having bounded width we show that such languages are recognizable if and only if they are regular in addition the regular bounded width sp languages are exactly those which can be described by series rational expressions that is expressions using the letters the operations of sequential and parallel product and sequential iterations we also give a strictly algebraic characterization of the bounded width property in terms of depth nilpotent series parallel algebras

jump number maximization for proper interval graphs and series parallel graphs in this paper the order theoretic problem of finding linear extensions of a partially ordered set poset with certain properties is mapped to the corresponding graphtheorectic problem given a poset a jump exists between two consecutive symbols in a topological sequence if there is no relation between these two symbols in the poset we want to find a topological sequence that minimizes or maximizes the total number of jumps in graph theoretic terms define the jump number optimization problem as finding a linear ordering of vertex sequence of a graph such that the number of pairs of consecutive vertices that are adjacent is maximized jump number minimization problem or minimized jump number maximization problem the complexities of both problems with respect to some special graphs are investigated first in this paper we then study the jump maximization problem for proper interval graphs and series parallel graphs from this study we hope that more researches can be derived from these interdisciplinary knowledge domains

functions comuted by monotone boolean formulas with no repeated variables abstract if g is a monotone boolean function depending on all its variables the property that each prime implicant of g intersects each prime clause of g in a singleton is a well known necessary condition for g to be computable by a formula with no repeated variable and only using the connectives and or we prove that the condition is also sufficient our proof uses matroid theory

regarding the rankings of optimization heuristics based on artificially constructed benchmark functions novel evolutionary algorithms are usually tested on sets of artificially constructed benchmark problems such problems are often created to make the search of one global extremum usually minimum tricky in this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially created functions with equal bounds and number of allowed function calls may lead to very different ranking of tested algorithms as evolutionary algorithms and other heuristic optimizers are developed in order to be applicable to real world problems such result may raise doubts on the practical meaning of benchmarking them on artificial functions as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum thirty optimization heuristics including a number of variants of differential evolution as well as other kinds of evolutionary algorithms particle swarm optimization direct search methods and following the idea borrowed from no free lunch pure random search are tested in the paper some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given

handling boundary constraints for particle swarm optimization in high dimensional search space despite the fact that the popular particle swarm optimizer pso is currently being extensively applied to many real world problems that often have high dimensional and complex fitness landscapes the effects of boundary constraints on pso have not attracted adequate attention in the literature however in accordance with the theoretical analysis in 11 our numerical experiments show that particles tend to fly outside of the boundary in the first few iterations at a very high probability in high dimensional search spaces consequently the method used to handle boundary violations is critical to the performance of pso in this study we reveal that the widely used random and absorbing bound handling schemes may paralyze pso for high dimensional and complex problems we also explore in detail the distinct mechanisms responsible for the failures of these two bound handling schemes finally we suggest that using high dimensional and complex benchmark functions such as the composition functions in 19 is a prerequisite to identifying the potential problems in applying pso to many real world applications because certain properties of standard benchmark functions make problems inexplicit

computational aspects of the 2 dimension of partially ordered sets a well known method to represent a partially ordered set p order for short consists in associating to each element of p a subset of a fixed set s 1 k such that the order relation coincides with subset inclusion such an embedding of p into 2s the lattice of all subsets of s is called a bit vector encoding of p these encodings provide an interesting way to store an order they are economical with space and comparisons between elements can be performed efficiently via subset inclusion tests given an order p minimizing the size of the encoding i e the cardinal of s is however a difficult problem the smallest size is called the 2 dimension of p and denoted by dim2 p in the literature the decision problem for the 2 dimension has been classified as np complete and generating small bit vector encodings is a challenging issue several works deal with bit vector encodings from a theoretical point of view in this article we focus on computational complexity results after a synthesis of known results we come back on the np completeness by detailing a proof and enforcing the conclusion with non approximability ratios besides this general result we investigate the complexity of the 2 dimension for the class of trees we describe a 4 approximation algorithm for this class it uses an optimal balancing strategy which solves a conjecture of krall vitek and horspool several interesting open problems are listed

parallel recognition of series parallel graphs recently he and yesha gave an algorithm for recognizing directed series parallel graphs in time o log2 n with linearly many erew processors we give a new algorithm for this problem based on a structural characterization of series parallel graphs in terms of their ear decompositions our algorithm can recognize undirected as well as directed series parallel graphs it can be implemented in the crcw model of parallel computation to take time o log n in the erew model the time is o log2 n but the number of processors required improves the bounds of the previous algorithm

minimum aggregate concave cost multicommodity flows in strong series parallel networks this work develops a polynomial time dynamic programming algorithm for minimum aggregate concave cost multicommodity flow problems in strong series parallel networks many important problems from production and inventory management capacity planning network design and transportation can be formulated in these terms our results include a characterization of extreme flows in strong series parallel networks and an algorithm based on this characterization that searches extreme flows efficiently to find an optimal one the algorithm runs in time proportional to a n k where a n and k are respectively the numbers of arcs nodes and commodities in the network and appears to be the first to solve the problem in polynomial time when applied to the dynamic economic order quantity problem the algorithm matches the performance of that of wagner and whitin 1958 moreover our algorithm has broader applications including the multi division capacity expansion problem and the generalization of the dynamic economic order quantity problem to series parallel production processes in which subassemblies are assembled into a finished product

lattice based sums in this contribution the well known ordinal sum technique of posets is generalized by allowing for a lattice ordered index set instead of a linearly ordered index set and we argue for the merits of this generalization we will call such a proposed sum type construction a lattice based sum our new approach of lattice based sum extends also the horizontal sum we show that the lattice based sum of posets is again a poset subsequently we apply the results for constructing new lattices by investigating lattice based sums when the summand posets are lattices we show that under certain assumptions the lattice based sum of lattices will be a lattice

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times

characterization and complexity of uniformly nonprimitive labeled 2 structures abstract according to the clan decomposition theorem of ehrenfeucht and rozenberg 1990 each labeled 2 structure has a decomposition into three types of basic 2 structures complete linear and primitive this decomposition can be expressed as a node labeled tree the shape of the 2 structure our main interest is in the uniformly nonprimitive 2 structures which do not have primitive substructures every directed graph can be considered as a restricted 2 structure with only two labels arc no arc it is proved that forbidding primitivity in the 2 structures gives a unified approach to some well known classes of graphs viz the cographs and the transitive vertex series parallel graphs we also study the parallel complexity of the decomposition of 2 structures it is shown that there is a logcf algorithm which recognizes the uniformly nonprimitive 2 structures and constructs their shapes we prove also that for every mso monadic second order definable property of 2 structures there is a logcf algorithm to decide whether or not a uniformly nonprimitive 2 structure has that property

a comparison of point based approaches to qualitative temporal reasoning we address the problem of implementing general qualitative point based temporal reasoning given a database of assertions concerning relative occurrences of points in time we are interested in various operations on this database including compiling the assertions into a representation that supports efficient reasoning determining whether a database is consistent and computing the strongest entailed relation between two points we begin by specifying a set of operations and their corresponding algorithms applicable to general point based temporal domains we next consider a special purpose reasoner based on series parallel graphs which performs very well in a temporal domain with a particular restricted structure we discuss the notion of a metagraph which encapsulates local structure inside metaedges and uses special purpose algorithms within such local structures to obtain a fast general point based reasoner that is specifically we use a very fast series parallel graph reasoner to speed up general point based reasoning we also analyse the timegraph reasoner of gerevini and schubert for purposes of comparison we have implemented four approaches a generic point based reasoner the generic point based reasoner with a ranking heuristic a reasoner based on series parallel graphs and a version of gerevini and schubert s timegraph reasoner we compare these different approaches as well as the original timegraph ii reasoner of gerevini and schubert on different data sets we conclude that the series parallel graph reasoner provides the best overall performance our results show that it dominated on domains exhibiting structure and it degraded gracefully when conditions were less than ideal in that it did worse than the generic approach by only a constant factor in this case

complexity of the discrete time cost tradeoff problem for project networks this note addresses the discrete version of the well known time cost tradeoff problem for project networks which has been studied previously in the standard project management literature as well as in the related literature on decision cpm all the algorithms proposed thus far for the solution of the general problem exhibit exponential worst case complexity with the notable exception of the pseudo polynomial dynamic program due to hindelang and muth we first demonstrate that this algorithm is flawed and that when we correct it it no longer remains pseudo polynomial continuing on in the main result of the note we show that this is not at all surprising since the problem is strongly np hard finally we discuss the complexities of various network structures and validate an old conjecture that certain structures are necessarily more difficult to solve

aggregation approach for the minimum binary cost tension problem the aggregation technique dedicated to two terminal series parallel graphs or ttsp graphs and introduced lately to solve the minimum piecewise linear cost tension problem is adapted here to solve the minimum binary cost tension problem or bct problem even on ttsp graphs the bct problem has been proved to be np complete as far as we know the aggregation is the only algorithm with mixed integer programming proposed to solve exactly the bct problem on ttsp graphs a comparison of the efficiency of both methods is presented here

self adaptive operator splitting methods for monotone variational inequalities solving a variational inequality problem vi f is equivalent to finding a solution of a system of nonsmooth equations a hard problem the peaceman rachford and or douglas rachford operator splitting methods are advantageous when they are applied to solve variational inequality problems because they solve the original problem via solving a series of systems of nonlinear smooth equations a series of easy problems although the solution of vi f is invariant under multiplying f by some positive scalar yet the numerical experiment has shown that the number of iterations depends significantly on the positive parameter which is a constant in the original operator splitting methods in general it is difficult to choose a proper parameter for individual problems in this paper we present a modified operator splitting method which adjusts the scalar parameter automatically per iteration based on the message of the iterates exact and inexact forms of the modified method with self adaptive variable parameter are suggested and proved to be convergent under mild assumptions finally preliminary numerical tests show that the self adaptive adjustment rule is proper and necessary in practice

discrete total variation flows without regularization we propose and analyze an algorithm for the solution of the l 2 subgradient flow of the total variation functional the algorithm involves no regularization thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy we propose an iterative scheme for the solution of the arising problems show that the iterations converge and develop a stopping criterion for them we present numerical experiments which illustrate the power of the method explore the solution behavior and compare with regularized flows

reduction algorithms for graphs of small treewidth this paper presents a number of new ideas and results on graph reduction applied to graphs of bounded treewidth s arnborg b courcelle a proskurowski and d seese j assoc comput mach 40 1134 1164 1993 have shown that many decision problems on graphs can be solved in linear time on graphs of bounded treewidth using a finite set of reduction rules these algorithms can be used to solve problems on graphs of bounded treewidth without the need to obtain a tree decomposition of the input graph first we show that the reduction method can be extended to solve the construction variants of many decision problems on graphs of bounded treewidth including all problems definable in monadic second order logic we also show that a variant of these reduction algorithms can be used to solve constructive optimization problems in o n time for example optimization and construction variants of independent set and hamiltonian completion number can be solved in this way on graphs of small treewidth additionally we show that the results of h l bodlaender and t hagerup siam j comput 27 1725 1746 1998 can be applied to our reduction algorithms which results in parallel reduction algorithms that use o n operations and o log n log n time on an erew pram or o log n time on a crcw pram

free shuffle algebras in language varieties we give simple concrete descriptions of the free algebras in the varieties generated by the shuffle semirings l p 0 1 or the semirings r r 0 1 where p is the collection of all subsets of the free monoid and r is the collection of all regular subsets the operation x y is the shuffle product

axiomatizing the subsumption and subword preorders on finite and infinite partial words we consider two sorted algebras of finite and infinite partial words equipped with the subsumption preorder and the operations of series and parallel product and omega power it is shown that the valid equations and inequations of these algebras can be described by an infinite collection of simple axioms and that no finite axiomatization exists we also prove similar results for two related preorders namely for the induced partial subword preorder and the partial subword preorder along the way of proving these results we provide a concrete description of the free algebras in the corresponding varieties in terms of generalized series parallel partial words

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

fast alternating linearization methods for minimizing the sum of two convex functions we present in this paper alternating linearization algorithms based on an alternating direction augmented lagrangian approach for minimizing the sum of two convex functions our basic methods require at most o 1 epsilon iterations to obtain an epsilon optimal solution while our accelerated i e fast versions of them require at most o 1 sqrt epsilon iterations with little change in the computational effort required at each iteration for both types of methods we present one algorithm that requires both functions to be smooth with lipschitz continuous gradients and one algorithm that needs only one of the functions to be so algorithms in this paper are gauss seidel type methods in contrast to the ones proposed by goldfarb and ma in fast multiple splitting algorithms for convex optimization columbia university 2009 where the algorithms are jacobi type methods numerical results are reported to support our theoretical conclusions and demonstrate the practical potential of our algorithms

two equational theories of partial words abstract partial words are in our terminology isomorphism classes of labeled partial orders we consider two structures starting with the partial orders reduced to a unique element the first one is defined as the closure under the three operations of series product parallel product and power series product of the same partial word and the second one as the closure under the three operations of series product parallel product and product series product of possibly different partial words we show that the two equational theories can be axiomatized by an infinite collection of simple identities and that no finite axiomatization exists we characterize the free algebras in the corresponding varieties as algebras of certain partial words subject to order and graph theoretic conditions we also show that the first equational theory is decidable

on the o 1 n convergence rate of the douglas rachford alternating direction method alternating direction methods adms have been well studied in the literature and they have found many efficient applications in various fields in this note we focus on the douglas rachford adm scheme proposed by glowinski and marrocco and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number the linearized version of this adm scheme which is known as the split inexact uzawa method in the image processing literature is also discussed

resource allocation via dynamic programming in activity networks abstract we investigate the application of dynamic programming to the problem of resource allocation in a project with the objective of minimizing the project completion time we assume that there is a relationship between the amount of the resource allocated to an activity and its duration which is monotone nonincreasing in its argument the motivation for this study is the recent development of a procedure which yields the minimum number of nodes to be reduced in the an this drastically alters the complexity of the dp approach from o u h to o u c where h is the number of common activities and c is the minimum number of reduced nodes since typically h c we present and illustrate the dp optimizing procedure which is easily seen to be still plagued by the curse of dimensionality despite the drastic reduction in complexity mentioned above we then present an elementary approximating procedure which provides an upper bound on the optimum and is computationally more economical for c 3 we illustrate both procedures by a small numerical example continuing research is devoted to evaluating the efficacy of the approximating procedure and investigating other approximations

computing the minimal relations in point based qualitative temporal reasoning through metagraph closure computing the minimal representation of a given set of constraints a csp over the point algebra pa is a fundamental temporal reasoning problem the main property of a minimal csp over pa is that the strongest entailed relation between any pair of variables in the csp can be derived in constant time we study some new methods for solving this problem which exploit and extend two prominent graph based representations of a csp over pa the timegraph and the series parallel sp metagraph essentially these are graphs partitioned into sets of chains and series parallel subgraphs respectively on which the search is supported by a metagraph data structure the proposed approach is based on computing the metagraph closure for these representations which can be accomplished by some methods studied in the paper in comparison with the known techniques based on enforcing path consistency under certain conditions about the structure of the input csp and the size of the generated metagraph the proposed metagraph closure approach has better worst case time and space complexity moreover for every sparse csp over the convex pa the time complexity is reduced to o n 2 from o n 3 where n is the number of variables involved in the csp an extensive experimental analysis presented in the paper compares the proposed techniques and other known algorithms these experimental results identify the best performing methods and show that in practice for csps exhibiting chain or sp graph structure and randomly generated both sparse and dense csps the metagraph closure approach is significantly faster than the approach based on enforcing path consistency

on line algorithms for orders partially ordered sets appear as a basic tool in computer science and are particularly accurate for modeling dynamic behavior of complex systems motivated by considerations on the diagnosis of distributed computations a new kind of algorithm on posets has been developed and is now widely considered in this paper we present this on line algorithmics on posets and we survey the main results obtained under this approach

on fast and accurate block based motion estimation algorithms using particle swarm optimization both fast and accurate block matching algorithms are critical to efficient compression of video frames using motion estimation and compensation while the particle swarm optimization approach holds the promise of alleviating the local optima problem suffered typically by existing very fast block matching methods motion estimation algorithms based on particle swarm optimization in the literature appear to be either much slower than some leading fast block matching methods for a given accuracy of motion estimation or less accurate for a given computational complexity in this paper we show that the conventional particle swarm optimization approach which was originally designed to solve general optimization problems where fast convergence of the algorithm might not be a primary concern could be modified appropriately so that it could provide accurate motion estimation with very low computational cost in the specific context of video motion estimation to this end we proposed a new block matching algorithm based on a set of strategies adapted from the standard particle swarm optimization approach extensive simulations showed that the proposed method could achieve significant improvements over leading fast block matching methods including the diamond search and the cross diamond search methods in terms of both estimation accuracy and computational cost in particular the proposed method based on particle swarm optimization is not only much faster but also remarkably more accurate about 2db higher in terms of the peak signal to noise ratio than the competing methods on video sequences with large motion

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

the equational theory of pomsets abstract pomsets have been introduced as a model of concurrency since a pomset is a string in which the total order has been relaxed to be a partial order in this paper we view them as a generalization of strings and investigate their algebraic properties in particular we investigate the axiomatic properties of pomsets sets of pomsets and ideals of pomsets under such operations as concatenation parallel composition union and their associated closure operations we find that the equational theory of sets pomsets under concatenation parallel composition and union is finitely axiomatizable whereas the theory of languages under the analogous operations is not a similar result is obtained for ideals of pomsets which incorporate the notion of subsumption which is also known as augmentation finally we show that the addition of any closure operation parallel or serial leads to nonfinite axiomatizability of the resulting equational theory

lattice based sum of t norms on bounded lattices abstract the concept of ordinal sums in the sense of clifford have long been blamed for their limitations in constructing new t norms including inability to cope with general bounded lattices motivated by this observation and based on the lattice based sum of lattices that has been recently introduced by el zekey et al we propose a new sum type construction of t norms called a lattice based sum of t norms for building new t norms on bounded lattices from given ones the proposed sum is generalizing the well known ordinal and horizontal sum constructions of t norms by allowing for lattice ordered index sets we demonstrate that like the ordinal sum of t norms the lattice based sum of t norms can be generalized using as summands so called t subnorms still leading to a t norm subsequently we apply the results for constructing several new families of t norms and t subnorms on bounded lattices in the same spirit by the duality we will also introduce lattice based sums of t conorms and t subconorms

spirality and optimal orthogonal drawings we deal with the problem of constructing the orthogonal drawing of a graph with the minimum number of bends along the edges the problem has been recently shown to be np complete in the general case in this paper we introduce and study the new concept of spirality which is a measure of how an orthogonal drawing is rolled up and develop a theory on the interplay between spirality and number of bends of orthogonal drawings we exploit this theory to present polynomial time algorithms for two significant classes of graphs series parallel graphs and 3 planar graphs series parallel graphs arise in a variety of problems such as scheduling electrical networks data flow analysis database logic programs and circuit layout also they play a central role in planarity problems furthermore drawings of 3 planar graphs are a classical field of investigation

logic and rational languages of scattered and countable series parallel posets abstract let a be an alphabet and s p a denote the class of all countable n free partially ordered sets labeled by a in which chains are scattered linear orderings and antichains are finite we characterize the rational languages of s p a by means of logic we define an extension of monadic second order logic by presburger arithmetic named p mso such that a language l of s p a is rational if and only if l is the language of a sentence of p mso with effective constructions from one formalism to the other as a corollary the p mso theory of s p a is decidable

single machine scheduling with precedence constraints of dimension 2 consider the set of tasks that are partially ordered by precedence constraints the tasks are to be sequenced so that a given objective function will assume its optimal value over the set of feasible solutions a subset of tasks is called feasible if for every task in the subset all of its predecessors are also in the subset we present a dynamic programming solution to the problem when the constraining partial order has a dimension 2 this is done by definining a compact labeling scheme and an efficient enumerative procedure for all the feasible subsets in this process a new characterization is given for 2 dimensional partial orders

a variable penalty alternating directions method for convex optimization we study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints the method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both lagrangian and proximal terms the minimizers determine the new proximal terms and a simple update of the lagrangian terms follows we prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers another novelty is that we allow penalty matrices and these may vary per iteration this can be beneficial in applications since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties as an application we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems

joins ears and castelnuovo mumford regularity abstract we introduce a new class of polynomial ideals associated to a simple graph g let k e g be the polynomial ring on the edges of g and k v g the polynomial ring on the vertices of g we associate to g an ideal i x g defined as the preimage of x i 2 x j 2 i j v g k v g by the map k e g k v g which sends a variable t e associated to an edge e i j to the product x i x j of the variables associated to its vertices we show that k e g i x g is a one dimensional cohen macaulay graded ring and we relate its degree with the number of vertices and connected components of the graph we show that i x g is a binomial ideal and that with respect to a fixed monomial order its initial ideal has a generating set independent of the field k we focus on the castelnuovo mumford regularity of i x g providing the following sharp upper and lower bounds g reg i x g v g b 0 g 1 where g is the maximum vertex join number of the graph and b 0 g is the number of its connected components we show that the lower bound is attained for a bipartite graph and use this to derive a new combinatorial result on the number of even length ears of nested ear decomposition

probabilistic optimization for conceptual rainfall runoff models a comparison of the shuffled complex evolution and simulated annealing algorithms automatic optimization algorithms are used routinely to calibrate conceptual rainfall runoff crr models the goal of calibration is to estimate a feasible and unique global set of parameter estimates that best fit the observed runoff data most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size discontinuities and long ridges and valleys extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years this study compares the performance of two probabilistic global optimization methods the shuffled complex evolution algorithm sce ua and the three phase simulated annealing algorithm sa sx both algorithms are used to calibrate two parameter sets of a modified version of boughton s 1984 sfb model using data from two australian catchments that have low and high runoff yields for the reduced well identified parameter set the algorithms have a similar efficiency for the low yielding catchment but sce ua is almost twice as robust although the robustness of the algorithms is similar for the high yielding catchment sce ua is six times more efficient than sa sx when fitting the full parameter set the performance of sa sx deteriorated markedly for both catchments these results indicated that sce ua s use of multiple complexes and shuffling provided a more effective search of the parameter space than sa sx s single simplex with stochastic step acceptance criterion especially when the level of parameterization is increased examination of the response surface for the low yielding catchment revealed some reasons why sce ua outperformed sa sx and why probabilistic optimization algorithms can experience difficulty in locating the global optimum

a k structure generalization of the theory of 2 structures the prime tree decomposition of graphs facilitates the solution of a number of important combinatorial problems the decomposition is also known as modular decomposition and substitution decomposition it has been generalized to 2 structures and to k ary relations but while both of these generalizations give the decomposition on graphs as a special case neither is a generalization of the other in this paper we propose a type of edge colored hypergraph which we will call a k structure we define the modular decomposition of k structures and generalize the essential algebraic properties this unifies the prime tree decompositions on 2 structures and k ary relations by giving them as special cases and extends the decomposition to k structures that are neither 2 structures nor k ary relations in addition we show that any indecomposable k structure on n 3 nodes contains a smaller indecomposable substructure that has at least n k nodes this is a generalization of a previously known result on graphs and 2 structures that is where k 2 the generalization to k ary relations that it gives as a special case is also new

series parallel languages on scattered and countable posets in this paper we investigate the recognition by finite automata of languages of countable labelled posets we unify and generalize several previous results from two different directions the theory of finite or wn free posets and automata over countable and scattered linear orderings first we establish that the smallest class of posets obtained from the empty set and the singleton and closed under finite parallel operation and sequential concatenation indexed by all linear orderings corresponds precisely to the class of scattered and countable n free posets without infinite antichains next we prove a kleene like theorem we define automata and rational expressions for languages of countable scattered n free labelled posets without infinite antichains and show that both formalisms have the same expressive power

an o e time algorithm for computing the reliability of a class of directed networks this paper studies the problem of computing the source to terminal reliability the probability that a source s can communicate with a terminal t in a probabilistic directed network it introduces a set of reliability preserving reductions called 2 neighbor node reductions we show that for a class of directed networks called bsp digraphs such reductions are always admissible and the source to terminal reliability can be computed in time linear in the size of the network a directed network d v e is a bsp digraph if its underlying undirected graph is series parallel the bsp digraphs considered can be cyclic or acyclic and both vertices as well as edges can fail any two vertices can be chosen as s and t previously no polynomial time algorithms were known for this class of digraphs the proposed method is also applicable to mixed graphs containing directed and undirected edges

efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimized thresholds for multilevel image segmentation however it involves expensive computation as the number of thresholds increases and often yields noisy segmentation results since spatial coherence is not enforced in this paper an iterative calculation scheme is presented for reducing redundant computations in entropy evaluation the efficiency of threshold selection is further improved through utilizing the artificial bee colony algorithm as the optimization technique finally instead of performing thresholding for each pixel independently the presented algorithm oversegments the input image into small regions and uses the probabilities of fuzzy events to define the costs of different label assignments for each region the final segmentation results is computed using graph cut which produces smooth segmentation results the experimental results demonstrate the presented iterative calculation scheme can greatly reduce the running time and keep it stable as the number of required thresholds increases quantitative evaluations over 20 classic images also show that the presented algorithm outperforms existing multilevel segmentation approaches

partition dimension of certain classes of series parallel graphs abstract the partition dimension problem is to decompose the vertex set of a graph into minimum number of vertex disjoint sets such that the ordered distances between every vertex of the graph and the disjoint sets of that decomposition have different values in the representation this problem has emerging applications in areas such as structure activity issues in drug design navigation of robots pattern recognition and image processing in the present study we provide an upper bound for the partition dimension of parallel composition of any graphs and derive an exact result for parallel composition of paths with different lengths on the other side we find the partition dimension of the series composition of cycles and complete graphs with different sizes and an upper bound is derived for series composition of any graphs further this problem is applied to a graph which has been generated by parallel and series composition together on paths

may the same numerical optimizer be used when searching either for the best or for the worst solution to a real world problem over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand evaluate or compare them all in principle optimization methods including the recently popular evolutionary computation or swarm intelligence based ones should be developed in order to solve real world problems yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only so their usefulness for various practical applications remains unverified as a result choosing the proper method for a particular real world problem is a difficult task this paper shows that such a choice is even more complicated if one wishes with good reason to use metaheuristics twice once to find the best and then to find the worst solutions for the specific numerical real world problem it often occurs that for either case different optimizers are to be recommended the above finding is based on testing 30 metaheuristics on numerical real world problems from cec2011 first we solve 22 minimization problems as defined for cec2011 then we reverse the objective function for each problem and search for its maximizing solution we also observe that algorithms that are highly ranked on average may not perform best for any given specific problem rather the highest average ranking may be achieved by methods that are never among the poorest ones in other words occasional winners may get less attention than rare losers

note on a linear time algorithm for computing k terminal reliability in a series parallel network in an original and very interesting paper satyanarayana and wood 1 concerning polygon to chain reductions in a stochastic network a small inconsistency occurs in the proof of theorem 1 in particular this happens in cases where the whole set of bit k vertices lies in the remaining polygon such an example is the case of polygon type 5 where the appropriate note has been made by the authors for hbox bit k 2 analogous notes must also be made for polygon types 4 6 and 7 when bit k 2 3 and 4 respectively the correct transformations are given in table 1 note that dark vertices are bit k vertices

on minimum average stretch spanning trees in polygonal 2 trees a spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges for a polygonal 2 tree on n vertices we present an algorithm to compute a minimum average stretch spanning tree in o n log n time this algorithm also finds a minimum fundamental cycle basis in polygonal 2 trees we show that there is a unique minimum cycle basis in a polygonal 2 tree and it can be computed in linear time

an o m m nlogn log nc time algorithm to solve the minimum cost tension problem this paper presents a new polynomial time algorithm to solve the minimum cost tension problem it runs in o m m nlogn log nc time where n m c denote the number of nodes number of arcs and maximum arc capacity value of an arc cost respectively the algorithm improves the o m 2nlogc time algorithm of maurras 1994 20 also our algorithm under the similarity assumption gabow 1985 12 runs in o m m nlogn logn time which improves the o n 4m 3logn time algorithm of hadjiat and maurras 1997 18

axiomatizing shuffle and concatenation in languages abstract we consider the varietylanggenerated by all language structures p 0 1 and the varietylg of ordered algebras generated by the structures p 0 1 wherep is the powerset of and whereb cis the complex concatenation of the languagesb c b cis their shuffle product andb cis their union we prove that for each finite seteof equations valid inlangthere is a finite modelseofein which some inequation valid inlg fails it follows that neither variety is finitely axiomatizable

a fast algorithm for the decomposition of graphs and posets many combinatorial optimization problems of graphs e g finding maximal independent sets or maximum matchings and acyclic networks e g finding shortest paths or maximum flows can be solved by means of decomposition of the graph network into autonomous subsets given a relation r on a a subset b of a is called autonomous if for each a b the following holds if 0 r for some 0 b then r for all b if 0 r for some 0 b then r for all b we present an algorithm which finds all autonomous subsets of graphs and posets with p points in o p3 time and o p2 space the ideas behind this algorithm reveal rather strong connections between graph decomposition homomorphisms of graphs and posets and comparability graph recognition furthermore the well known series parallel decomposition for graphs and posets is contained as a special case

niching particle swarm optimization with local search for multi modal optimization multimodal optimization is still one of the most challenging tasks for evolutionary computation in recent years many evolutionary multi modal optimization algorithms have been developed all these algorithms must tackle two issues in order to successfully solve a multi modal problem how to identify multiple global local optima and how to maintain the identified optima till the end of the search for most of the multi modal optimization algorithms the fine local search capabilities are not effective if the required accuracy is high these algorithms fail to find the desired optima even after converging near them to overcome this problem this paper integrates a novel local search technique with some existing pso based multimodal optimization algorithms to enhance their local search ability the algorithms are tested on 14 commonly used multi modal optimization problems and the experimental results suggest that the proposed technique not only increases the probability of finding both global and local optima but also reduces the average number of function evaluations