criticizing solutions to relaxed models yields powerful admissible heuristics abstract branch and bound techniques allow intractable problems to be solved by using heuristics to bound the cost of partial solutions the use of admissible heuristics can guarantee that the solutions found are optimal this paper examines one paradigm problem relaxation by constraint deletion which has been used to develop many admissible heuristics the paradigm suggests three steps simplify or relax a problem solve the simplified problem and use that solution to guide the search for a solution to the original problem we introduce the following extension to this methodology by criticizing the feasibility of a relaxed solution we arrive at a closer approximation of the solution to the original problem we apply this methodology to two well studied problems in operations research and artificial intelligence for the traveling salesman problem iteration of our technique yields a series of novel heuristics culminating in held and karp s minimum spanning tree heuristic for the eight puzzle it yields a heretofore undiscovered heuristic which is shown to perform significantly better than any previously known

disjoint pattern database heuristics we describe a new technique for designing more accurate admissible heuristic evaluation functions based on pattern databases j culberson j schaeffer comput intelligence 14 3 1998 318 334 while many heuristics such as manhattan distance compute the cost of solving individual subgoals independently pattern databases consider the cost of solving multiple subgoals simultaneously existing work on pattern databases allows combining values from different pattern databases by taking their maximum if the subgoals can be divided into disjoint subsets so that each operator only affects subgoals in one subset then we can add the pattern database values for each subset resulting in a more accurate admissible heuristic function we used this technique to improve performance on the fifteen puzzle by a factor of over 2000 and to find optimal solutions to 50 random instances of the twenty four puzzle

hybridization and regularization schemes applied to identify rough acoustic impedance profiles in slender structures with noisy data the modified sequential algebraic algorithm msaa is a routine developed to solve the longitudinal acoustic wave propagation problem in inhomogeneous media this method accurately predicts the echo generated by the inhomogeneities particularly when the acoustic impedance variation profile in the damaged part of the structure is non smooth used for solving the inverse problem by a stochastic optimization approach msaa efficiently identifies rough profiles of impedance with low noise level in the input data as noise level increases the inverse problem turns out to be ill posed and often yields inappropriate solutions the purpose of this paper is to apply a regularization scheme and to use a hybrid optimization strategy to reduce the error in the damage estimation in the numerical examples 40 parameters are successfully identified for a signal to noise ratio of 20 db for all tested damage profiles the regularization and hybridization procedures decreased the maximum absolute error to levels lowe

ck invariant manifolds for maps of banach spaces abstract in this work we give a unified proof for the existence under appropriate gap conditions of the standard invariant manifolds for a ck map of a banach space near a fixed point where k 1 is an integer

sharp regularity of linearization for c 1 1 hyperbolic diffeomorphisms c 1 linearization is of special significance because it preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions however c 1 smoothness is not enough to guarantee c 1 linearization for c 1 1 hyperbolic diffeomorphisms on banach spaces c 1 linearization was proved under a gap condition together with a band condition of the spectrum in this paper the result of c 1 linearization in banach spaces is strengthened to c 1 beta linearization with a constant beta 0 under a weaker band condition by a decomposition with invariant foliations the weaker band condition allows the spectrum to be a union of more than two but finitely many bands but restricts those bands to be bounded by a number depending on the supremum of contractive spectrum and the infimum of expansive spectrum furthermore we give an estimate for the exponent beta and prove that the estimate is sharp in the planar case

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

best first fixed depth minimax algorithms abstract this article has three main contributions to our understanding of minimax search first a new formulation for stockman s sss algorithm based on alpha beta is presented it solves all the perceived drawbacks of sss finally transforming it into a practical algorithm in effect we show that sss alpha beta transposition tables the crucial step is the realization that transposition tables contain so called solution trees structures that are used in best first search algorithms like sss having created a practical version we present performance measurements with tournament game playing programs for three different minimax games yielding results that contradict a number of publications second based on the insights gained in our attempts at understanding sss we present a framework that facilitates the construction of several best first fixed depth game tree search algorithms known and new the framework is based on depth first null window alpha beta search enhanced with storage to allow for the refining of previous search results it focuses attention on the essential differences between algorithms third a new instance of this framework is presented it performs better than algorithms that are currently used in most state of the art game playing programs we provide experimental evidence to explain why this new algorithm mtd f performs better than other fixed depth minimax algorithms

weighted a search unifying view and application the a algorithm is a well known heuristic best first search method several performance accelerated extensions of the exact a approach are known interesting examples are approximate algorithms where the heuristic function used is inflated by a weight often referred to as weighted a these methods guarantee a bounded suboptimality as a technical contribution this paper presents the previous results related to weighted a from authors like pohl pearl kim likhachev and others in a more condensed and unifying form with this unified view a novel general bound on suboptimality of the result is derived in the case of avoiding any reopening of expanded states for e 0 this bound is 1 e n 2 where n is an upper bound on an optimal solution length binary decision diagrams bdds are well known to ai e g from set based exploration of sparse memory and symbolic manipulation of state spaces the problem of exact or approximate bdd minimization is introduced as a possible new challenge for heuristic search like many classical ai domains this problem is motivated by real world applications several variants of weighted a search are applied to problems of bdd minimization and the more classical domains like blocksworld and sliding tile puzzles for bdd minimization the comparison of the evaluated methods also includes previous heuristic and simulation based methods such as rudell s hill climbing based sifting algorithm simulated annealing and evolutionary algorithms a discussion of the results obtained in the different problem domains gives our experiences with weighted a which is of value for the ai practitioner

subdimensional expansion for multirobot path planning abstract planning optimal paths for large numbers of robots is computationally expensive in this paper we introduce a new framework for multirobot path planning called subdimensional expansion which initially plans for each robot individually and then coordinates motion among the robots as needed more specifically subdimensional expansion initially creates a one dimensional search space embedded in the joint configuration space of the multirobot system when the search space is found to be blocked during planning by a robot robot collision the dimensionality of the search space is locally increased to ensure that an alternative path can be found as a result robots are only coordinated when necessary which reduces the computational cost of finding a path we present the m algorithm an implementation of subdimensional expansion that adapts the a planner to perform efficient multirobot planning m is proven to be complete and to find minimal cost paths simulation results are presented that show that m outperforms existing optimal multirobot path planning algorithms

breadth first heuristic search recent work shows that the memory requirements of a and related graph search algorithms can be reduced substantially by only storing nodes that are on or near the search frontier using special techniques to prevent node regeneration and recovering the solution path by a divide and conquer technique when this approach is used to solve graph search problems with unit edge costs we show that a breadth first search strategy can be more memory efficient than a best first strategy we also show that a breadth first strategy allows a technique for preventing node regeneration that is easier to implement and can be applied more widely the breadth first heuristic search algorithms introduced in this paper include a memory efficient implementation of breadth first branch and bound search and a breadth first iterative deepening a algorithm that is based on it computational results show that they outperform other systematic search algorithms in solving a range of challenging graph search problems

decision making with multiple objectives using gai networks this paper deals with preference representation on combinatorial domains and preference based recommendation in the context of multicriteria or multiagent decision making the alternatives of the decision problem are seen as elements of a product set of attributes and preferences over solutions are represented by generalized additive decomposable gai utility functions modeling individual preferences or criteria thanks to decomposability utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees the so called gai network using this structure we present preference based search algorithms for multicriteria or multiagent decision making although such models are often non decomposable over attributes we actually show that gai networks are still useful to determine the most preferred alternatives provided preferences are compatible with pareto dominance we first present two algorithms for the determination of pareto optimal elements then the second of these algorithms is adapted so as to directly focus on the preferred solutions we also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems

local contractions of banach spaces and spectral gap conditions abstract we study the linearization problem for a c k 1 k 1 contraction of a banach space e near a fixed point which satisfies a spectral gap condition and a narrow band condition both of order k we also assume that the part of the spectrum in each band satisfies a finite non resonant condition of order k relative to itself together with the part that lies in the larger bands we show that there is a c k linearization for sufficiently small 0 we give a precise estimate on in terms of the gap and band conditions

α holder linearization abstract a well known theorem of hartman and grobman says that a c 2 diffeomorphism f r n r n with a hyperbolic fixed point at 0 can be topologically conjugated to the linear diffeomorphism l df 0 in a neighborhood of 0 on the other hand if a non planar map has resonance then linearization may not be c 1 a counter example is due to p hartman see h2 in this paper we will show that for any 0 1 there exists an holder linearization in a neighborhood of 0 for the counterexample of hartman no resonance condition will be required a linearization of a more general map will be discussed

linear time disk based implicit graph search many search algorithms are limited by the amount of memory available magnetic disk storage is over two orders of magnitude cheaper than semiconductor memory and individual disks can hold up to a terabyte we augment memory with magnetic disks to perform brute force and heuristic searches that are orders of magnitude larger than any previous such searches the main difficulty is detecting duplicate nodes which is normally done with a hash table due to long disk latencies however randomly accessed hash tables are infeasible on disk and are replaced by a mechanism we call delayed duplicate detection in contrast to previous work we perform delayed duplicate detection without sorting which runs in time linear in the number of nodes in practice using this technique we performed the first complete breadth first searches of the 2 7 3 5 4 times 4 and 2 8 sliding tile puzzles verifying the radius of the 4 4 puzzle and determining the radius of the others we also performed the first complete breadth first searches of the four peg towers of hanoi problem with up to 22 discs discovering a surprising anomaly regarding the radii of these problems in addition we performed the first heuristic searches of the four peg towers of hanoi problem with up to 31 discs verifying a conjectured optimal solution length to these problems we also performed partial breadth first searches of rubik s cube to depth ten in the face turn metric and depth eleven in the quarter turn metric confirming previous results

maximizing over multiple pattern databases speeds up heuristic search a pattern database pdb is a heuristic function stored as a lookup table this paper considers how best to use a fixed amount m units of memory for storing pattern databases in particular we examine whether using n pattern databases of size m n instead of one pattern database of size m improves search performance in all the state spaces considered the use of multiple smaller pattern databases reduces the number of nodes generated by ida the paper provides an explanation for this phenomenon based on the distribution of heuristic values that occur during search

graph search methods for non order preserving evaluation functions applications to job sequencing problems abstract graph search with a is frequently faster than tree search but a graph search operates correctly only when the evaluation function is order preserving in the non orderpreserving case no paths can be discarded and the entire explicit graph must be stored in memory such situations arise in one machine minimum penalty job sequencing problems when setup times are sequence dependent grec the unlimited memory version of a memory constrained search algorithm of the authors called mrec has a clear advantage over a in that it is able to find optimal solutions to such problems at the same time it is as efficient as a in solving graph search problems with order preserving evaluation functions experimental results indicate that in the non order preserving case grec is faster than both best first and depth first tree search and can solve problem instances of larger size than best first tree search

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

goupillaud inverse problem with arbitrary input a new impulse inverse formula and it s generalization including arbitrary input are proposed the new generalized inverse formula has the advantage of not being necessary to specify the first digital value of the input numerical instability of the inverse formula for arbitrary input is investigated carefully an analysis of the perturbed stability and lyapunov exponent are carried out as the result of this analysis it is shown that the estimated error is sensitive to the experimental error and previously estimated error as a sequential algorithm simulation using experimental data is also shown in the paper

enhanced a algorithms for multiple alignments optimal alignments for several sequences and k opt approximate alignments for large cases abstract the multiple alignment of the sequences of dna and proteins is applicable to various important fields in molecular biology although the approach based on dynamic programming is well known for this problem it requires enormous time and space to obtain the optimal alignment on the other hand this problem corresponds to the shortest path problem and the a algorithm which can efficiently find the shortest path with an estimator is usable first this paper directly applies the a algorithm to multiple sequence alignment problem with more powerful estimator in more than two dimensional case and discusses the extensions of this approach utilizing an upper bound of the shortest path length and of modification of network structure the algorithm to provide the upper bound is also proposed in this paper the basic part of these results was originally shown in ikeda and imai 11 this part is similar to the branch and bound techniques implemented in msa program in gupta et al 6 our framework is based on the edge length transformation to reduce the problem to the shortest path problem which is more suitable to generalizations to enumerating suboptimal alignments and parametric analysis as done in shibuya and imai 15 17 by this enhanced a algorithm optimal multiple alignments of several long sequences can be computed in practice which is shown by computational results second this paper proposes a k group alignment algorithm for multiple alignment as a practical method for much larger size problem of say multiple alignments of 50 100 sequences a basic part of these results were originally presented in imai and ikeda 13 in existing iterative improvement methods for multiple alignment the so called group to group two dimensional dynamic programming has been used and in this respect our proposal is to extend the ordinary two group dynamic programming to a k group alignment programming this extension is conceptually straightforward and here our contribution is to demonstrate that the k group alignment can be implemented so as to run in a reasonable time and space under standard computing environments this is established by generalizing the above a search approach the k group alignment method can be directly incorporated in existing methods such as iterative improvement algorithms 2 5 and tree based iterative algorithms 9 this paper performs computational experiments by applying the k group method to iterative improvement algorithms and shows that our approach can find better alignments in reasonable time for example through larger scale computational experiments here 34 protein sequences with very high homology can be optimally 10 group aligned and 64 sequences with high homology can be optimally 5 group aligned

dispersion of stress waves in one dimensional semi infinite weakly coupled layared systems an analytical study of the dispersion of transient stress waves in the first layer of a weakly coupled semi infinite bi layered system is carried out the analysis is based on approximate fourier transform inversions and makes use of the fact that the weakly coupled system possesses small propagation zones pzs in the frequency domain low and high frequency asymptotic approximations to the transient waves are computed taking into account frequency components of the transfer function in the first and second pzs respectively the derived analytic expressions are superpositions of non oscillating terms and convolution integrals with decaying oscillatory kernels it is shown that depending on the frequency and the amplitude of the convolution kernels the dispersed waves overshoot or undershoot the applied impulsive excitation this result is of significant practical importance in the design of layered systems as stress attenuators

real time heuristic search abstract we apply the two player game assumptions of limited search horizon and commitment to moves in constant time to single agent heuristic search problems we present a variation of minimax lookahead search and an analog to alpha beta pruning that significantly improves the efficiency of the algorithm paradoxically the search horizon reachable with this algorithm increases with increasing branching factor in addition we present a new algorithm called real time a for interleaving planning and execution we prove that the algorithm makes locally optimal decisions and is guaranteed to find a solution we also present a learning version of this algorithm that improves its performance over successive problem solving trials by learning more accurate heuristic values and prove that the learned values converge to their exact values along every optimal path these algorithms effectively solve significantly larger problems than have previously been solvable using heuristic evaluation functions

speeding up dynamic programming algorithms for finding optimal lattice paths many problems can be reduced to finding an optimal lattice path for example minimum path integrals can be computed by discretizing to a lattice graph and then using the optimal lattice path to approximate the minimum continuous path finding an optimal alignment between two sequences can also be reduced to finding an optimal lattice path dynamic programming algorithms are generally well suited to such problems but can be slow and require too much storage if the lattice is too large for example if the lattice dimension is too high faster algorithms requiring less computer storage can often be constructed by restricting calculations to a computational volume known to contain the optimal path upper and lower bounds on path distances from the problem domain can often help to produce small computational volumes

mm a bidirectional search algorithm that is guaranteed to meet in the middle abstract bidirectional search algorithms interleave two separate searches a normal search forward from the start state and a search backward from the goal it is well known that adding a heuristic to unidirectional search dramatically reduces the search effort by contrast despite decades of research bidirectional heuristic search has not yet had a major impact additionally no comprehensive theory was ever devised to understand the nature of bidirectional heuristic search in this paper we aim to close this gap we first present mm a novel bidirectional heuristic search algorithm unlike previous bidirectional heuristic search algorithms mm s forward and backward searches are guaranteed to meet in the middle i e never expand a node beyond the solution midpoint based on this unique attribute we present a novel framework for comparing mm a and their brute force variants we do this by dividing the entire state space into disjoint regions based on their distance from the start and goal this allows us to perform a comparison of these algorithms on a per region basis and identify conditions favoring each algorithm finally we present experimental results that support our theoretical analysis

open constraint programming traditionally constraint satisfaction problems csp have assumed closed world scenarios where all domains and constraints are fixed from the beginning with the internet many of the traditional csp applications in resource allocation scheduling and planning pose themselves in open world settings where domains and constraints must be discovered from different sources in a network to model this scenario we define open constraint satisfaction problems ocsp as csp where domains and constraints are incrementally discovered through a network we then extend the concept to open constraint optimization ocop ocsp can be solved without complete knowledge of the variable domains and we give sound and complete algorithms we show that ocop require the additional assumption that variable domains and relations are revealed in non decreasing order of preference we present a variety of algorithms for solving ocop in the possibilistic and weighted model we compare the algorithms through experiments on randomly generated problems we show that in certain cases open constraint programming can require significantly less information than traditional methods where gathering information and solving the csp are separated this leads to a reduction in network traffic and server load and improves privacy in distributed problem solving

the pn search algorithm application to tsume shogi abstract this paper proposes a new search algorithm denoted pn for and or tree search the algorithm is based on proof number pn search a best first search algorithm proposed by allis et al artificial intelligence 66 1 1994 91 124 and on korf s rbfs algorithm artificial intelligence 62 1 1993 41 78 pn combines several existing ideas it transforms a best first pn search algorithm into an iterative deepening depth first approach moreover it is enhanced by methods such as recursive iterative deepening dynamic evaluation efficient successor ordering and pruning by dependency relations the resulting algorithm turns out to be highly efficient as witnessed by the experimental results the pn algorithm is implemented in a tsume shogi japanese chess mating problem program and evaluated by testing it on 295 notoriously difficult tsume shogi problems one problem has a depth of search of over 1500 plies the experimental results are compared with those of other programs the pn program shows by far the best results solving all problems but one needless to say it outperforms the best human tsume shogi problem solvers by far

minimax search algorithms with and without aspiration windows investigation of several algorithms for computing exact minimax values of game trees utilizing backward pruning are discussed the focus is on trees with an ordering similar to that actually found in game playing practice the authors compare the algorithms using two different distributions of the static values the uniform distribution and a distribution estimated from practical data a systematic comparison of using aspiration windows for all of the usual minimax algorithms is presented the effects of aspiration windows of varying size and position are analyzed increasing the ordering of moves to near the optimum results in unexpectedly high savings algorithms with linear space complexity benefit most although the ordering of the first move is of predominant importance that of the remainder has only second order effects the use of an aspiration window not only makes alpha beta search competitive but there also exist dependencies of its effects on certain properties of the trees

a fast algorithm to solve the inverse scattering problem in layered media with arbitrary input a new sequential algorithm to solve the one dimensional inverse scattering problem in layered media with arbitrary inlet pulse is presented the procedure consists of the mathematical inversion of the exact algebraic solution for the direct problem derived in tenenbaum and zindeluk j acoust soc am xx xxxx xxxx 1992 and features computational efficiency together with improved numerical stability simulated examples of successful impedance profile identification with noisy data are reported and a detailed analysis of the stability improvement is provided impact tests on variable cross section long bars monitored with strain gauges are also reported and the method is applied to actual parameter profile identification with success

smooth linearization of hyperbolic fixed points without resonance conditions a well known theorem of hartman grobman says that a c1 diffeomorphism f rn rn with a hyperbolic fixed point at 0 can be conjugated to the linear diffeomorphism l df 0 at least in a neighbourhood of 0 in this paper we will show that if is c2 then is differentiably conjugate to l at 0 moreover the conjugacy is holder outside 0 no resonance conditions will be required

a heuristic search algorithm with modifiable estimate abstract this paper describes an improved version of two previously published algorithms in the area a and b the new approach is based on considering the estimate n on node n as a variable rather than as a constant the new algorithm thus improves the estimate as it goes on avoiding some useless node expansions it is proved to never expand more nodes than b or a and to expand a much smaller number of them in some cases another result of the paper is a proof that no overall optimal algorithm exists if the cost of an algorithm is measured by the total number of node expansions

structural health monitoring using empirical mode decomposition and the hilbert phase abstract this paper discusses a new signal processing tool involving the use of empirical mode decomposition and its application to health monitoring of structures empirical mode decomposition is a time series analysis method that extracts a custom set of basis functions to describe the vibratory response of a system in conjunction with the hilbert transform the empirical mode decomposition method provides some unique information about the nature of the vibratory response in this paper the method is used to process time series data from a variety of 1 d structures with and without structural damage empirically derived basis functions are processed through the hilbert huang transform to obtain magnitude phase and damping information this magnitude phase and damping information is later processed to extract the underlying incident energy propagating through the structure this incident energy is also referred to as the dereverberated response of a structure using simple physics based models of 1 d structures it is possible to determine the location and extent of damage by tracking phase properties between successive degrees of freedom this paper also presents experimental validation of this approach using a civil building model results illustrate that this new time series method is a powerful signal processing tool that tracks unique features in the vibratory response of structures

sokoban improving the search with relevance cuts humans can effectively navigate through large search spaces enabling them to solve problems with daunting complexity this is largely due to an ability to successfully distinguish between relevant and irrelevant actions moves in this paper we present a new single agent search pruning technique that is based on a move s influence the influence measure is a crude form of relevance in that it is used to differentiate between local relevant moves and non local irrelevant moves with respect to the sequence of moves leading up to the current state our pruning technique uses the m previous moves to decide if a move is relevant in the current context and if not to cut it off this technique results in a large reduction in the search effort required to solve sokoban problems

iterative version spaces an incremental depth first algorithm for computing the s and set of mitchell s candidate elimination and mellish s description identification algorithm is presented as in mellish s approach lowerbounds examples as well as upperbounds can be handled instead of storing the complete s and sets only one element s s and g is stored together with backtrack information the worst case space complexity of our algorithm is linear in the number of lower and upperbounds for the candidate elimination algorithm this can be exponential we introduce a test for membership of s and with a number of coverage tests linear in the number of examples consequently the worst case time complexity to compute s and for each example is only a linear factor worse than the candidate elimination algorithm s

wave propagation modelling in 1d structures using spectral finite elements abstract the application of spectral finite elements sfe to one dimensional 1d elastic wave propagation problems is presented travelling waves in an isotropic rod and timoshenko beam have been investigated the rod has been modelled using 1d sfes while the beam has been modelled using 1d and 2d sfes numerical results have been compared to those obtained from the classical finite element approach this comparison highlighted the efficiency of the sfe method the numerical results have been also verified experimentally a high degree of accuracy has been observed

a high performance explanation based learning algorithm abstract the main contribution of this paper is a new domain independent explanation based learning ebl algorithm the new ebl di algorithm significantly outperforms traditional ebl algorithms both by learning in situations where traditional algorithms cannot learn as well as by providing greater problem solving performance improvement in general the superiority of the ebl di algorithm is demonstrated with experiments in three different application domains the ebl di algorithm is developed using a novel formal framework in which traditional ebl techniques are reconstructed as the structured application of three explanation transformation operators we extend this basic framework by introducing two additional operators that when combined with the first three operators allow us to prove a completeness result in the formal framework every ebl algorithm is equivalent to the application of the five transformation operators according to some control strategy the ebl di algorithm employs all five proof transformation operators guided by five domain independent control heuristics

rational deployment of multiple heuristics in optimal state space search abstract the obvious way to use several admissible heuristics in searching for an optimal solution is to take their maximum in this paper we aim to reduce the time spent on computing heuristics within the context of a and i d a we discuss lazy a and lazy i d a variants of a and i d a respectively where heuristics are evaluated lazily only when they are essential to a decision to be made in the search process while these lazy algorithms outperform naive maximization we can do even better by intelligently deciding when to compute the more expensive heuristic we present a new rational metareasoning based scheme which decides whether to compute the more expensive heuristics at all based on a myopic regret estimate this scheme is used to create rational lazy a and rational lazy i d a we also present different methods for estimating the parameters necessary for making such decisions an empirical evaluation in several domains supports the theoretical results and shows that the rational variants rational lazy a and rational lazy i d a are better than their non rational counterparts

on the speed of convergence of value iteration on stochastic shortest path problems we establish a bound on the convergence time of the value iteration algorithm on stochastic shortest path problems the bound which applies for admissible initial vectors as for example j equiv 0 implies a polynomial time convergence of value iteration for all problems with polynomially bounded vert j vert underline g this result gives a partial answer to the open problem of bounding the convergence time of value iteration on arbitrary initial vectors the proof is obtained by analyzing a stochastic process associated with the shortest path problem

smooth linearization near a fixed point in this paper we extend a theorem of sternberg and bi leckii we study a vector field or a diffeomorphism in the vicinity of a hyperbolic fixed point we assume that the eigenvalues of the linear part a at the fixed point satisfy qth order algebraic inequalities where q 2 2 then there is ck linearization in the vicinity of the fixed point where k is the q smoothness of a we give an explicit and simple algorithm for com puting k an illustrative example from celestial mechanics is included which shows that our main theorem is an improvement over previously known theories we also show that if the vector field or diffeomorphism depends smoothly on a parameter then the linearizing conjugation de pends smoothly on the parameter

adopt asynchronous distributed constraint optimization with quality guarantees the distributed constraint optimization problem dcop is a promising approach for modeling distributed reasoning tasks that arise in multiagent systems unfortunately existing methods for dcop are not able to provide theoretical guarantees on global solution quality while allowing agents to operate asynchronously we show how this failure can be remedied by allowing agents to make local decisions based on conservative cost estimates rather than relying on global certainty as previous approaches have done this novel approach results in a polynomial space algorithm for dcop named adopt that is guaranteed to find the globally optimal solution while allowing agents to execute asynchronously and in parallel detailed experimental results show that on benchmark problems adopt obtains speedups of several orders of magnitude over other approaches adopt can also perform bounded error approximation it has the ability to quickly find approximate solutions and unlike heuristic search methods still maintain a theoretical guarantee on solution quality

best first minimax search we describe a very simple selective search algorithm for two player games called best first minimax it always expands next the node at the end of the expected line of play which determines the minimax value of the root it uses the same information as alpha beta minimax and takes roughly the same time per node generation we present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth but at significant time cost our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move pruning subtrees below moves not chosen by either player we also show how to efficiently generate a class of incremental random game trees on uniform random game trees best first minimax outperforms alpha beta when both algorithms are given the same amount of computation on random trees with random branching factors best first outperforms alpha beta for shallow depths but eventually loses at greater depths we obtain similar results in the game of othello finally we present a hybrid best first extension algorithm that combines alpha beta with best first minimax and performs significantly better than alpha beta in both domains even at greater depths in othello it beats alpha beta in two out of three games

simplified analytical models for transient uniaxial waves in a layered periodic stack abstract a physical understanding is gained of some results acquired in the analysis of transient propagation of uniaxial elastic waves in weakly coupled periodic stacks using simple analytical models three simplified models are examined a mass spring chain a single mass spring attached to a delayed moving base and high frequencies of an elastic mass reacted upon by a spring closed form expressions and asymptotic behavior are obtained for attenuation of maximum stress characteristic velocities internal stress distribution and transmission or suppression of highfrequency oscillations the results provide insights in the design of impact resistant structural systems using layered periodic stacks

sharpness for c 1 linearization of planar hyperbolic diffeomorphisms abstract c 1 linearization preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions planar hyperbolic diffeomorphisms are the most elementary ones of representatively technical difficulties in the study of c 1 linearization in the poincare domain both eigenvalues inside the unit circle s 1 a lower bound 0 was given such that c 1 smoothness with 0 1 admits c 1 linearization our first purpose of this paper is to prove the sharpness of 0 and give a weaker linearization for 0 in the siegel domain one eigenvalue inside s 1 but the other outside s 1 it is known that c 1 smoothness admits c 1 linearization for all 0 1 the second purpose is to prove that the c 1 linearization is actually a c 1 linearization and give sharp estimates for

predicting optimal solution costs with bidirectional stratified sampling in regular search spaces optimal planning and heuristic search systems solve state space search problems by finding a least cost path from start to goal as a byproduct of having an optimal path they also determine the optimal solution cost in this paper we focus on the problem of determining the optimal solution cost for a state space search problem directly i e without actually finding a solution path of that cost we present an algorithm biss which is a hybrid of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost biss is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity we show empirically that biss produces accurate predictions in several domains in addition we show that biss scales to state spaces much larger than can be solved optimally in particular we estimate the average solution cost for the 6 6 7 7 and 8 8 sliding tile puzzle and provide indirect evidence that these estimates are accurate as a practical application of biss we show how to use its predictions to reduce the time required by another system to learn strong heuristic functions from days to minutes in the domains tested

quantitatively relating abstractness to the accuracy of admissible heuristics abstract admissible lower bound heuristics are worth discovering because they have desirable properties in various search algorithms one well known source of admissible heuristics is from abstractions of a problem using standard definitions of heuristic accuracy and abstractness we prove that heuristic accuracy decreases inversely with abstractness this is the first quantitative result linking abstractness to the heuristic accuracy using this result it may be possible to predict the accuracy of an abstraction derived heuristic without testing it on a sample set of problems it may also be possible for a heuristic discovery system to use the theory to predict the accuracy of a heuristic thereby better focusing its search

perimeter search in restricted memory abstract in this paper we consider the problem of finding a minimum cost path in a graph in particular we consider the perimeter search technique and we investigate the possibility of using very large perimeters we present an algorithm designed to use perimeters of arbitrary size our algorithm generates the perimeter incrementally and makes use of a technique called backward pruning for reducing the search effort a qualitative analysis and experimental results show that our algorithm can effectively use perimeters of very large size

performance of linear space search algorithms abstract search algorithms that use space linear in the search depth are widely employed in practice to solve difficult problems optimally such as planning and scheduling in this paper we study the average case performance of linear space search algorithms including depth first branch and bound dfbnb iterative deepening id and recursive best first search rbfs to facilitate our analyses we use a random tree t b d that has mean branching factor b depth d and node costs that are the sum of the costs of the edges from the root to the nodes we prove that the expected number of nodes expanded by dfbnb on a random tree is no more than bd times the expected number of nodes expanded by best first search bfs on the same tree which usually requires space that is exponential in depth d we also show that dfbnb is asymptotically optimal when bfs runs in exponential time and id and rbfs are asymptotically optimal when the edge costs of t b d are integers if bp 0 is the expected number of children of a node whose costs are the same as that of their parent then the expected number of nodes expanded by these three linear space algorithms is exponential when bp o d 4 when bp 0 1 and at most quadratic when bp 0 1 in addition we study the heuristic branching factor of t b d and the effective branching factor of bfs dfbnb id and rbfs on t b d furthermore we use our analytic results to explain a surprising anomaly in the performance of these algorithms and to predict the existence of a complexity transition in the asymmetric traveling salesman problem

a modified sequential algebraic algorithm applied to identify rough acoustic impedance profiles in slender structures this paper develops and examines a modified technique for identifying damage in slender structures an algorithm called modified sequential algebraic algorithm is presented to solve the longitudinal acoustic wave propagation problem in inhomogeneous media this method accurately predicts the echo generated by the inhomogeneities when the acoustic impedance variation profile in the damaged part of the structure is non smooth for these cases the available algorithms fail to provide the actual regressive wave component in the following a stochastic optimization scheme the differential evolution method is applied to solve the inverse problem numerical examples with smooth and non smooth impedance profiles are considered it is shown that for smooth profiles both the available techniques and the modified algorithm succeed in identifying the actual damage nevertheless in situations where a rough profile is to be reconstructed only the modified algorithm succeeds the technique is found to be robust with respect to additive noise in the signals

reducing reexpansions in iterative deepening search by controlling cutoff bounds abstract it is known that a best first search algorithm like a 5 6 requires too much space which often renders it unusable and a depth first search strategy does not guarantee an optimal cost solution the iterative deepening algorithm ida 4 achieves both space and cost optimality for a class of tree searching problems however for many other problems it takes too much of computation time due to excessive reexpansion of nodes this paper presents a modification of ida to an admissible iterative depth first branch and bound algorithm ida cr for trees which overcomes this drawback of ida and operates much faster using the same amount of storage algorithm ida cra a bounded suboptimal cost variation of ida cr is also presented in order to reduce the execution time still further results with the 0 1 knapsack problem traveling salesman problem and the flow shop scheduling problem are shown

c1 linearization for planar contractions c1 linearization is of special interests because it can distinguish characteristic directions of dynamical systems it is known that planar c1 contractions with a fixed point at the origin o admit c1 linearization with sufficiently small 0 if 1 and admit c1 linearization if log 1 log 2 1 1 where 1 and 2 are eigenvalues of the linear parts of the contractions at o with 0 1 2 1 in this paper we improve the lower bound of to lower the condition of c1 linearization for planar contractions furthermore we prove that the derivatives of transformations in our c1 linearization are holder continuous and give estimates for the holder exponent finally we give a counter example to show that those estimates cannot be improved anymore

on the sensitivity of elastic waves due to structural damages time frequency based indexing method time frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform wt and hilbert huang transform hht and their performances are compared in context of quantifying the damages spectral finite element method is employed for numerical simulation of wave scattering an analytical study is carried out to study the effects of higher order damage parameters on the reflected wave from a damage based on this study error bounds are computed for the signals in the spectral and also on the time frequency domains it is shown how such an error bound can provide an estimate of error in the modelling of wave propagation in structure with damage measures of damage based on wt and hht is derived to quantify the damage information hidden in the signal the aim of this study is to obtain detailed insights into the problem of 1 identifying localised damages 2 dispersion of multifrequency non stationary signals after they interact with various types of damage and 3 quantifying the damages sensitivity analysis of the signal due to scattered wave based on time frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors

sub stable and weak stable manifolds associated with finitely non resonant spectral subspaces in this work we study c k delta 2 leq k leq infty 0 leq delta leq 1 maps of a banach space near a fixed point we show the existence and uniqueness of a class of c k delta local invariant sub manifolds of the stable manifold which correspond to a spectral subspace satisfying a finite non resonance condition of order l leq k and an overriding condition of order l leq k condition 3 of theorem 1 we study the dependence of these invariant manifolds on a parameter that lies in a banach space we also show that a c k delta local weak stable manifold that satisfies these two conditions is unique in the class of c k delta maps the uniqueness is due to the fact that our method does not require a cut off function an infinite dimensional banach space does not always admit smooth cut off functions

benefits of using multivalued functions for minimaxing abstract minimaxing has been very successful in game playing practice although a complete explanation of why it has been that successful has not yet been given in particular it has not been shown why it should be useful as it is in practice to use multivalued evaluation functions such functions have many distinct values as their result and can discriminate between positions according to the heuristic knowledge represented in these values in this paper we modify a basic pathological model by adding two assumptions regarding multivalued evaluation functions these assumptions non uniformity of error distribution and dependency of heuristic values directly relate to the properties of multivalued evaluation functions as used in practice simulation studies of our multivalued model have exhibited sharp error reductions for deeper searches using minimaxing this behavior corresponds to observations in practice the error reductions are primarily due to the improved evaluation quality as search depth increases this phenomenon of lower probability of static evaluation errors with increasing search depth is revealed through our model although the same evaluation function is used at all levels of the tree and although its general error probability is independent of the depth essentially with increasing search depth the evaluation function is more frequently used on such positions which can be more reliably evaluated by a multivalued function with the assumed properties this effect together with the ability to discriminate between positions of different goodness leads to the benefits of using multivalued evaluation functions of appropriate granularity for minimaxing

probabilistic conflicts in a search algorithm for estimating posterior probabilities in bayesian networks abstract this paper presents a search algorithm for estimating posterior probabilities in discrete bayesian networks it shows how conflicts as used in consistency based diagnosis can be adapted to speed up the search this algorithm is especially suited to the case where there are skewed distributions although nothing about the algorithm or the definitions depends on skewness of distributions the general idea is to forward simulate the network based on the normal values for each variable the value with high probability given its parents when a predicted value is at odds with the observations we analyse which variables were responsible for the expectation failure these form a conflict and continue forward simulation considering different values for these variables this results in a set of possible worlds from which posterior probabilities together with error bounds can be derived empirical results with bayesian networks having tens of thousands of nodes are presented

frontier search the critical resource that limits the application of best first search is memory we present a new class of best first search algorithms that reduce the space complexity the key idea is to store only the open list of generated nodes but not the closed list of expanded nodes the solution path can be recovered by a divide and conquer technique either as a bidirectional or unidirectional search for many problems frontier search dramatically reduces the memory required by best first search we apply frontier search to breadth first search of sliding tile puzzles and the 4 peg towers of hanoi problem dijkstra s algorithm on a grid with random edge costs and the a algorithm on the fifteen puzzle the four peg towers of hanoi problem and optimal sequence alignment in computational biology

real time bidirectional search coordinated problem solving in uncertain situations this paper investigates real time bidirectional search rtbs algorithms where two problem solvers starting from the initial and goal states physically move toward each other to evaluate the rtbs performance two kinds of algorithms are proposed and are compared to real time unidirectional search one is called centralized rtbs where a supervisor always selects the best action from all possible moves of the two problem solvers the other is called decoupled rtbs where no supervisor exists and the two problem solvers independently select their next moves experiments on mazes and n puzzles show that 1 in clear situations decoupled rtbs performs better while in uncertain situations centralized rtbs becomes more efficient and 2 rtbs is more efficient than real time unidirectional search for 15 and 24 puzzles but not for randomly generated mazes it is shown that the selection of the problem solving organization is the selection of the problem space which determines the baseline of the organizational efficiency once a difficult problem space is selected the local coordination among problem solvers hardly overcome the deficit

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

controlling the learning process of real time heuristic search real time search provides an attractive framework for intelligent autonomous agents as it allows us to model an agent s ability to improve its performance through experience however the behavior of real time search agents is far from rational during the learning convergence process in that they fail to balance the efforts to achieve a short term goal i e to safely arrive at a goal state in the present problem solving trial and a long term goal to find better solutions through repeated trials as a remedy we introduce two techniques for controlling the amount of exploration both overall and per trial the weighted real time search reduces the overall amount of exploration and accelerates convergence it sacrifices admissibility but provides a nontrivial bound on the converged solution cost the real time search with upper bounds insures solution quality in each trial when the state space is undirected these techniques result in a convergence process more stable compared with that of the learning real time a algorithm

agent searching in a tree and the optimality of iterative deepening the agent searching framework models the effort of a search strategy in terms of the distance traversed by an agent while exploring the search space the framework has been found to be useful in modeling search problems where the cost of backtracking and retracing search paths is important in determining search complexity in this paper we show that depth first iterative deepening dfid strategies are optimal for an agent searching in a line in m concurrent rays and in uniform b ary trees in the conventional search model it is known that dfid is asymptotically optimal for uninformed search of uniform b ary trees in this paper we prove the stronger result that for agent searching in uniform b ary trees iterative deepening is optimal up to lower order terms we also discuss the problems involved in optimally performing agent search in a graph

time complexity of iterative deepening a abstract we analyze the time complexity of iterative deepening a ida we first show how to calculate the exact number of nodes at a given depth of a regular search tree and the asymptotic brute force branching factor we then use this result to analyze ida with a consistent admissible heuristic function previous analyses relied on an abstract analytic model and characterized the heuristic function in terms of its accuracy but do not apply to concrete problems in contrast our analysis allows us to accurately predict the performance of ida on actual problems such as the sliding tile puzzles and rubik s cube the heuristic function is characterized by the distribution of heuristic values over the problem space contrary to conventional wisdom our analysis shows that the asymptotic heuristic branching factor is the same as the brute force branching factor thus the effect of a heuristic function is to reduce the effective depth of search by a constant relative to a brute force search rather than reducing the effective branching factor

an exact solution for the one dimensional elastic wave equation in layered media a new approach to the direct scattering problem in one dimensional inhomogeneous bodies is presented a general formulation considering density wave speed and cross section variation is introduced and a compact form for the wave equation in the characteristic plane with a generalized acoustical impedance profile as a parameter is established with the aid of a nonsingular variable transformation the wave propagation pattern in layered or discretized continuous media is then examined and an exact algebraic solution for the reflected wave is obtained the resulting formula is adequate to an arbitrary input pulse furnishing a quick computation of all multiple reflection contributions to the final echo

linear space best first search abstract best first search is a general heuristic search algorithm that always expands next a frontier node of lowest cost it includes as special cases breadth first search dijkstra s single source shortest path algorithm and the a algorithm its applicability however is limited by its exponential memory requirement previous approaches to this problem such as iterative deepening do not expand nodes in best first order if the cost function can decrease along a path we present a linear space best first search algorithm rbfs that always explores new nodes in best first order regardless of the cost function and expands fewer nodes than iterative deepening with a nondecreasing cost function on the sliding tile puzzles rbfs with a nonmonotonic weighted evaluation function dramatically reduces computation time with only a small penalty in solution cost in general rbfs reduces the space complexity of best first search from exponential to linear at the cost of only a constant factor in time complexity in our experiments

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

invariant foliations near normally hyperbolic invariant manifolds for semiflows let m be a compact c1 manifold which is invariant and normally hyperbolic with respect to a c1 semiflow in a banach space then in an neighborhood of m there exist local c1 center stable and center unstable manifolds w cs and w cu respectively here we show that w cs and w cu may each be decomposed into the disjoint union of c1 submanifolds leaves in such a way that the semiflow takes leaves into leaves of the same collection furthermore each leaf intersects m in a single point which determines the asymptotic behavior of all points of that leaf in either forward or backward time

cut and solve an iterative search strategy for combinatorial optimization problems branch and bound and branch and cut use search trees to identify optimal solutions to combinatorial optimization problems in this paper we introduce an iterative search strategy which we refer to as cut and solve and prove optimality and termination for this method this search is different from traditional tree search as there is no branching at each node in the search path a relaxed problem and a sparse problem are solved and a constraint is added to the relaxed problem the sparse problems provide incumbent solutions when the constraining of the relaxed problem becomes tight enough its solution value becomes no better than the incumbent solution value at this point the incumbent solution is declared to be optimal this strategy is easily adapted to be an anytime algorithm as an incumbent solution is found at the root node and continuously updated during the search cut and solve enjoys two favorable properties since there is no branching there are no wrong subtrees in which the search may get lost furthermore its memory requirement is negligible for these reasons it has potential for problems that are difficult to solve using depth first or best first search tree methods in this paper we demonstrate the cut and solve strategy by implementing a generic version of it for the asymmetric traveling salesman problem atsp our unoptimized implementation outperformed state of the art solvers for five out of seven real world problem classes of the atsp for four of these classes cut and solve was able to solve larger sometimes substantially larger problems our code is available at our websites

learning heuristic functions for large state spaces we investigate the use of machine learning to create effective heuristics for search algorithms such as ida or heuristic search planners such as ff our method aims to generate a sequence of heuristics from a given weak heuristic h 0 and a set of unsolved training instances using a bootstrapping procedure the training instances that can be solved using h 0 provide training examples for a learning algorithm that produces a heuristic h 1 that is expected to be stronger than h 0 if h 0 is so weak that it cannot solve any of the given instances we use random walks backward from the goal state to create a sequence of successively more difficult training instances starting with ones that are guaranteed to be solvable by h 0 the bootstrap process is then repeated using h i in lieu of h i 1 until a sufficiently strong heuristic is produced we test this method on the 24 sliding tile puzzle the 35 pancake puzzle email protected s cube and the 20 blocks world in every case our method produces a heuristic that allows ida to solve randomly generated problem instances quickly with solutions close to optimal the total time for the bootstrap process to create strong heuristics for these large state spaces is on the order of days to make the process effective when only a single problem instance needs to be solved we present a variation in which the bootstrap learning of new heuristics is interleaved with problem solving using the initial heuristic and whatever heuristics have been learned so far this substantially reduces the total time needed to solve a single instance while the solutions obtained are still close to optimal

the partition of unity finite element method for elastic wave propagation in reissner mindlin plates this paper reports a numerical method for modelling the elastic wave propagation in plates the method is based on the partition of unity approach in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment the technique is general such that it can be applied to the lagrangian family of finite elements with specific waveform enrichment schemes depending on the dominant modes of wave propagation in the physical system a four noded element for the reissner mindlin plate is derived in this paper which is free of shear locking such a locking free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain as a result the frequency dependent stiffness matrix and the mass matrix are obtained which capture the higher frequency response with even coarse meshes accurately the steps involved in the numerical implementation of such element are discussed in details numerical studies on the performance of the proposed element are reported by considering a number of cases which show very good accuracy and low computational cost copyright 2006 john wiley sons ltd

heuristic search in restricted memory research note abstract this paper presents heuristic search algorithms which work within memory constraints these algorithms ma for ordinary graphs and mao for and or graphs guarantee admissible solutions within specified memory limitations above the minimum required the memory versus node expansions tradeoff is analyzed for the worst case in the case of ordinary graphs some experiments using the fifteen puzzle problem are carried out under various pruning conditions these parameterized algorithms are found to encompass a wide class of best first search algorithms

duality in permutation state spaces and the dual search algorithm geometrical symmetries are commonly exploited to improve the efficiency of search algorithms a new type of symmetry in permutation state spaces duality is introduced each state has a dual state both states share important attributes such as their distance to the goal given a state s it is shown that an admissible heuristic of the dual state of s is an admissible heuristic for s this provides opportunities for additional heuristic evaluations an exact definition of the class of problems where duality exists is provided a new search algorithm dual search is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster the decision of when to switch is very important and several policies for doing this are investigated experimental results show significant improvements for a number of applications for using the dual state s heuristic evaluation and or dual search

inconsistent heuristics in theory and practice in the field of heuristic search it is usually assumed that admissible heuristics are consistent implying that consistency is a desirable attribute the term inconsistent heuristic has at times been portrayed negatively as something to be avoided part of this is historical early research discovered that inconsistency can lead to poor performance for a nodes might be re expanded many times however the issue has never been fully investigated and was not re considered after the invention of ida this paper shows that many of the preconceived notions about inconsistent heuristics are outdated the worst case exponential time of inconsistent heuristics is shown to only occur on contrived graphs with edge weights that are exponential in the size of the graph furthermore the paper shows that rather than being something to be avoided inconsistent heuristics often add a diversity of heuristic values into a search which can lead to a reduction in the number of node expansions inconsistent heuristics are easy to create contrary to the common perception in the ai literature to demonstrate this a number of methods for achieving effective inconsistent heuristics are presented pathmax is a way of propagating inconsistent heuristic values in the search from parent to children this technique is generalized into bidirectional pathmax bpmx which propagates values from a parent to a child node and vice versa bpmx can be integrated into ida and a when inconsistent heuristics are used with bpmx experimental results show a large reduction in the search effort required by ida positive results are also presented for a searches

bida an improved perimeter search algorithm abstract in this paper we present a new bidirectional heuristic search algorithm our algorithm can be viewed as a perimeter search algorithm and it uses a new technique for reducing the number of heuristic evaluations we also prove some general results on the behavior of iterative deepening perimeter search algorithms and we discuss some new lazy evaluation techniques for improving their performance the theoretical and experimental results show that perimeter search algorithms outperform the other bidirectional algorithms and we believe it is worthwhile to give them a deep look in subsequent research

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

iterative state space reduction for flexible computation abstract flexible computation is a general framework for decision making under limited computational resources it enables an agent to allocate limited computational resources to maximize its overall performance or utility in this paper we present a strategy for flexible computation which we call iterative state space reduction the main ideas are to reduce a problem space that is difficult to search to one that is relatively easy to explore to use the optimal solution from the reduced space as an approximate solution to the original problem and to iteratively apply multiple reductions to progressively find better solutions the basic operation for state space reduction is heuristic node pruning which excludes the nodes that do not seem to lead to high quality solutions from further examination iterative state space reduction can be combined with a state space search such as best first search or depth first branch and bound dfbnb the resulting algorithm can run as an anytime algorithm which provides a tradeoff between solution quality and computation based on an analytical modal we analyze the probability that one iteration of the iterative process finds a solution furthermore by combining it within dfbnb we apply iterative state space reduction to three combinatorial problems the maximum boolean satisfiability the symmetric tsp and asymmetric tsp our experimental results show that iterative state space reduction is effective and efficient making dfbnb find better solutions with less computation

on the equivalence of cost functions in the design of circuits by cost table in the cost table approach to logic design a function is realized as a combination of functions from a table the objective of the synthesis is to find the least cost realization where realization cost is the sum of the costs of the functions used plus the cost of combining them the costs of cost table functions are defined by a cost function which represents chip area speed power dissipation or a combination of these factors it is shown that there is an arbitrarily large set s of cost functions which yield the same cost table this implies for example that every minimal realization of any function over a cost function in s is independent of the actual cost function used with any cost function if the cost of combining functions from a cost table f is sufficiently large the realizations behave as if the cost function belonged to s that is any minimal realization of a function f using cost table f is one of the minimal realizations of f using f and a cost function in s the interpretation of these results is that there are not as many distinct cost tables as originally thought

proof number search abstract proof number search pn search is designed for finding the game theoretical value in game trees it is based on ideas derived from conspiracy number search and its variants such as applied cn search and cn search while in cn search the purpose is to continue searching until it is unlikely that the minimax value of the root will change pn search aims at proving the true value of the root therefore pn search does not consider interim minimax values pn search selects the next node to be expanded using two criteria the potential range of subtree values and the number of nodes which must conspire to prove or disprove that range of potential values these two criteria enable pn search to treat efficiently game trees with a non uniform branching factor it is shown that in non uniform trees pn search outperforms other types of search such as iterative deepening search even when enhanced with transposition tables move ordering for the full principal variation etc pn search has been used to establish the game theoretical values of connect four qubic and go moku there pn search was able to find a forced win for the player to move first the experiments described here are in the domain of awari a game which has not yet been solved the experiments are repeatable for other games with a non uniform branching factor this article describes the underlying principles of pn search presents an appropriate implementation and provides an analysis of its strengths and weaknesses