permutation modules over table algebras and applications to association schemes abstract inspired by the notion of an action of a finite hypergroup on a finite set we introduce the more general concept of a permutation module over a table algebra it is easy to see that each permutation module over a table algebra is a direct sum of transitive permutation modules among the transitive permutation modules the w maximal and the maximal permutation modules are the most interesting ones we give various characterizations of these modules and we shall see that a standard table algebra admits a maximal transitive permutation module if and only if it arises from a finite association scheme we also show that the regular module of a standard table algebra is isomorphic to a direct summand of each w maximal transitive permutation module as a consequence one obtains 1 m for any irreducible character of the bose mesner algebra of a finite association scheme and its multiplicity m

on wreath products of c algebras table algebras and association schemes abstract in this paper we will first present characterizations of wreath products of c algebras and show that the dual of the wreath product of c algebras is isomorphic to the wreath product of the duals of those c algebras in the reverse order then we prove the krull schmidt type theorems for the wreath products of table algebras as well as for the wreath products of association schemes

a memetic approach to construct transductive discrete support vector machines abstract transductive learning involves the construction and application of prediction models to classify a fixed set of decision objects into discrete groups it is a special case of classification analysis with important applications in web mining corporate planning and other areas this paper proposes a novel transductive classifier that is based on the philosophy of discrete support vector machines we formalize the task to estimate the class labels of decision objects as a mixed integer program a memetic algorithm is developed to solve the mathematical program and to construct a transductive support vector machine classifier respectively empirical experiments on synthetic and real world data evidence the effectiveness of the new approach and demonstrate that it identifies high quality solutions in short time furthermore the results suggest that the class predictions following from the memetic algorithm are significantly more accurate than the predictions of a cplex based reference classifier comparisons to other transductive and inductive classifiers provide further support for our approach and suggest that it performs competitive with respect to several benchmarks

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

character products of association schemes since group algebras of finite groups are hopf algebras products of characters of finite groups are characters too in the present paper we prove that products of characters of finite schemes g are characters if one of the two factors contains the thin residue of g in its kernel we also give details in this situation

on morphisms of association schemes abstract in this paper we present a necessary and sufficient condition under which a combinatorial morphism between association schemes induces an algebra homomorphism between their scheme rings we will also discuss scheme ring homomorphisms of naturally valenced association schemes

approximation algorithms for knapsack problems with cardinality constraints abstract we address a variant of the classical knapsack problem in which an upper bound is imposed on the number of items that can be selected this problem arises in the solution of real life cutting stock problems by column generation and may be used to separate cover inequalities with small support within cutting plane approaches to integer linear programs we focus our attention on approximation algorithms for the problem describing a linear storage polynomial time approximation scheme ptas and a dynamic programming based fully polynomial time approximation scheme fptas the main ideas contained in our ptas are used to derive ptas s for the knapsack problem and its multi dimensional generalization which improve on the previously proposed ptas s we finally illustrate better ptas s and fptas s for the subset sum case of the problem in which profits and weights coincide

optimization models for targeted offers in direct marketing exact and heuristic algorithms this paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign we show that the problem is strongly np hard and that it is unlikely that a constant factor approximation algorithm can be proposed for solving this problem we propose an alternative set covering formulation and develop a branch and price algorithm to solve it we also describe eight heuristics to approximate an optimal solution including a depth first branch and price heuristic and a tabu search algorithm we perform extensive computational experiments both with the exact as well as with the heuristic algorithms based on our experiments we suggest the use of optimal algorithms for small and medium size instances while heuristics especially tabu search and branch and price based routines are preferable for large instances and when time is an important factor

irreducible characters of wreath products in reality based algebras and applications to association schemes abstract wreath products in reality based algebras are generalizations of wreath products of table algebras and generalized camina frobenius pairs of c algebras in this paper we present characterizations of the wreath product in a reality based algebra by its irreducible characters and by the size of the zero submatrix of its character table applications to finite groups table algebras and association schemes are also discussed in particular we will show that the wreath product of one class association schemes is characterized by the zeros in its first eigenmatrix

tabu search for the multilevel generalized assignment problem abstract the multilevel generalized assignment problem mgap differs from the classical gap in that agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be formulated as mgaps however the large number of variables in the related 0 1 integer program makes the use of commercial optimization packages impractical in this paper we present a heuristic approach to the solution of the mgap which consists of a novel application of tabu search ts our ts method employs neighborhoods defined by ejection chains that produce moves of greater power without significantly increasing the computational effort

on thin residues and basis digraphs of nilpotent table algebras and applications to nilpotent groups abstract in this paper we study characterizations of nilpotent table algebras in terms of thin residues thin residue matrices thin residue digraphs and basis digraphs we will also discuss applications to nilpotent groups in particular we give a conceptual explanation of the results in takegahara and yoshida 2008 ty

some structure theory of table algebras and applications to association schemes abstract in this paper we prove some basic structure theorems for arbitrary table algebras in particular we prove a krull schmidt theorem for arbitrary table algebras and give applications to association schemes

aliasing probability calculations for arbitrary compaction under independently selected random test vectors this paper discusses a systematic methodology for calculating the exact aliasing probability associated with schemes that use an arbitrary finite state machine to compact the response of a combinational circuit to a sequence of independently selected random test input vectors the proposed approach identifies the strong influence of fault activation probabilities on the probability of aliasing and uses an asymmetric error model to simultaneously track the states of two fictitious compactors one driven by the response of the fault free combinational circuit and one driven by the response of the faulty combinational circuit by deriving the overall markov chain that describes the combined behavior of these two compactors we are able to calculate the exact aliasing probability for any test sequence length in particular for long enough sequences the probability of aliasing is shown to only depend on the stationary distribution of the markov chain the insights provided by our analysis are used to evaluate the testing performance of simple examples of nonlinear compactors and to demonstrate regimes where they exhibit lower aliasing probability than linear compactors with the same number of states finally by establishing connections with previous work that evaluated aliasing probability in linear compactors our analysis clarifies the role played by the entropy of the stationary distribution of the compactor states

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

a new framework for designing and analyzing bist techniques and zero aliasing compression a general framework for shift register based signature analysis is presented and a mathematical model for this framework based on coding theory is developed there are two key features of this formulation first it allows for uniform treatment of lfsr misr and multiple misr based signature analyzer in addition using this formulation a new compression scheme for multiple output cut is proposed this scheme referred to as multiinput lfsr has the potential to achieve better aliasing than other schemes such as the multiple misr scheme of comparable hardware complexity several results on aliasing are presented and certain known results are shown to be direct consequences of the formulation also developed are error models that take into account the circuit topology and the effect of faults at the outputs using these models exact closed form expressions for aliasing probability are developed a closed form aliasing expression for misr under an independent error model is provided

schur rings and association schemes whose thin residues are thin abstract the thin residue is an important concept in the theory of association schemes association schemes whose thin residues are thin have been studied in several papers in this paper we construct a new class of association schemes whose thin residues are thin and give a characterization of their automorphism groups in particular we give a formula for the order of the automorphism group and a necessary and sufficient condition under which the association scheme is schurian schur rings are used as a tool in our approach

parallel signature analysis design with bounds on aliasing this paper presents parallel signature design techniques that guarantee the aliasing probability to be less than 2 l where l is the test length using y signature samples a parallel signature analysis design is proposed that guarantees the aliasing probability to be less than y l sup y 2 inaccuracies and incompleteness in previously published bounds on the aliasing probability are discussed simple bounds on the aliasing probability are derived for parallel signature designs using primitive polynomials

on semisimple varietal terwilliger algebras whose non primary ideals are 1 dimensional abstract as an abstraction of the terwilliger algebra of a commutative association scheme the notion of a varietal terwilliger algebra was introduced in 11 in this paper we first prove that there exists a varietal terwilliger algebra defined by any given standard c algebra and a generalized terwilliger algebra 6 is also a varietal terwilliger algebra then we present a necessary and sufficient condition under which a quotient algebra of a varietal terwilliger algebra is also a varietal terwilliger algebra we will also give a characterization of a semisimple varietal terwilliger algebra whose non primary ideals are all 1 dimensional and prove that a semisimple regular varietal terwilliger algebra with 1 dimensional non primary ideals is characterized by the structure of its base c subalgebra as direct consequences we obtain some results in 18 for finite association schemes and a conceptual explanation of the results in 9

simple bounds on serial signature analysis aliasing for random testing it is shown that the aliasing probability is bounded above by 1 epsilon l approximately 1 l epsilon small for large l for test lengths l less than the period l sub c of the signature polynomial for test lengths l that are multiples of l sub c the aliasing probability is bounded above by 1 for test lengths l greater than l sub c and not a multiple of l sub c the aliasing probability is bounded above by 2 l sub c 1 these simple bounds avoid any exponential complexity associated with the exact computation of the aliasing probability simple bounds also apply to signature analysis based on any linear finite state machine including linear cellular automaton from these simple bounds it follows that the aliasing probability in a signature analysis design using beta intermediate signatures is bounded by 1 epsilon sup beta beta sup beta l sup beta for beta