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

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

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

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

on a partial order defined by the weighted moore penrose inverse the weighted moore penrose inverse of a matrix can be used to define a partial order on the set of mxn complex matrices and to introduce the concept of weighted ep matrices in this paper we study the weighted star partial order on the set of weighted ep matrices in addition some properties that relate the eigenprojection at zero with the weighted star partial order are obtained

partial orders based on core nilpotent decomposition abstract in this paper we study partial orders in terms of the core nilpotent decomposition we derive some characterizations of the c n partial ordering create a new partial ordering the g drazin partial ordering which is a generalization of c n partial ordering and give some properties and characterizations of the g drazin partial ordering

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

the star partial order and the eigenprojection at 0 on ep matrices abstract the space of n n complex matrices with the star partial order is considered in the first part of this paper the class of ep matrices is analyzed and several properties related to this order are given in addition some information about predecessors and successors of a given ep matrix is obtained the second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders

g outer inverse of banach spaces operators abstract the aim of this paper is to present a new generalized inverse which is called a g outer inverse of operators between two banach spaces as a generalization of g drazin inverses of square matrices and banach space operators several characterizations of this new inverse are given based on the g outer inverse we define and characterize the g outer partial order extending the g drazin partial order to operators between two banach spaces we also relate this new partial order to the minus partial order in the end we study an outer binary relation which is an equivalence relation on the corresponding set

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

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

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

the dirichlet problem in non smooth domains dirichlet problem for an elliptic operator 2s laj jaj with smooth coefficients aij in domains d in rm m 3 with non smooth boundaries the domains we treat are given locally in some cm coordinate system by the graph of a continuous function qs with vq5 e li for some p 1 p oo such domains are called li domains see section 1 for the precise definitions note that l domains are usually called lipschitz domains if d is an li domain and x e d we study the elliptic measure a7 associated with s and d at x thus for f a continuous function on ad the formula u x hf x f doh gives the perron wiener brelot generalized soluid

homogenization of elliptic boundary value problems in lipschitz domains in this paper we study the lp boundary value problems for mathcal l u 0 in mathbb r d 1 where mathcal l rm div a nabla is a second order elliptic operator with real and symmetric coefficients assume that a is periodic in xd 1 and satisfies some minimal smoothness condition in the xd 1 variable we show that the lp neumann and regularity problems are uniquely solvable for 1 p 2 we also present a new proof of dahlberg s theorem on the lp dirichlet problem for 2 p dahlberg s original unpublished proof is given in the appendix as the periodic and smoothness conditions are imposed only on the xd 1 variable these results extend directly from mathbb r d 1 to regions above lipschitz graphs consequently by localization techniques we obtain uniform lp estimates for the dirichlet neumann and regularity problems on bounded lipschitz domains for a family of second order elliptic operators arising in the theory of homogenization the results on the neumann and regularity problems are new even for smooth domains

a distance constrained p facility location problem on the real line letv v 1 v n be a set ofn points on the real line existing facilities the problem considered is to locatep new point facilities f 1 f p inv while satisfying distance constraints between pairs of existing and new facilities and between pairs of new facilities fori 1 p j 1 n the cost of locatingf i at pointv j isc ij the objective is to minimize the total cost of setting up the new facilities we present ano p 3 n 2 logn algorithm to solve the model

on a generalized core inverse abstract the paper introduces the concept of a generalized core inverse of a matrix which extends the notion of the core inverse defined by baksalary and trenkler 1 while the original core inverse is restricted to matrices of index one the generalized core inverse exists for any square matrix several properties of the new concept are identified with the derivations based essentially on partitioned representations of matrices some of the features of the generalized core inverse coincide with those attributed to the core inverse but there are also such which characterize the core inverse only and not its generalization

weighted binary relations involving the drazin inverse the drazin inverse of a matrix has been used in the literature to define a pre order on the set of square complex matrices in this paper we analyze new binary relations defined on the set of rectangular complex matrices and some relationships to the w support idempotent we introduce the class of weighted drazin equal projectors and analyze the pre orders on this class moreover adjacent matrices are studied under the considered relations finally some observations on weighted partial orders are given

weighted g drazin inverses and a new pre order on rectangular matrices abstract this paper deals with weighted g drazin inverses which is a new class of matrices introduced to extend to the rectangular case g drazin inverses recently considered by wang and liu for square matrices first we define and characterize weighted g drazin inverses next we consider a new pre order defined on complex rectangular matrices based on weighted g drazin inverses finally we characterize this pre order and relate it to the minus partial order and to the weighted drazin pre order

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

the dirichlet problem for higher order equations in composition form the present paper commences the study of higher order differential equations in composition form specifically we consider the equation lu divb adiva u 0 where a and b are elliptic matrices with complex valued bounded measurable coefficients and a is an accretive function elliptic operators of this type naturally arise for instance via a pull back of the bilaplacian 2 from a lipschitz domain to the upper half space more generally this form is preserved under a lipschitz change of variables contrary to the case of divergence form fourth order differential equations we establish well posedness of the dirichlet problem for the equation lu 0 with boundary data in l2 and with optimal estimates in terms of nontangential maximal functions and square functions

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

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

partial orders based on outer inverses classes of outer inverses are used to create new partial orders and unify the classification of some of the old partial orders these classes are then compared with those obtained by using g inverses inner inverses

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

equivalent mathematical programming formulations of monotonic tree network location problems we consider the optimization problem of locating several new facilities on a tree network with respect to existing facilities and to each other the new facilities are not restricted to be at vertices of the network but the locations are subject to constraints each constraint function and the objective function is an arbitrary nondecreasing function of any finite collection of tree distances between new and existing facilities and or between distinct pairs of new facilities and represents some sort of transport or travel cost the new facilities are to be located so as to minimize the objective function subject to upper bounds on the constraint functions we show that such problems are equivalent to mathematical programming problems which when each function is expressed using only maximization and summation operations on nonnegatively weighted arguments are linear programming problems of polynomial dimensions the latter problems can be solved using duality theory with special purpose column generation and shortest path algorithms for column pricing

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

a new approach to absolute continuity of elliptic measure with applications to non symmetric equations in the late 1950s and early 1960s the work of de giorgi degi and nash n and then moser mo initiated the study of regularity of solutions to divergence form elliptic equations with merely bounded measurable coefficients weak solutions in a domain 0 a priori only in a sobolev space w 1 loc 0 were shown to be ho lder continuous of some order depending just on ellipticity and maximum principles and harnack inequalities were established the dirichlet problem for such operators with continuous data on the boundary was established in lsw this in turn paved the way for a more systematic and detailed study of the properties of the elliptic measures d l associated to l div a on a domain 0 the classical properties of existence of non tangential limits of solutions fatou type theorems and comparison principles appeared in cfms but owed a great deal to the earlier work of carleson ca and hunt and wheeden h w on harmonic functions in lipschitz domains all the results mentioned above were carried out for elliptic operators l div a where the matrix a aij has bounded measurable coefficients and is symmetric however it turns out that the symmetry of the matrix is not needed to get these results morrey mor first observed this in connection with the de giorgi nash moser theory for the results in cfms this fact has not been formally observed until now with appropriate reformulation in terms of adjoint operators and adjoint green s functions the results of cfms are valid without the symmetry assumption see section 1 doi 10 1006 aima 1999 1899 available online at http www idealibrary com on

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

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

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

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

matrix partial orders through generalized inverses unified theory the unified theory presented here covers as special cases the star order of drazin the minus order of hartwig and nambooripad the sharp order and other partial orders introduced by the author

partial orders in rings based on generalized inverses unified theory abstract the unified theory for matrix partial orders based on generalized inverses has already been done by mitra we consider a special kind of ring r which generalizes the ring of linear operators on finite dimensional vector space and extend mitra s approach to it thus we find necessary and sufficient condition for a g based relation to be a partial order on r also some known results are generalized and some new results are proved

the neumann problem for elliptic equations with non smooth coefficients in this paper we study the neumann and regularity problems for divergence form symmetric elliptic operators l div av where a aifix is a matrix of bounded measurable functions and ellipticity is the existence of a 0 such that 2 114 2 ais ir 21412 for all i r we assume that l is defined in the unit ball b but the methods of proof are sufficiently general to allow b to be a bounded starlike lipschitz domain the neumann problem lu 0 in b avun q f

relationships between different sets involving group and drazin projectors and nonnegativity abstract this paper deals with nonnegativity of matrices and their group or drazin inverses firstly the nonnegativity of a square matrix a its group inverse a and its group projector aa is used to define different sets for which relationships and characterizations are given next an extension of the previous results for index greater than 1 is presented similar sets are introduced and studied for drazin inverses and drazin projectors considering the core nilpotent decomposition in addition the results are applied to study the l drazin periodic matrices for l 1

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

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

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

an o nm algorithm for a special case of the multimedian location problem on a tree abstract the multimedian location problem on a connected network g is concerned with locating m new facilities on the network the network g has one existing facility customer at each of the n nodes of g the objective is to locate the new facilities so as to minimize total cost which is the sum of a weighted distances between pairs of new and existing facilities and b weighted distances between certain pairs of new facilities we show that this problem can be solved in o nm when g is a tree and the set of pairs of new facilities which interact has special structure

the connections between dirichlet regularity and neumann problems for second order elliptic operators with complex bounded measurable coefficients abstract the present paper discusses relations between regularity dirichlet and neumann problems we investigate the boundary problems for block operators and prove in particular that the solvability of the regularity problem does not imply the solvability of the dual dirichlet problem for general elliptic operators with complex bounded measurable coefficients this is strikingly different from the case of real operators for which such an implication was established in 1993 by c kenig j pipher invent math 113 3 1993 447 509 and since then has served as an integral part of many results

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

functional calculus of dirac operators and complex perturbations of neumann and dirichlet problems we prove that the neumann dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in l 2 for small complex l infty perturbations of a coefficient matrix which is either real symmetric of block form or constant all matrices are assumed to be independent of the transversal coordinate we solve the neumann dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order dirac type operator we establish quadratic estimates for this dirac operator which implies that the associated hardy projection operators are bounded and depend continuously on the coefficient matrix we also prove that certain transmission problems for k forms are well posed for small perturbations of block matrices

on group inverses and the sharp order abstract in this work the group inverse of a matrix is used to define the order on square matrices of index 1 the order is similar to the order of drazin 2 and the minus order of hartwig 6 10 and nambooripad 17 the order and the order are compared and contrasted many conditions are given which assure the equivalence of the various partial orders studied

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

core inverse and core partial order of hilbert space operators abstract the core inverse of matrix is generalized inverse which is in some sense in between the group and moore penrose inverse in this paper a generalization of core inverse and core partial order to hilbert space operator case is presented some properties are generalized and some new ones are proved connections with other generalized inverses are obtained the useful matrix representations of operator and its core inverse are given it is shown that a is less than b under the core partial order if and only if they have specific kind of simultaneous diagonalization induced by appropriate decompositions of hilbert space the relation is also characterized by the inclusion of appropriate sets of generalized inverses the spectral properties of core inverse are also obtained

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

nonsymmetric systems on nonsmooth planar domains we study boundary value problems in the sense of dahlberg for second order constant coefficient strongly elliptic systems in this class are systems without a variational formulation viz the nonsymmetric systems various similarities and differences between this subclass and the symmetrizable systems are examined in nonsmooth domains

weighted maximal regularity estimates and solvability of non smooth elliptic systems i we develop new solvability methods for divergence form second order real and complex elliptic systems above lipschitz graphs with l 2 boundary data the coefficients a may depend on all

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

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

the regularity problem for second order elliptic operators with complex valued bounded measurable coefficients the present paper establishes a certain duality between the dirichlet and regularity problems for elliptic operators with t independent complex bounded measurable coefficients t being the transversal direction to the boundary to be precise we show that the dirichlet boundary value problem is solvable in l p subject to the square function and non tangential maximal function estimates if and only if the corresponding regularity problem is solvable in l p moreover the solutions admit layer potential representations in particular we prove that for any elliptic operator with t independent real possibly non symmetric coefficients there exists a p 1 such that the regularity problem is well posed in l p

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

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

core ep decomposition and its applications abstract in this paper we introduce a new decomposition called the core ep decomposition in the present paper for square matrices and give some of its applications by applying the decomposition we derive several characterizations of the core ep inverse introduce two orders the core ep order and the core minus partial order and characterize their properties we also give some properties of the decomposition

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

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

the neumann problem for higher order elliptic equations with symmetric coefficients in this paper we establish well posedness of the neumann problem with boundary data in l 2 or the sobolev space dot w 2 1 in the half space for linear elliptic differential operators with coefficients that are constant in the vertical direction and in addition are self adjoint this generalizes the well known well posedness result of the second order case and is based on a higher order and one sided version of the classic rellich identity and is the first known well posedness result for an elliptic divergence form higher order operator with rough variable coefficients and boundary data in a lebesgue or sobolev space