hidden sl n symmetry in conformal field theories we prove that an irreducible representation of the virasoro algebra can be extracted from an irreducible representation space of thesl 2 current algebra by putting a constraint on the latter using the becchi rouet stora tyutin formalism thus there is asl 2 symmetry in the virasoro algebra but it is gauged and hidden this construction of the virasoro algebra is the quantum analogue of the hamiltonian reduction we then are naturally lead to consider a constrainedsl 2 wess zumino witten model this system is also related to quantum field theory of coadjoint orbit of the virasoro group based on this result we present a canonical derivation of thesl 2 current algebra in polyakov s theory of two dimensional gravity it is a manifestation of thesl 2 symmetry in conformal field theory hidden by the quantum hamiltonian reduction we also discuss the quantum hamiltonian reduction of thesl 2 current algebra and its relation to thew n algebra of zamolodchikov this makes it possible to define a natural generalization of the geometric action for thew n algebra despite its non lie algebraic nature

blossom quad a non uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm a new indirect way of producing all quad meshes is presented the method takes advantage of a wellknown algorithm of the graph theory namely the blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time the new blossom quad algorithm is compared with standard indirect procedures meshes produced by the new approach are better both in terms of element shape and in terms of size eld ef ciency

generating functional in cft on riemann surfaces ii homological aspects we revisit and generalize our previous algebraic construction of the chiral effective action for conformal field theory on higher genus riemann surfaces we show that the action functional can be obtained by evaluating a certain deligne cohomology class over the fundamental class of the underlying topological surface this deligne class is constructed by applying a descent procedure with respect to a cech resolution of any covering map of a riemann surface detailed calculations are presented in the two cases of an ordinary cech cover and of the universal covering map which was used in our previous approach we also establish a dictionary that allows to use the same formalism for different covering morphisms

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

enumerating k best paths in length order in dags abstract we address the problem of finding the k best paths connecting a given pair of nodes in a directed acyclic graph dag with arbitrary lengths one of the main results in this paper is the proof that a tree representing the k th shortest path is obtained by an arc exchange in one of the previous k 1 trees each of which contains a previous best path an o m k n log k time and o k m space algorithm is designed to explicitly determine the k shortest paths in a dag with n nodes and m arcs the algorithm runs in o m kn time using o k m space in dags with integer length arcs empirical results confirming the superior performance of the algorithm to others found in the literature for randomly generated graphs are reported

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

an algorithm for finding k minimum spanning trees this paper presents an algorithm for finding k minimum spanning trees in an undirected graph the required time is o km min n 2 m log log n and the space is o k m where n is the number of vertices and m is the number of edges the algorithm is based on three subroutines the first two subroutines are used to obtain the second minimum spanning tree in o min n 2 m alpha m n steps where alpha m n is tarjan s inverse of ackermann s function 12 which is very slowly growing the third one obtains the kth minimum spanning tree in o m steps when the jth minimum spanning trees for j 1 2 cdots k 1 are given

revisiting k sum optimization in this paper we address continuous integer and combinatorial k sum optimization problems we analyze different formulations of this problem that allow to solve it through the minimization of a relatively small number of minisum optimization problems this approach provides a general tool for solving a variety of k sum optimization problems and at the same time improves the complexity bounds of many ad hoc algorithms previously reported in the literature for particular versions of this problem moreover the results developed for k sum optimization have been extended to the more general case of the convex ordered median problem improving upon existing solution approaches

a genetic based framework for solving multi criteria weighted matching problems abstract the purpose of this paper is to present a flexible genetic based framework for solving the multi criteria weighted matching problem mc wmp in the first part of this paper we design a genetic based framework for solving the ordinary weighted matching problem we present an extensive analysis of the quality of the results and introduce a methodology for tuning its parameters in the second part we develop a modified genetic based algorithm for solving the mc wmp the algorithm generates a significant and representative portion of the pareto optimal set to assess the performance of the algorithm we conduct computational experiments with two and three criteria the potential of the proposed algorithm is demonstrated by comparing to a multi objective simulated annealing algorithm

syzygy modules for quasi k gorenstein rings abstract let be a right quasi k gorenstein ring for each dth syzygy module m in mod where 0 d k 1 we obtain an exact sequence 0 b m p c 0 in mod with the properties that it is dual exact p is projective c is a d 1 st syzygy module b is a dth syzygy of ext op d 1 tr m and the right projective dimension of b is less than or equal to d 1 we then give some applications of such an exact sequence as follows 1 we obtain a chain of epimorphisms concerning m and by dualizing it we then get the spherical filtration of auslander and bridger for m 2 we get auslander and bridger s approximation theorem for each reflexive module in mod op 3 we show that for any 0 d k 1 each dth syzygy module in mod has an evans griffith presentation as an immediate consequence of 3 we have that if is a commutative noetherian ring with finite self injective dimension then for any non negative integer d each dth syzygy module in mod has an evans griffith presentation which generalizes an evans and griffith s result to much more general setting

a polynomial dual simplex algorithm for the generalized circulation problem this paper presents a polynomial time dual simplex algorithm for the generalized circulation problem an efficient implementation of this algorithm is given that has a worst case running time of o m2 m nlogn logb where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the rational gain factors and integral capacities in the network this running time is as fast as the running time of any combinatorial algorithm that has been proposed thus far for solving the generalized circulation problem

improving space efficiency with path length prediction for finding k shortest simple paths finding mbi k shortest simple paths in a directed graph is a fundamental problem in many engineering applications most existing algorithms such as yen s algorithm and its variants have polynomial worst case time complexity but their average case running time is very high the heuristic algorithm mps can run significantly faster in practice however it requires an excessive amount of memory space in this paper we provide a new heuristic algorithm that achieves high space efficiency while maintaining similar average case running time we first propose a sidetrack representation of path with which a path can be stored in mbi o bf 1 space we then show how to categorize a candidate path as either partial or complete and restrict the number of paths added to the queue in addition we provide an empirical equation that can very accurately predict the mbi k th shortest path length provided that a much smaller number of shortest paths have been found extensive experiments prove that our algorithm can achieve an mbi o n speedup in practice over yen s algorithm in comparison with mps it runs up to three times faster and uses less space by an order of magnitude

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

the polyakov conjecture and the µ holomorphy equation relationship we determine the iterative solution on the complex plane of the holomorphy equation then we obtain the holomorphic projective connection as a neumann series in powers of the beltrami differential since it has been shown that the polyakov action of a conformal model with a central charge k is expressed in terms of the holomorphic projective connection we then prove the polyakov conjecture

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

a shortest augmenting path algorithm for the semi assignment problem the objective of this study is to develop a shortest augmenting path algorithm for solving the semi assignment problem and conduct an extensive computational comparison with the best alternative approaches the algorithm maintains dual feasibility and complementary slackness and works toward satisfying primal feasibility effective heuristics arc used to achieve an excellent advanced start and convergence is assured via the use of the shortest augmenting path procedure using reduced costs for arc lengths unlike other algorithms such as the primal simplex or the auction algorithm each iteration during the final phase of the procedure also known as the end game achieves one additional assignment the software implementations of our algorithm are fastest for the semi assignment problems that we tested our dense code is also faster than the best software for assignment problems in addition the algorithm has the best polynomial worst case running time bound that we have seen and the memory requirements are relatively small

a polyakov action on riemann surfaces ii we continue the model independent study of the polyakov action on an arbitrary compact surface without boundary of genus larger than 2 as the general solution of the relevant conformal ward identity a general formula for the polyakov action and an explicit calculation of the energy momentum tensor density is provided it is further shown how polyakov s sl 2 c symmetry emerges in a curved base surface

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

on the bicriterion minimal cost minimal label spanning tree problem we address a bicriterion spanning tree problem relevant in some application fields such as telecommunication networks or transportation networks each edge is assigned with a cost value and a label such as a color the first criterion intends to minimize the total cost of the spanning tree the summation of its edge costs while the second intends to get the solution with a minimal number of different labels since these criteria in general are conflicting criteria we developed an algorithm to generate the set of non dominated spanning trees computational experiments are presented and results discussed

algorithmic applications of baur strassen s theorem shortest cycles diameter and matchings consider a directed or an undirected graph with integral edge weights from the set w w that does not contain negative weight cycles in this article we introduce a general framework for solving problems on such graphs using matrix multiplication the framework is based on the usage of baur strassen s theorem and of strojohann s determinant algorithm it allows us to give new and simple solutions to the following problems finding shortest cycles we give a simple o wn time algorithm for finding shortest cycles in undirected and directed graphs for directed graphs and undirected graphs with nonnegative weights this matches the time bounds obtained in 2011 by roditty and williams on the other hand no algorithm working in o wn time was previously known for undirected graphs with negative weights furthermore our algorithm for a given directed or undirected graph detects whether it contains a negative weight cycle within the same running time computing diameter and radius we give a simple o wn time algorithm for computing a diameter and radius of an undirected or directed graphs to the best of our knowledge no algorithm with this running time was known for undirected graphs with negative weights finding minimum weight perfect matchings we present an o wn time algorithm for finding minimum weight perfect matchings in undirected graphs this resolves an open problem posted by sankowski 2009 who presented such an algorithm but only in the case of bipartite graphs these three problems that are solved in the full generality demonstrate the utility of this framework hence we believe that it can find applications for solving larger spectra of related problems as an illustrative example we apply it to the problem of computing a set of vertices that lie on cycles of length at most t for some given t we give a simple o wn time algorithm for this problem that improves over the o wn t time algorithm given by yuster in 2011 besides giving this flexible framework the other main contribution of this article is the development of a novel combinatorial interpretation of the dual solution for the minimum weight perfect matching problem despite the long history of the matching problem such a combinatorial interpretation was not known previously this result sheds a new light on the problem as there exist many structural theorems about unweighted matchings but almost no results that could cope with the weighted case

a fast minimum spanning tree algorithm based on k means we present a fast minimum spanning tree algorithm mst on the complete graph of n points divide and conquer scheme is applied to produce an approximate mst with time complexity of o n 1 5 the produced approximate mst does not degrade the effect of its practical applications minimum spanning trees msts have long been used in data mining pattern recognition and machine learning however it is difficult to apply traditional mst algorithms to a large dataset since the time complexity of the algorithms is quadratic in this paper we present a fast mst fmst algorithm on the complete graph of n points the proposed algorithm employs a divide and conquer scheme to produce an approximate mst with theoretical time complexity of o n 1 5 which is faster than the conventional mst algorithms with o n 2 it consists of two stages in the first stage called the divide and conquer stage k means is employed to partition a dataset into n clusters then an exact mst algorithm is applied to each cluster and the produced n msts are connected in terms of a proposed criterion to form an approximate mst in the second stage called the refinement stage the clusters produced in the first stage form n 1 neighboring pairs and the dataset is repartitioned into n 1 clusters with the purpose of partitioning the neighboring boundaries of a neighboring pair into a cluster with the n 1 clusters another approximate mst is constructed finally the two approximate msts are combined into a graph and a more accurate mst is generated from it the proposed algorithm can be regarded as a framework since any exact mst algorithm can be incorporated into the framework to reduce its running time experimental results show that the proposed approximate mst algorithm is computationally efficient and the approximation is close to the exact mst so that in practical applications the performance does not suffer

choquet based optimisation in multiobjective shortest path and spanning tree problems this paper is devoted to the search of choquet optimal solutions in finite graph problems with multiple objectives the choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives we first present a condition on preferences name hereafter preference for interior points that characterizes preferences favouring compromise solutions a natural attitude in various contexts such as multicriteria optimisation robust optimisation and optimisation with multiple agents within choquet expected utility theory this condition amounts to using a submodular capacity and a convex utility function under these assumptions we focus on the fast determination of choquet optimal paths and spanning trees after investigating the complexity of these problems we introduce a lower bound for the choquet integral computable in polynomial time then we propose different algorithms using this bound either based on a controlled enumeration of solutions ranking approach or an implicit enumeration scheme branch and bound finally we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes

personalized pagerank clustering a graph clustering algorithm based on random walks abstract graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications in addition exponential growth of real world graphs such as social networks biological networks and electrical circuits demands clustering algorithms with nearly linear time and space complexity in this paper we propose personalized pagerank clustering ppc that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph we combine random walks and modularity to precisely and efficiently reveal the clusters of a graph ppc is a top down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly linear approaches that are mainly bottom up it also gives a hierarchy of clusters that is useful in many applications ppc has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets furthermore its top down approach makes it a flexible solution for clustering problems with different requirements

on the k shortest path trees problem abstract we address the problem of finding the k best path trees connecting a source node with any other non source node in a directed network with arbitrary lengths the main result in this paper is the proof that the k th shortest path tree is adjacent to at least one of the previous k 1 shortest path trees consequently we design an o f n m c max km time and o k m space algorithm to determine the k shortest path trees in a directed network with n nodes m arcs and maximum absolute length c max where o f n m c max is the best time needed to solve the shortest simple paths connecting a source node with any other non source node

simulation relations for pattern matching in directed graphs we consider the problem of finding the occurrences of a pattern tree t in a directed graph g and propose two algorithms one for preprocessing and one for searching for t in g it is assumed that

fast approximate graph partitioning algorithms we study graph partitioning problems on graphs with edge capacities and vertex weights the problems of b balanced cuts and k balanced partitions are unified into a new problem called minimum capacity rho separators a rho separator is a subset of edges whose removal partitions the vertex set into connected components such that the sum of the vertex weights in each component is at most rho times the weight of the graph we present a new and simple o log n approximation algorithm for minimum capacity rho separators which is based on spreading metrics yielding an o log n approximation algorithm both for b balanced cuts and k balanced partitions in particular this result improves the previous best known approximation factor for k balanced partitions in undirected graphs by a factor of o log k we enhance these results by presenting a version of the algorithm that obtains an o log opt approximation factor the algorithm is based on a technique called spreading metrics that enables us to formulate directly the minimum capacity rho separator problem as an integer program we also introduce a generalization called the simultaneous separator problem where the goal is to find a minimum capacity subset of edges that separates a given collection of subsets simultaneously we extend our results to directed graphs for values of rho geq 1 2 we conclude with an efficient algorithm for computing an optimal spreading metric for rho separators this yields more efficient algorithms for computing b balanced cuts than were previously known

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

weighting factor extensions for finite multiple objective vector minimization problems abstract this paper develops two procedures for finding the efficient set of finite action multiple objective problems the first gives an exact characterization of the efficient set in terms of the weighted q th powers of the objective functions for a fixed q and gives a lower bound for q the second gives an exact characterization of the efficient set in the t th order minima of the weighted objective functions some consideration is given to problems whose feasible action sets correspond to the vertices of certain polytopes and connectedness conjectures are given for which no counterexamples have yet been found

efficient implementation of graph algorithms using contraction the component merging problem is a new graph problem versions of this problem appear as bottlenecks in various graph algorithms a new data structure solves this problem efficiently and two special cases of the problem have even more efficient solutions based on other data structures the performance of the data structures is sped up by introducing a new algorithmic tool called packets the algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures specifically trees can be used simultaneously as a priority queue and a concatenable queue similarly f heaps support some kinds of split operations with no loss of efficiency an immediate application of the solution to the simplest version of the merging problem is an o t m n algorithm for finding minimum spanning trees in undirected graphs without using f heaps where t m n m log 2 log 2 log d n the graph has n vertices and m edges and d max m n 2 packets also improve the f heap minimum spanning tree algorithm giving the fastest algorithm currently known for this problem the efficient solutions to the merging problem and the new observation about f heaps lead to an o n t m n n log n algorithm for finding a maximum weighted matching in general graphs this settles an open problem posed by tarjan 15 p 123 where the weaker bound of o nm log n 2 m was conjectured

time version of the shortest path problem in a stochastic flow network many studies on hardware framework and routing policy are devoted to reducing the transmission time for a flow network a time version of the shortest path problem thus arises to find a quickest path which sends a given amount of data from the unique source to the unique sink with minimum transmission time more specifically the capacity of each arc in the flow network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc should be stochastic due to failure maintenance etc such a network is named a stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent under the time constraint t such a probability is named the system reliability in particular the data are transmitted through two minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all d t mps and the system reliability can then be computed in terms of d t mps moreover the optimal pair of minimal paths with highest system reliability could be obtained

on the np completeness of the perfect matching free subgraph problem given a bipartite graph g u v e such that u v and every edge is labelled true or false or both the perfect matching free subgraph problem is to determine whether or not there exists a subgraph of g containing for each node u of u either all the edges labelled true or all the edges labelled false incident to u and which does not contain a perfect matching this problem arises in the structural analysis of differential algebraic systems the purpose of this paper is to show that this problem is np complete we show that the problem is equivalent to the stable set problem in a restricted case of tripartite graphs then we show that the latter remains np complete in that case we also prove the np completeness of the related minimum blocker problem in bipartite graphs with perfect matching

on finding optimal polytrees we study the np hard problem of finding a directed acyclic graph dag on a given set of nodes so as to maximize a given scoring function the problem models the task of inferring a probabilistic network from data which has been studied extensively in the fields of artificial intelligence and machine learning several variants of the problem where the output dag is constrained in several ways are np hard as well for example when the dag is required to have bounded in degree or when it is required to be a polytree polynomial time algorithms are known only for rare special cases perhaps most notably for branchings that is polytrees in which the in degree of every node is at most one in this paper we generalize this polynomial time result to polytrees that can be turned into a branching by deleting a constant number of arcs our algorithm stems from a matroid intersection formulation as the order of the polynomial time bound depends on the number of deleted arcs the algorithm does not establish fixed parameter tractability when parameterized by that number we show that certain additional constraints on the sought polytree render the problem fixed parameter tractable we contrast this positive result by showing that if we parameterize by the number of deleted nodes a somewhat more powerful parameter the problem is not fixed parameter tractable subject to a complexity theoretic assumption

an o ev log v algorithm for finding a maximal weighted matching in general graphs we define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue we show that they can be implemented efficiently consequently each operation takes o log n time we use these generalized priority queues to construct an o ev log v algorithm for finding a maximal weighted matching in general graphs

data structures for on line updating of minimum spanning trees with applications data structures are presented for the problem of maintaining a minimum spanning tree on line under the operation of updating the cost of some edge in the graph for the case of a general graph mai

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

all pairs shortest paths in o n 2 time with high probability we present an all pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from 0 1 is o n2 in expectation and with high probability this resolves a long standing open problem the algorithm is a variant of the dynamic all pairs shortest paths algorithm of demetrescu and italiano 2006 the analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is o n2 in expectation and with high probability we also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in o log2n expected time

solving biobjective combinatorial max ordering problems by ranking methods and a two phases approach abstract in this paper we propose a new method to solve biobjective combinatorial optimization problems of the max ordering type the method is based on the two phases method and ranking algorithms to efficiently construct k best solutions for the underlying single objective combinatorial problem we show that the method overcomes some of the difficulties of procedures proposed earlier we illustrate this by an example and discuss the difficulties in extending it to more than two objectives

technical note a note on parametric analysis in linear assignment a classic application of the linear assignment problem is the assignment of people to jobs or jobs to people in this context it is interesting to measure competition for jobs and to generate a suitable list of jobs from which a person can choose the length of the list is a parameter a known list generation procedure is based on an interior point method followed by a parametric analysis we describe a more efficient procedure exploiting linear assignment theory and shortest path computations further we propose an alternative list generation procedure based on a special type of dual values for the linear assignment problem

self adjusting heaps in this paper we explore two themes in data structure design amortized computational complexity and self adjustment we are motivated by the following observations in most applications of data structures we wish to perform not just a single operation but a sequence of operations possibly having correlated behavior by averaging the running time per operation over a worst case sequence of operations we can sometimes obtain an overall time bound much smaller than the worst case time per operation multiplied by the number of operations we call this kind of averaging amortization standard kinds of data structures such as the many varieties of balanced trees are specifically designed so that the worst case time per operation is small such efficiency is achieved by imposing an explicit structural constraint that must be maintained during updates at a cost of both running time and storage space however if amortized running time is the complexity measure of interest we can guarantee efficiency withou

incremental assignment problem in this paper we introduce the incremental assignment problem in this problem a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known and the maximum weighted matching of the extended graph is sought we propose an o v 2 algorithm for the problem

a frontal delaunay quad mesh generator using the l norm a new indirect way of producing all quad meshes is presented the method takes advantage of a well known algorithm of the graph theory namely the blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time then the triangulation itself is taylored with the aim of producing right triangles in the domain this is done using the infinity norm to compute distances in the meshing process the alignement of the triangles is controlled by a cross field that is defined on the domain meshes constructed this way have their points aligned with the cross field direction and their triangles are almost right everywhere then recombination with our blossom based approach yields quadrilateral meshes of excellent quality

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs

generating functional in cft and effective action for two dimensional quantum gravity on higher genus riemann surfaces we formulate and solve the analog of the universal conformal ward identity for the stress energy tensor on a compact riemann surface of genus g 1 and present a rigorous invariant formulation of the chiral sector in the induced two dimensional gravity on higher genus riemann surfaces our construction of the action functional uses various double complexes naturally associated with a riemann surface with computations that are quite similar to descent calculations in brst cohomology theory we also provide an interpretation of the action functional in terms of the geometry of different fiber spaces over the teichmuller space of compact riemann surfaces of genus g 1