an o n log log n time algorithm for triangulating a simple polygon given a simple n vertex polygon the triangulation problem is to partition the interior of the polygon into n 2 triangles by adding n 3 nonintersecting diagonals we propose an o n log log n time algorithm for this problem improving on the previously best bound of o n log n and showing that triangulation is not as hard as sorting improved algorithms for several other computational geometry problems including testing whether a polygon is simple follow from our result

on the efficiency of pairing heaps and related data structures the pairing heap is well regarded as an efficient data structure for implementing priority queue operations it is included in the gnu c library strikingly simple in design the pairing heap data structure nonetheless seems difficult to analyze belonging to the genre of self adjusting data structures with its design originating as a self adjusting analogue of the fibonacci heap it has been previously conjectured that the pairing heap provides constrant amortized time decrease key operations and experimental studies have supported this conjecture this paper demonstrates contrary to conjecture that the pairing heap requires more than constant amortized time to perform decrease key operations moreover new experimental findings are presented that reveal detectable growth in the amortized cost of the decrease key operation second a unifying framework is developed that includes both pairing heaps and fibonacci heaps the parameter of interest in this framework is the storage capacity available in the nodes of the data structure for auxiliary balance information fields in this respect fibonacci heaps require log log n bits per node when n items are present this is shown to be asymptotically optimal for data structures that achieve the same asymptotic performance bounds as fibonacci heaps and fall within this framework

a dual element based geometric element transformation method for all hexahedral mesh smoothing abstract due to their increased complexity hexahedral elements are more challenging with respect to mesh generation and mesh improvement techniques than tetrahedral elements in particular there is a lack of geometry based all hexahedral smoothing methods for mesh quality improvement being easy to implement practicable and efficient the recently introduced geometric element transformation method represents a new promising element oriented smoothing concept to resolve this deficiency by giving a dual octahedron based regularizing transformation this new approach is adapted in order to smooth all hexahedral meshes first numerical tests indicate that the resulting smoothing method yields high quality results at least comparable to those of a state of the art global optimization based approach while being significantly faster

automatic mesh generation over intersecting surfaces a fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets by carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections pieces of surfaces can be arbitrarily combined and merged a great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections the new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces in fact it is a powerful surface mesh manipulator and through the repeated use of the process complex structures can be rapidly and accurately constructed

logarithmic lower bounds in the cell probe model we develop a new technique for proving cell probe lower bounds on dynamic data structures this technique enables us to prove an amortized randomized omega lg n lower bound per operation for several data structural problems on n elements including partial sums dynamic connectivity among disjoint paths or a forest or a graph and several other dynamic graph problems by simple reductions such a lower bound breaks a long standing barrier of omega lg n lg lg n for any dynamic language membership problem it also establishes the optimality of several existing data structures such as sleator and tarjan s dynamic trees we also prove the first omega log b n lower bound in the external memory model without assumptions on the data structure such as the comparison model our lower bounds also give a query update trade off curve matched e g by several data structures for dynamic connectivity in graphs we also prove matching upper and lower bounds for partial sums when parameterized by the word size and the maximum additive change in an update

use of dynamic trees in a network simplex algorithm for the maximum flow problem goldfarb and hao 1990 have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann vertex m arc network in at mostnm pivots and o n 2 m time in this paper we describe how to extend the dynamic tree data structure of sleator and tarjan 1983 1985 to reduce the running time of this algorithm to o nm logn this bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem our extension of dynamic trees is interesting in its own right and may well have additional applications

a group theoretic approach to a family of 2 local finite groups constructed by levi and oliver we extend the notion of a p local finite group defined in blo03 to the notion of a p local group we define morphisms of p local groups obtaining thereby a category and we introduce the notion of a representation of a p local group via signalizer functors associated with groups we construct a chain g g 0 g 1 of 2 local finite groups via a representation of a chain g g 0 g 1 of groups such that g 0 is the 2 local finite group of the third conway sporadic group co 3 and for n 0 g n is one of the 2 local finite groups constructed by levi and oliver in lo02 we show that the direct limit g of g exists in the category of 2 local groups and that it is the 2 local group of the union of the chain g the 2 completed classifying space of g is shown to be the classifying space b di 4 of the exotic 2 compact group of dwyer and wilkerson dw93

randomized algorithms for metrical task systems abstract borodin et al 1992 introduce a general model for online systems in 3 called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n 1 for any metrical task system with n states we present a randomized algorithm which achieves a competitive ratio of e e 1 n 1 e 1 1 5820n 0 5820 for this same problem for the uniform metric space borodin et al present an algorithm which achieves a competitive ratio of 2hn and they show a lower bound of hn for any randomized algorithm we improve their upper bound for the uniform metric space by showing a randomized algorithm which is hn o log n competitive

approximation algorithms for the shortest common superstring problem abstract the object of the shortest common superstring problem scs is to find the shortest possible string that contains every string in a given set as substrings as the problem is np complete approximation algorithms are of interest the value of an aproximate solution to scs is normally taken to be its length and we seek algorithms that make the length as small as possible a different measure is given by the sum of the overlaps between consecutive strings in a candidate solution when considering this measure the object is to find solutions that make it as large as possible these two measures offer different ways of viewing the problem while the two viewpoints are equivalent with respect to optimal solutions they differ with respect to approximate solutions we describe several approximation algorithms that produce solutions that are always within a factor of two of optimum with respect to the overlap measure we also describe an efficient implementation of one of these using mccreight s compact suffix tree construction algorithm the worstcase running time is o m log n for small alphabets where m is the sum of the lengths of all the strings in the set and n is the number of strings for large alphabets the algorithm can be implemented in o m log m time by using sleator and tarjan s lexicographic splay tree data structure

on the dynamic finger conjecture for splay trees part ii the proof the following result is shown on an n node splay tree the amortized cost of an access at distance d from the preceding access is o log d 1 in addition there is an o n initialization cost the accesses include searches insertions and deletions

ultimate robustness in meshing an arbitrary polyhedron given a boundary surface mesh a set of triangular facets of a polyhedron the problem of deciding whether or not a triangulation exists is reported to be np hard in this paper an algorithm to triangulate a general polyhedron is presented which makes use of a classical delaunay triangulation algorithm a phase for recovering the missing boundary facets by means of facet partitioning and a final phase that makes it possible to remove the additional points defined in the previous step following this phase the resulting mesh conforms to the given boundary surface mesh the proposed method results in a discussion of theoretical interest about existence and complexity issues in practice however the method should provide what we call ultimate robustness in mesh generation methods copyright 2003 john wiley sons ltd

better analysis of binary search tree on decomposable sequences abstract in their seminal paper sleator and tarjan 1985 15 the authors conjectured that the splay tree is a dynamically optimal binary search tree bst in spite of decades of intensive research the problem remains open perhaps a more basic question which has also attracted much attention is if there exists any dynamically optimal bst algorithm one such candidate is which is a simple and intuitive bst algorithm lucas 1988 11 munro 2000 12 demaine et al 2009 6 demaine et al 2009 6 showed a novel connection between a geometric problem and the binary search tree problem related to the above conjecture however there has been little progress in solving this geometric problem too since dynamic optimality conjecture in its most general form remains elusive despite much effort researchers have studied this problem on special sequences recently chalermsook et al 2015 2 studied a type of sequences known as k decomposable sequences in this context where k parametrizes easiness of the sequence using tools from forbidden submatrix theory they showed that takes n 2 o k 2 time on this sequence and explicitly raised the question of improving this bound in this paper we show that takes o n log k time on k decomposable sequences in contrast to the previous approach ours is based on first principles one of the main ingredients of our result is a new construction of a lower bound certificate on the performance of any algorithm this certificate is constructed using the execution of and is more nuanced and possibly more flexible than the previous independent set certificate of demaine et al this result which is applicable to all sequences may be of independent interest and may lead to further progress in analyzing on k decomposable as well as general sequences

a ghost ring for the left free double burnside ring and an application to fusion systems abstract for a finite group g we define a ghost ring and a mark homomorphism for the double burnside ring b g g of left free g g bisets in analogy to the case of the burnside ring b g the ghost ring has a much simpler ring structure and after tensoring with q one obtains an isomorphism of q algebras as an application of a key lemma we obtain a very general formula for the brauer construction applied to a tensor product of two p permutation bimodules m and n in terms of brauer constructions of the bimodules m and n over a field of characteristic 0 we determine the simple modules of the left free double burnside algebra and prove semisimplicity results for the bifree double burnside algebra these results carry over to results about biset functor categories finally we apply the ghost ring and mark homomorphism to fusion systems on a finite p group we extend a remarkable bijection due to ragnarsson and stancu between saturated fusion systems and certain idempotents of the bifree double burnside algebra over z p to a bijection between all fusion systems and a larger set of idempotents in the bifree double burnside algebra over q

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

transfer and characteristic idempotents for saturated fusion systems abstract we construct a well behaved transfer map from the p local burnside ring of the underlying p group s to the p local burnside ring of a saturated fusion system f using this transfer map we give new results on the characteristic idempotent of f the unique idempotent in the p local double burnside ring of s satisfying properties of linckelmann and webb we describe this idempotent explicitly both in terms of fixed points and as a linear combination of transitive bisets additionally using fixed points we determine the map for burnside rings given by multiplication with the characteristic idempotent and show that this is the transfer map previously constructed applying these results we show that for every saturated fusion system the ring generated by all not necessarily idempotent characteristic elements in the p local double burnside ring is isomorphic as rings to the p local single burnside ring of the fusion system and we disprove a conjecture by park ragnarsson stancu on the composition product of fusion systems

improved algorithms for bipartite network flow in this paper network flow algorithms for bipartite networks are studied a network g v e is called bipartite if its vertex set v can be partitioned into two subsets v 1 and v 2 such that all edges have one endpoint in v 1 and the other in v 2 let n v n 1 v 1 n 2 v 2 m e and assume without loss of generality that n 1 leq n 2 a bipartite network is called unbalanced if n 1 ll n 2 and balanced otherwise this notion is necessarily imprecise it is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks the basic idea in these improvements is a two edge push rule that allows one to charge most computation to vertices in v 1 and hence develop algorithms whose running times depend on n 1 rather than n for example it is shown that the two edge push version of goldberg and tarjan s fifo preflow push algorithm runs in o n 1 m n 1 3 time and that the analogous version of ahuja and orlin s excess scaling algorithm runs in o n 1 m n 1 2 log u time where u is the largest edge capacity these ideas are also extended to dynamic tree implementations parametric maximum flows and minimum cost flows

the pseudoflow algorithm a new algorithm for the maximum flow problem we introduce the pseudoflow algorithm for the maximum flow problem that employs only pseudoflows and does not generate flows explicitly the algorithm solves directly a problem equivalent to the minimum cut problem the maximum blocking cut problem once the maximum blocking cut solution is available the additional complexity required to find the respective maximum flow is o m log n a variant of the algorithm is a new parametric maximum flow algorithm generating all breakpoints in the same complexity required to solve the constant capacities maximum flow problem the pseudoflow algorithm has also a simplex variant pseudoflow simplex that can be implemented to solve the maximum flow problem one feature of the pseudoflow algorithm is that it can initialize with any pseudoflow this feature allows it to reach an optimal solution quickly when the initial pseudoflow is close to an optimal solution the complexities of the pseudoflow algorithm the pseudoflow simplex and the parametric variants of pseudoflow and pseudoflow simplex algorithms are all o mn log n on a graph with n nodes and m arcs therefore the pseudoflow simplex algorithm is the fastest simplex algorithm known for the parametric maximum flow problem the pseudoflow algorithm is also shown to solve the maximum flow problem on s t tree networks in linear time where s t tree networks are formed by joining a forest of capacitated arcs with nodes s and t adjacent to any subset of the nodes

optimal biweighted binary trees and the complexity of maintaining partial sums let a be an array the partial sum problem concerns the design of a data structure for implementing the following operations the operation update j x has the effect a j leftarrow a j x and the query operation ssum j returns the partial sum sum i 1 j a i our interest centers upon the optimal efficiency with which sequences of such operations can be performed and we derive new upper and lower bounds in the semigroup model of computation our analysis relates the optimal complexity of the partial sum problem to optimal binary trees relative to a type of weighting scheme that defines the notion of biweighted binary tree

incremental convex planarity testing an important class of planar straight line drawings of graphs are convex drawings in which all the faces are drawn as convex polygons a planar graph is said to be convex planar if it admits a convex drawing we give a new combinatorial characterization of convex planar graphs based on the decomposition of a biconnected graph into its triconnected components we then consider the problem of testing convex planarity in an incremental environment where a biconnected planar graph is subject to on line insertions of vertices and edges we present a data structure for the on line incremental convex planarity testing problem with the following performance where n denotes the current number of vertices of the graph strictly convex planarity testing takes o 1 worst case time insertion of vertices takes o log n worst case time insertion of edges takes o log n amortized time and the space requirement of the data structure is o n

dynamic optimality almost we present an o lg lg n competitive online binary search tree improving upon the best previous trivial competitive ratio of o lg n this is the first major progress on sleator and tarjan s dynamic optimality conjecture of 1985 that o 1 competitive binary search trees exist

optimal binary search trees abstract we consider the problem of building optimal binary search trees the binary search tree is a widely used data structure for information storage and retrieval a binary search tree t for a set of keys from a total order is a binary tree in which each node has a key value and all the keys of the left subtree are less than the key at the root and all the keys of the right subtree are greater than the key at the root this property holding recursively for the left and right subtrees of the tree t suppose we are given n keys and the probabilities of accessing each key and those occurring in the gap between two successive keys the optimal binary search tree problem is to construct a binary search tree on these n keys that minimizes the expected access time one variant of this problem is when only the gaps have nonzero access probabilities and is called the optimal alphabetic tree problem another related problem is when there is no order between the keys and there are probabilities associated only with the gaps and the objective is to build a binary tree with minimum expected weighted path length from the root this is called the huffman tree problem in this survey we assess known results on the structural properties of the optimal trees algorithms and lower bounds to construct and to verify optimal trees and heuristics to construct nearly optimal trees and other related results

on the table of marks of a direct product of finite groups abstract we present a method for computing the table of marks of a direct product of finite groups in contrast to the character table of a direct product of two finite groups its table of marks is not simply the kronecker product of the tables of marks of the two groups based on a decomposition of the inclusion order on the subgroup lattice of a direct product as a relation product of three smaller partial orders we describe the table of marks of the direct product essentially as a matrix product of three class incidence matrices each of these matrices is in turn described as a sparse block diagonal matrix as an application we use a variant of this matrix product to construct a ghost ring and a mark homomorphism for the rational double burnside algebra of the symmetric group s 3

idempotents of double burnside algebras l enriched bisets and decomposition of p biset functors abstract let r be a unital commutative ring and g be a finite group with order invertible in r we introduce new idempotents t s g in the double burnside algebra r b g g of g over r indexed by conjugacy classes of minimal sections t s of g i e sections such that s t these idempotents are orthogonal and their sum is equal to the identity it follows that for any biset functor f over r the evaluation f g splits as a direct sum of specific r modules indexed by minimal sections of g up to conjugation the restriction of these constructions to the biset category of p groups where p is a prime number invertible in r leads to a decomposition of the category of p biset functors over r as a direct product of categories f l indexed by atoric p groups l up to isomorphism we next introduce the notions of l enriched biset and l enriched biset functor for an arbitrary finite group l and show that for an atoric p group l the category f l is equivalent to the category of l enriched biset functors defined over elementary abelian p groups finally the notion of vertex of an indecomposable p biset functor is introduced when p r and when r is a field of characteristic different from p the objects of the category f l are characterized in terms of vertices of their composition factors

lower bounds for accessing binary search trees with rotations two methods are given for obtaining lower bounds on the cost of accessing a sequence of nodes in a symmetrically ordered binary search tree in a model where rotations can be done on the tree and the entire sequence is known before accessing begins but the accesses must be done in the order given for example it can be proven that the bit reversal permutation requires theta n log n time to access in this model it is also shown that the expected cost of accessing random sequences in this model is the same as it is for the case where the tree is static

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

boundary recovery after 3d delaunay tetrahedralization without adding extra nodes in this paper we investigate boundary recovery the problem that has troubled researchers ever since delaunay based methods were applied to generate mesh there are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes in this paper we make an effort to seek a method to recover boundaries without using extra nodes it was noted that some previous algorithms imposed artificial boundary constraints on a meshing problem at the recovering stage we first try to discard these artificial constraints and thus make things easier then a new method is proposed by which the boundaries can be recovered by means of two operations 1 creating a segment in the mesh and 2 removing a segment from the mesh both operations are special cases of a general local transformation called small polyhedron reconnection operation the method works well when coupled with the sphere packing method proposed by the first author if the mesh sizing function is suitable a good configuration of nodes will be created accordingly by the sphere packing method and the boundary can be recovered by the local transformation presented here without inserting extra nodes

a unified access bound on comparison based dynamic dictionaries we present a dynamic comparison based search structure that supports insertions deletions and searches within the unified bound the unified bound specifies that it is quick to access an element that is near a recently accessed element more precisely if w y distinct elements have been accessed since the last access to element y and d x y denotes the rank distance between x and y among the current set of elements then the amortized cost to access element x is o minylog w y d x y 2 this property generalizes the working set and dynamic finger properties of splay trees

the list update problem and the retrieval of sets we consider the list update problem under a sequence of requests of sets of items and for this problem we investigate the competitiveness features of two algorithms we prove that algorithm move set to front msf is 1 s competitive where is the size of the largest requested set and that a lower bound is roughly 2 we provide an upper bound to the msf competitive ratio by relating it to the size n of the list obtaining that the algorithm is 1 n 4 competitive in general and o n competitive if we add a not too restrictive constraint to the sizes of the requested sets

trivial source bimodule rings for blocks and p permutation equivalences we associate with any p block of a finite group a grothendieck ring of certain p permutation bimodules we extend the notion of p permutation equivalences introduced by boltje and xu 4 to source algebras of p blocks of finite groups we show that a p permutation equivalence between two source algebras a b of blocks with a common defect group and same local structure induces an isotypy

a study on splay trees abstract we study the dynamic optimality conjecture which predicts that splay trees are a form of universally efficient binary search tree for any access sequence we reduce this claim to a regular access bound which seems plausible and might be easier to prove this approach may be useful to establish dynamic optimality

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

construction de foncteurs entre categories deg ensembles resume sommaire 1 le produit g 1 1 definition 1 2 classification de foncteurs 1 2 1 la seconde assertion 1 2 2 reduction au cas transitif 1 2 3 sous groupes minimaux 1 2 4 existence de e f 1 2 5 unicite de e f 1 3 le foncteur identite 1 4 associativite 1 5 calcul des produits 2 l anneau de grothendieck 2 1 un sous anneau de g 2 2 des idempotents orthogonaux 2 2 1 projecteurs dans l anneau de burnside 2 2 2 calcul de e p g g g h l 2 2 3 calcul de h g l g e p g 2 2 4 orthogonalite 2 2 5 calcul de la somme des e p g 2 3 un morphisme de b g dans g 2 4 semi simplicite en caracteristique 0 2 4 1 produits par formula 2 4 2 definition des f k h g 2 4 3 orthogonalite et somme des f k h g 2 4 4 identification de k g 3 categories associees 3 1 ensembles p libres q 3 2 la categorie c p q 3 3 la categorie f r p q 3 3 1 structure des foncteurs simples 3 3 2 exemples de foncteurs simples 3 3 3 action sur les foncteurs simples 3 4 semisimplicite 3 4 1 des idempotents orthogonaux 3 4 2 identification de end k p g 3 4 3 residus 3 4 4 decomposition 4 applications 4 1 foncteurs de mackey 4 1 1 composition 4 1 2 identification 4 1 3 fonctorialite 4 2 classes de conjugaison et cohomologie de hochschild 4 3 foncteurs de mackey et conjecture d alperin 4 4 p sous groupes et residu de steinberg 4 4 1 autres expressions de s g 4 4 2 autre expression de e p g 4 4 3 rsidus de steinberg 4 5 adjonction et modules de steinberg generalises

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

biased search trees we consider the problem of storing items from a totally ordered set in a search tree so that the access time for a given item depends on a known estimate of the access frequency of the item we describe two related classes of biased search trees whose average access time is within a constant factor of the minimum and that are easy to update under insertions deletions and more radical update operations we present and analyze efficient update algorithms for biased search trees we list several applications of such trees

delaunay triangulation of non convex planar domains this paper investigates the possibility of integrating the two currently most popular mesh generation techniques namely the method of advancing front and the delaunay triangulation algorithm the merits of the resulting scheme are its simplicity efficiency and versatility with the introduction of non delaunay line segments the concept of using delaunay triangulation as a means of mesh generation is clarified an efficient algorithm is proposed for the construction of delaunay triangulations over non convex planar domains interior nodes are first generated within the planar domain these interior nodes and the boundary nodes are then linked up together to produce a valid triangulation in the mesh generation process the delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle in contrast to convex domains intersection between the proposed triangle and the domain boundary has to be checked this can be simply done by considering only the non delaunay segments on the generation front through the study of numerous examples of various characteristics it is found that high quality triangular element meshes are obtained by the proposed algorithm and the mesh generation time bears a linear relationship with the number of elements nodes of the triangulation

a linear time algorithm for binary tree sequences transformation using left arm and right arm rotations in this paper we consider a transformation on binary trees using new types of rotations each of the newly proposed rotations is permitted only at nodes on the left arm or the fight arm of a tree consequently we develop a linear time algorithm with at most n 1 rotations for converting weight sequences between any two binary trees in particular from an analysis of aggregate method for a sequence of rotations each rotation of the proposed algorithm can be performed in a constant amortized time next we show that a specific directed rooted tree called rotation tree can be constructed using one of the new type rotations as a by product a naive algorithm for enumerating weight sequences of binary trees in lexicographic order can be implemented by traversing the rotation tree

on compressing permutations and adaptive sorting we prove that given a permutation p over 1 n formed of nruns sorted blocks of sizes given by the vector r there exists a compressed data structure encoding p in n 1 h r n i 1 n r u n sr ilog 2nr i

blocks of mackey categories abstract for a suitable small category f of homomorphisms between finite groups we introduce two subcategories of the biset category namely the deflation mackey category m f and the inflation mackey category m f let g be the subcategory of f consisting of the injective homomorphisms we shall show that for a field k of characteristic zero the k linear category k m g k m g k m g has a semisimplicity property and in particular every block of k m g owns a unique simple functor up to isomorphism on the other hand we shall show that when f is equivalent to the category of finite groups the k linear categories k m f and k m f each have a unique block

the generalized work function algorithm is competitive for the generalized 2 server problem the generalized 2 server problem is an online optimization problem where a sequence of requests has to be served at minimal cost requests arrive one by one and need to be served instantly by at least one of two servers we consider the general model where the cost function of the two servers may be different formally each server moves in its own metric space and a request consists of one point in each metric space it is served by moving one of the two servers to its request point requests have to be served without knowledge of future requests the objective is to minimize the total traveled distance the special case where both servers move on the real line is known as the cnn problem we show that the generalized work function algorithm mathrm wfa lambda is constant competitive for the generalized 2 server problem further we give an outline for a possible extension to k geqslant2 servers and discuss the applicability of our techniques and of the work function algorithm in general we co

efficiency of the primal network simplex algorithm for the minimum cost circulation problem we study the number of pivots required by the primal network simplex algorithm to solve the minimum cost circulation problem we propose a pivot selection rule with a bound of n logn 2 o 1 on the number of pivots for an n vertex network this is the first known subexponential bound the network simplex algorithm with this rule can be implemented to run in n logn 2 o 1 time in the special case of planar graphs we obtain a polynomial bound on the number of pivots and the running time we also consider the relaxation of the network simplex algorithm in which cost increasing pivots are allowed as well as cost decreasing ones for this algorithm we propose a pivot selection rule with a bound of o nm min log nc m log n on the number of pivots for a network with n vertices m arcs and integer arc costs bounded in magnitude by c the total running time is o nm log n min log nc m log n this bound is within a logarithmic factor of those of the best previously known algorithms for the minimum

an algorithm for the intersection of quadrilateral surfaces by tracing of neighbours the use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform boolean operations between groups of quadrilateral and triangular surfaces in the intersection process an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections an algorithm based on tracing the neighbours of intersecting quadrilaterals is proposed to determine the intersection lines a background grid is employed to limit the scope of searching for candidate quadrilaterals that may intersect this will drastically cut down the time of geometrical check for intersections between quadrilaterals making the surface intersection and mesh generation a quasi linear process with respect to the number of elements involved given the node numbers at the vertices of the candidate quadrilaterals the neighbour relationship is then established in the determination of intersection each quadrilateral is divided into two triangles and four fundamental cases are identified and treated systematically to enhance robustness and reliability tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm

the cost of offline binary search tree algorithms and the complexity of the request sequence in evaluating the performance of online algorithms for search trees one wants to compare them to the best offline algorithm available in this paper we lower bound the cost of an optimal offline binary search tree using the kolmogorov complexity of the request sequence we obtain several applications for this result first any offline binary search tree algorithm can be at most a constant factor away from the entropy of the process producing the request sequence second for a fraction 1 1 2 m of request sequences of length m on n items the cost of any offline algorithm is w m logn 1 third the expected cost of splay trees is within a constant factor of the expected cost of an optimal offline binary search tree algorithm in a subset of markov chains

the geometric element transformation method for tetrahedral mesh smoothing the geometric element transformation method getme has been introduced as a new element driven approach to mesh smoothing it is based on simple geometric transformations which if applied iteratively lead to the regularization of mesh elements global mesh smoothing can be accomplished by successively improving the worst elements or by averaging node positions obtained by the simultaneous transformation of all elements getme smoothing has been successfully applied in the case of surface meshes as shown in this paper this approach also naturally extends to tetrahedral mesh smoothing without major conceptual modifications a regularizing transformation for tetrahedra is presented and a combined approach of simultaneous and sequential getme smoothing is described first numerical examples yield high quality meshes superior to those obtained by other geometry based methods in fact the presented results are in a majority of cases at least comparable to those obtained by a state of the art global optimization based method

fibonacci bsts a new balancing method for binary search trees this paper presents a new method to balance binary search trees which has the following properties i the only information stored for the balance is the size of every subtree ii inserting or deleting an element can be done in the most traditional way first the element is recursively inserted deleted in from the appropriate subtree afterwards a single or double rotation takes place if necessary iii checking whether or not those rotations are required is computable in constant time per visited node iv the worst case height of these trees is never worse than approximately 1 44042log 2n where n is the number of elements

a simpler and faster 1 5 approximation algorithm for sorting by transpositions an important problem in genome rearrangements is sorting permutations by transpositions the complexity of the problem is still open and two rather complicated 1 5 approximation algorithms for sorting linear permutations are known bafna and pevzner 98 and christie 99 the fastest known algorithm is the quadratic algorithm of bafna and pevzner in this paper we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions hence all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations our main result is a new o n3 2 log n 1 5 approximation algorithm which is considerably simpler than the previous ones and whose analysis is significantly less involved

generation of fusion systems of characteristic 2 type we prove that if is a saturated fusion system on a finite 2 group s then either is known or is generated by the normalizers of two canonically defined characteristic subgroups of s there are various corollaries for finite groups of characteristic 2 type

extensions of p local finite groups a p local finite group consists of a finite p group s together with a pair of categories which encode conjugacy relations among subgroups of s and which are modelled on the fusion in a sylow p subgroup of a finite group it contains enough information to define a classifying space which has many of the same properties as p completed classifying spaces of finite groups in this paper we study and classify extensions of p local finite groups and also compute the fundamental group of the classifying space of a p local finite group

on p permutation equivalences between rickard equivalences and isotypies broue and rickard defined in their landmark papers from 1990 and 1996 the notions of an isotypy and a splendid equivalence between p blocks of finite groups here we define a notion of equivalence which we call a p permutation equivalence that implies an isotypy and is implied by a splendid equivalence moreover we study properties of p permutation equivalences

robust balancing in b trees robust balancing is a technique that substantially decreases the worst case cost of rebalancing b trees when intermixed insertions and deletions occur from theta k log k to 0 k for k insertions and deletions it requires a slight extension to the standard data structure robust b trees but it uses the same simple operations as the standard algorithm to rebalance robust and standard b tree algorithms have identical behavior and 0 k cost when only insertions occur on intermixed insertions and deletions a robust algorithm substantially decreases rebalancing cost and increases space utilization and search cost slightly this is most significant when the cost of rebalancing dominates the total cost as in applications with localized accesses and finger access points in the active localities in applications that use top down searching search cost and total cost are 0 k log k and a robust algorithm improves total cost by a large constant factor because of the larger coefficient for rebalancing than for searching this dissertation makes a thorough study of robust balancing and its impact on maintenance cost we examine the choices for rebalancing that robust b trees introduce and define new algorithms to exploit these choices we develop powerful and uniform techniques for deriving upper bounds on rebalancing cost using the bank account paradigm a method for analyzing the cost of a sequence of operations the power of these techniques is demonstrated by strong lower bounds including several tight bounds and by simple extensions which show the dependence of rebalancing cost on different types of operations the mix of insertions and deletions and the height of rebalancing further refinements show strong bounds on subasymptotic rebalancing cost in a nonempty initial tree and on rebalancing cost in b trees a b tree generalization with improved space utilization robust algorithms for b trees can significantly improve rebalancing cost and total cost even when only insertions occur we use this analysis to find the best algorithms for several applications these include some algorithms whose rebalancing cost is sublinear in the sense of having maximum cost k c for some c 1 previous work done independently by this author mehlhorn and maier and salveter considered only one robust algorithm with a linear rebalancing cost our original contributions include new algorithms for robust b trees and b trees development of the accounting techniques and their use in identifying the best algorithms

a feature preserving volumetric technique to merge surface triangulations several extensions and improvements to surface merging procedures based on the extraction of iso surfaces from a distance map defined on an adaptive background grid are presented the main objective is to extend the application of these algorithms to surfaces with sharp edges and corners in order to deal with objects of different length scales the initial background grids are created using a delaunay triangulation method and local voxelizations a point enrichment technique that introduces points into the background grid along detected surface features such as ridges is used to ensure that these features are preserved in the final merged surface the surface merging methodology is extended to include other boolean operations between surface triangulations the iso surface extraction algorithms are modified to obtain the correct iso surface for multi component objects the procedures are demonstrated with various examples ranging from simple geometrical entities to complex engineering applications the present algorithms allow realistic modelling of a large number of complex engineering geometries using overlapping components defined discretely i e via surface triangulations this capability is very useful for grid generation starting from data originated in measurements or images copyright 2002 john wiley sons ltd

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

efficient simulation of the random cluster model the simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down a number of cluster algorithms usually based on the fortuin kasteleyn representation of the potts model and suitable generalizations for continuous spin models have been used to increase simulation efficiency the first algorithm making use of this representation suggested by sweeny in 1983 has not found widespread adoption due to problems in its implementation however it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well known algorithm due to swendsen and wang here we present an efficient implementation of sweeny s approach for the random cluster model using recent algorithmic advances in dynamic connectivity algorithms

dynamic trees as search trees via euler tours applied to the network simplex algorithm thedynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges linking and splitting by deleting edges cutting while at the same time allowing reporting of certain combinations of vertex or edge values for many applications of dynamic trees values must be combined along paths for other applications values must be combined over entire trees for the latter situation an idea used originally in parallel graph algorithms to represent trees by euler tours leads to a simple implementation with a time of o logn per tree operation wheren is the number of tree vertices we apply this representation to the implementation of two versions of the network simplex algorithm resulting in a time of o logn per pivot wheren is the number of vertices in the problem network

automatic merging of tetrahedral meshes summary a generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh the intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects the tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet there is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition whereas mesh compatibility has already been established on the boundary of the solid objects mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection tetrahedra intersected by the cut surfaces are removed and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces upon restoring compatibility on the bounding surfaces of the regions of intersection the objects are ready to be merged together as all regions of intersection can be detached freely from the objects all operations besides the determination of intersections structurally in the form of loops are virtually topological and no parameter and tolerance is needed in the entire merging process examples are presented to show the steps and the details of the mesh merging procedure copyright 2012 john wiley sons ltd

optimal expected case planar point location point location is the problem of preprocessing a planar polygonal subdivision s of size n into a data structure in order to determine efficiently the cell of the subdivision that contains a given query point we consider this problem from the perspective of expected query time we are given the probabilities p z that the query point lies within each cell z in s the entropy h of the resulting discrete probability distribution is the dominant term in the lower bound on the expected case query time we show that it is possible to achieve query time h o sqrt h 1 with space o n which is optimal up to lower order terms in the query time we extend this result to subdivisions with convex cells assuming a uniform query distribution within each cell in order to achieve space efficiency we introduce the concept of entropy preserving cuttings

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

an efficient feedback coding scheme with low error probability for discrete memoryless channels existing fixed length feedback communication schemes are either specialized to particular channels schalkwijk kailath horstein or apply to general channels but either have high coding complexity block feedback schemes or are difficult to analyze posterior matching this paper introduces a new fixed length feedback coding scheme which achieves the capacity for all discrete memoryless channels has an error exponent that approaches the sphere packing bound as the rate approaches the capacity and has o n log n coding complexity these benefits are achieved by judiciously combining features from previous schemes with new randomization technique and encoding decoding rule these new features make the analysis of the error probability for the new scheme easier than for posterior matching

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

on the sequential access theorem and deque conjecture for splay trees we give a new simple proof for the sequential access theorem for splay trees for an n node splay tree our bound on the number of rotations is 4 5n with a smaller constant than the bound of 10 8n concluded by tarjan we extend our proof to prove the deque conjecture for output restricted deques our proofs provide additional insights into the workings of splay trees

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

the homotopy theory of fusion systems the main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p completed classifying spaces of finite groups these spaces occur as the classifying spaces of certain algebraic objects which we call p local finite groups a p local finite group consists roughly speaking of a finite p group s and fusion data on subgroups of s encoded in a way explained below our starting point is our earlier paper blo on p completed classifying spaces of finite groups together with the axiomatic treatment by lluis puig pu pu2 of systems of fusion among subgroups of a given p group the p completion of a space x is a space xp which isolates the properties of x at the prime p and more precisely the properties which determine its mod p cohomology for example a map of spaces x f y induces a homotopy equivalence xp y p if and only if f induces an isomorphism in mod p cohomology and h xp fp h x fp in favorable cases if x is p good when g is a finite group the p completion bgp of its classifying space encodes many of the properties of g at p for example not only the mod p cohomology of bg but also the sylow p subgroup of g together with all fusion among its subgroups are determined up to isomorphism by the homotopy type of bgp our goal here is to give a direct link between p local structures and homotopy types which arise from them this theory tries to make explicit the essence of what it means to be the p completed classifying space of a finite group and at the same time yields new spaces which are not of this type but which still enjoy most of the properties a space of the form bgp would have we hope that the ideas presented here will have further applications and generalizations in algebraic topology but this theory also fits well with certain aspects of modular representation theory in particular it may give a way of constructing classifying spaces for blocks in the group ring of a finite group over an algebraically closed field of characteristic p a saturated fusion system f over a p group s consists of a set homf p q of monomorphisms for each pair of subgroups p q s which form a category under composition include all monomorphisms induced by conjugation in s and satisfy certain other axioms formulated by puig definitions 1 1 and 1 2 below in particular these axioms are satisfied by the conjugacy homomorphisms in a finite group we refer to pu and pu2 for more details of puig s work on saturated

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result