space time tradeoffs for emptiness queries we develop the first nontrivial lower bounds on the complexity of online hyperplane and halfspace emptiness queries our lower bounds apply to a general class of geometric range query data structures called partition graphs informally a partition graph is a directed acyclic graph that describes a recursive decomposition of space we show that any partition graph that supports hyperplane emptiness queries implicitly defines a halfspace range query data structure in the fredman yao semigroup arithmetic model with the same asymptotic space and time bounds thus results of bronnimann chazelle and pach imply that any partition graph of size s that supports hyperplane emptiness queries in time t satisfies the inequality st d omega n log n d d 1 d 1 using different techniques we improve previous lower bounds for hopcroft s problem given a set of points and hyperplanes does any hyperplane contain a point in dimensions four and higher using this offline result we show that for online hyperplane emptiness queries omega n d mbox polylog n space is required to achieve polylogarithmic query time and omega n d 1 d mbox polylog n query time is required if only o n polylog n space is available these two lower bounds are optimal up to polylogarithmic factors for two dimensional queries we obtain an optimal continuous tradeoff st 2 omega n 2 between these two extremes finally using a lifting argument we show that the same lower bounds hold for both offline and online halfspace emptiness queries in mathbb r d d 3 2

nonoblivious hashing nonoblivious hashing where information gathered from unsuccessful probes is used to modify subsequent probe strategy is introduced and used to obtain the following results for static lookup on full tables 1 an o 1 time worst case scheme that uses only logarithmic additional memory and no memory when the domain size is linear in the table size which improves upon previously linear space requirements 2 an almost sure o 1 time probabilistic worst case scheme which uses no additional memory and which improves upon previously logarithmic time requirements 3 enhancements to hashing 1 and 2 are solved for multikey recors where search can be performed under any key in time o 1 these schemes also permit properties such as nearest neighbor and rank to be determined in logarithmic time

new amortized cell probe lower bounds for dynamic problems abstract we build upon the recent papers by weinstein and yu 11 larsen 7 and clifford et al 3 to present a general framework that gives amortized lower bounds on the update and query times of dynamic data structures using our framework we present two concrete results 1 for the dynamic polynomial evaluation problem where the polynomial is defined over a finite field of size n 1 1 and has degree n any dynamic data structure must either have an amortized update time of lg n lg lg n 2 or an amortized query time of lg n lg lg n 2 2 for the dynamic online matrix vector multiplication problem where we get an n n matrix whose entires are drawn from a finite field of size n 1 any dynamic data structure must either have an amortized update time of lg n lg lg n 2 or an amortized query time of n lg n lg lg n 2 for these two problems the previous works by larsen 7 and clifford et al 3 gave the same lower bounds but only for worst case update and query times our bounds match the highest unconditional lower bounds known till date for any dynamic problem in the cell probe model

applications of ramsey s theorem to decision tree complexity combinatorial techniques for extending lower bound results for decision trees to general types of queries are presented problems that are defined by simple inequalities between inputs called order invariant problems are considered a decision tree is called k bounded if each query depends on at most k variables no further assumptions on the type of queries are made it is proved that one can replace the queries of any k bounded decision tree that solves an order invariant problem over a large enough input domain with k bounded queries whose outcome depends only on the relative order of the inputs as a consequence all existing lower bounds for comparison based algorithms are valid for general k bounded decision trees where k is a constant an o n log n lower bound for the element uniqueness problem and several other problems for any k bounded decision tree such that k o n c and c n 1 2 bounded decision trees of complexity o n that solve the element uniqueness problem all the lower bounds mentioned above are shown to hold for nondeterministic and probabilistic decision trees as well

membership in constant time and almost minimum space this paper deals with the problem of storing a subset of elements from the bounded universe mathcal m 0 ldots m 1 so that membership queries can be performed efficiently in particular we introduce a data structure to represent a subset of n elements of mathcal m in a number of bits close to the information theoretic minimum b left lceil lg m choose n right rceil and use the structure to answer membership queries in constant time

the hierarchical basis multigrid method we derive and analyze the hierarchical basis multigrid method for solving discretizations of self adjoint elliptic boundary value problems using piecewise linear triangular finite elements the method is analyzed as a block symmetric gau seidel iteration with inner iterations but it is strongly related to 2 level methods to the standard multigridv cycle and to earlier jacobi like hierarchical basis methods the method is very robust and has a nearly optimal convergence rate and work estimate it is especially well suited to difficult problems with rough solutions discretized using highly nonuniform adaptively refined meshes

state space control system design based on non minimal state variable feedback further generalization and unification results this paper shows how proportional integral plus linear quadratic pip lq control based on non minimal state space nmss control system design can be constrained to yield exactly the same control algorithm as both generalized predictive control gpc and standard minimal state linear quadratic gaussian lqg design methods however while nmss includes these other approaches as special cases it is less constrained and so more flexible in general terms for example while pip lq has the simplicity of gpc it is formulated like lqg in the powerful context of state variable feedback svf control which allows for ready access to modern robust control methods furthermore the paper suggests that the nmss approach provides the greater design freedom with a wider range of possible lq solutions than its minimal state space equivalent

electing a leader in a synchronous ring the problem of electing a leader in a synchronous ring of n processors is considered both positive and negative results are obtained on the one hand if processor ids are chosen from some countable set then there is an algorithm that uses only o n messages in the worst case on the other hand any algorithm that is restricted to use only comparisons of ids requires o n log n messages in the worst case alternatively if the number of rounds is required to be bounded by some t in the worst case and ids are chosen from any set having at least n t elements for a certain very fast growing function then any algorithm requires o n log n messages in the worst case

non minimal state variable feedback decoupling control for multivariable continuous time systems most research into non minimal state variable feedback control in which the state vector is implemented directly from the measured input and output signals of the controlled process has considered discrete time systems represented using either the backward shift or delta operator however mechanistic models with physically meaningful parameters are often expressed in terms of differential equations represented using the laplace transform or s operator and this article is concerned with multivariable design for such models the controllability conditions are developed and it is shown how the introduction of a diagonal polynomial matrix for filtering yields a control system that is immediately realisable in practice worked examples include optimal control with multi objective optimisation and pole assignment design with analytical multivariable decoupling with the latter illustrated by its application to a nonlinear wind turbine simulation

new lower bound techniques for dynamic partial sums and related problems we study the complexity of the dynamic partial sum problem in the cell probe model we give the model access to nondeterministic queries and prove that the problem remains hard we give the model access to the right answer pm 1 as an oracle and prove that the problem remains hard this suggests which kind of information is hard to maintain from these results we derive a number of lower bounds for dynamic algorithms and data structures we prove lower bounds for dynamic algorithms for existential range queries reachability in directed graphs planarity testing planar point location incremental parsing and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits we prove a lower bound for reachability in grid graphs in terms of the graph s width we characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string

on the cell probe complexity of polynomial evaluation abstract we consider the cell probe complexity of the polynomial evaluation problem with preprocessing of coefficients for polynomials of degree at most n over a finite field k we show that the trivial cell probe algorithm for the problem is optimal if k is sufficiently large compared to n as an application we give a new proof of the fact that p incr time o log n log log n

a fully dynamic algorithm for recognizing and representing proper interval graphs in this paper we study the problem of recognizing and representing dynamically changing proper interval graphs the input to the problem consists of a series of modifications to be performed on a graph where a modification can be a deletion or an addition of a vertex or an edge the objective is to maintain a representation of the graph as long as it remains a proper interval graph and to detect when it ceases to be so the representation should enable one to efficiently construct a realization of the graph by an inclusion free family of intervals this problem has important applications in physical mapping of dna we give a near optimal fully dynamic algorithm for this problem it operates in o log n worst case time per edge insertion or deletion we prove a close lower bound of omega log n log log n log b amortized time per operation in the cell probe model with word size b we also construct optimal incremental and decremental algorithms for the problem which handle each edge operation in o 1 time as a byproduct of our algorithm we solve in o log n worst case time the problem of maintaining connectivity in a dynamically changing proper interval graph

non linear control by input output state variable feedback pole assignment this article considers pole assignment control of non linear dynamic systems described by state dependent parameter sdp models the approach follows from earlier research into linear proportional integral plus methods but in sdp system control the control coefficients are updated at each sampling instant on the basis of the latest sdp relationships alternatively algebraic solutions can be derived off line to yield a practically useful control algorithm that is relatively straightforward to implement on a digital computer requiring only the storage of delayed system variables coupled with straightforward arithmetic expressions in the control software although the analysis is limited to the case when the open loop system has no zeros time delays are handled automatically this article shows that the closed loop system reduces to a linear transfer function with the specified design poles hence assuming pole assignability at each sample global stability of the non linear system is guaranteed at

hash functions for priority queues the complexity of priority queue operations is analyzed with respect to the cell probe computational model of a yao j assoc comput mach 28 no 3 1981 615 628 a method utilizing families of hash functions is developed which permits priority queue operations to be implemented in constant worst case time provided that a size constraint is satisfied the minimum necessary size of a family of hash functions for computing the rank function is estimated and contrasted with the minimum size required for perfect hashing

should tables be sorted we examine optimality questions in the following information retrieval problem given a set s of n keys store them so that queries of the form is x in s can be answered quickly it is shown that in a rather general model including al1 the commonly used schemes lceil lg n l rceil probes to the table are needed in the worst case provided the key space is sufficiently large the effects of smaller key space and arbitrary encoding are also explored

error correcting data structures we study data structures in the presence of adversarial noise we want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object even if the data structure has been corrupted by a constant fraction of errors we measure the efficiency of a data structure in terms of its length the number of bits in its representation and query answering time measured by the number of bit probes to the possibly corrupted representation the main issue is the trade off between these two this new model is the common generalization of static data structures and locally decodable error correcting codes ldcs we prove a number of upper and lower bounds on various natural error correcting data structure problems in particular we show that the optimal length of t probe error correcting data structures for the membership problem where we want to store subsets of size s from a universe of size n such that membership queries can be answered effic

direct digital and adaptive control by input output state variable feedback pole assignment the paper describes a general approach to state variable feedback pole assignment for linear discrete time systems this is based on the definition of a non minimal state space nmss whose state variables are defined only in terms of the present and past values of the system output and the past values of its input in more conventional block diagram terms it can be interpreted as an extension to a proportional integral pi control system in which linear feedback and forward path digital filters are introduced to ensure the required closed loop pole assignment for this reason we refer to it as a proportional integral plus or pip system the paper discusses the conditions for pole assignability practical examples which illustrate the performance of the pip system in fixed gain and self tuning adaptive applications are also discussed

determining membership with 2 simultaneous queries abstract alice and bob are playing a cooperative game in which alice must devise a scheme to store n elements in an array from a universe u of size m her goal is to store in such a way that for every x u bob can observe the values of two positions dependent on x in the array and determine whether x is in the array or not alice may share her storage scheme with bob and they win if such an arrangement is made the question is how large can the universe u be in terms of n so that alice and bob can win in this paper we give upper and lower bounds on this question for general n and the special case when n 3 we also pose conjectures and further questions for research

on a model of indexability and its bounds for range queries we develop a theoretical framework to characterize the hardness of indexing data sets on block access memory devices like hard disks we define an indexing workload by a data set and a set of potential queries for a workload we can construct an indexing scheme which is a collection of fixed sized subsets of the data we identify two measures of efficiency for an indexing scheme on a workload storage redundancy r how many times each item in the data set is stored and access overhead a how many times more blocks than necessary does a query retrieve for many interesting families of workloads there exists a trade off between storage redundancy and access overhead given a desired access overhead a there is a minimum redundancy that any indexing scheme must exhibit we prove a lower bound theorem for deriving the minimum redundancy by applying this theorem we show interesting upper and lower bounds and trade offs between a and r in the case of multidimensional range queries and set queries

upper and lower bounds on the power of advice proving superpolylogarithmic lower bounds for dynamic data structures has remained an open problem despite years of research p trascu proposed an exciting approach for breaking this barrier via a two player communication model in which one player gets private advice at the beginning of the protocol he gave reductions from the problem of solving an asymmetric version of set disjointness in his model to a diverse collection of natural dynamic data structure problems in the cell probe model he also conjectured that for any hard problem in the standard two party communication model the asymmetric version of the problem is hard in his model provided not too much advice is given in this paper we prove several surprising results about his model we show that there exist boolean functions requiring linear randomized communication complexity in the two party model for which the asymmetric versions in his model have deterministic protocols with exponentially smaller complexity for set disjointness which