On the memory requirements of XPath evaluation over XML streams

The important challenge of evaluating XPath queries over XML streams has sparked much interest in the past few years. A number of algorithms have been proposed, supporting wider fragments of the query language, and exhibiting better performance and memory utilization. Nevertheless, all the algorithms known to date use a prohibitively large amount of memory for certain types of queries. A natural question then is whether this memory bottleneck is inherent or just an artifact of the proposed algorithms.In this paper we initiate the first systematic and theoretical study of lower bounds on the amount of memory required to evaluate XPath queries over XML streams. We present a general lower bound technique, which given a query, specifies the minimum amount of memory that any algorithm evaluating the query on a stream would need to incur. The lower bounds are stated in terms of new graph-theoretic properties of queries. The proofs are based on tools from communication complexity.We then exploit insights learned from the lower bounds to obtain a new algorithm for XPath evaluation on streams. The algorithm uses space close to the optimum. Our algorithm deviates from the standard paradigm of using automata or transducers, thereby avoiding the need to store large transition tables.     

Efficient approximation of correlated sums on data streams

In many applications such as IP network management, data arrives in streams and queries over those streams need to be processed online using limited storage. Correlated-sum (CS) aggregates are a natural class of queries formed by composing basic aggregates on (x, y) pairs and are of the form SUM{g(y) : x /spl les/ f(AGG(x))}, where AGG(x) can be any basic aggregate and f(), g() are user-specified functions. CS-aggregates cannot be computed exactly in one pass through a data stream using limited storage; hence, we study the problem of computing approximate CS-aggregates. We guarantee a priori error bounds when AGG(x) can be computed in limited space (e.g., MIN, MAX, AVG), using two variants of Greenwald and Khanna's summary structure for the approximate computation of quantiles. Using real data sets, we experimentally demonstrate that an adaptation of the quantile summary structure uses much less space, and is significantly faster, than a more direct use of the quantile summary structure, for the same a posteriori error bounds. Finally, we prove that, when AGG(x) is a quantile (which cannot be computed over a data stream in limited space), the error of a CS-aggregate can be arbitrarily large.     

Obtaining lower bounds using artificial components

In this paper, we consider the technique of creating artificial components to obtain good lower bounds in the fixed order algebraic decision tree model, for geometric decision problems whose solution space (set of Yes instances) consists of very few connected components. Using this technique, we obtain an Ω(log m) lower bound for the Convex Polygon Inclusion problem for convex m-gons, and an Ω(n log n) lower bound for the Max Gap problem, and the Path Testing problem.     

New Linear Program Performance Bounds for Closed Queueing Networks

We develop new linear program performance bounds for closed reentrantqueueing networks based on an inequality relaxation of the averagecost equation. The approach exploits the fact that the transitionprobabilities under certain policies of closed queueing networksare invariant within certain regions of the state space. Thisinvariance suggests the use of a piecewise quadratic functionas a surrogate for the differential cost function. The linearprogramming throughput bounds obtained are provably tighter thanpreviously known bounds at the cost of increased computationalcomplexity. Functional throughput bounds parameterized by thefixed customer population N are obtained, alongwith a bound on the limiting throughput as N + .We show that one may obtain reduced complexity bounds while stillretaining superiority.     

多接收多重认证码的新构造

基于(n, w, q)集和纠错码给出(w, k, n)多接收多重认证码的新构造。这种构造使得阶欺骗攻击的成功率Pdu达到了下界1/q,还使最大接收者人数和信源个数分别为m(k, q)和m(w, q),与前人构造中的 对比发现,当k, w=2时,改进的数量为1或2,当k, w≥q时,改进的数量为w-q+1。此外当q为素数幂时,改进的下界为1。     

Finding Similar Users in Social Networks

We consider a system where users wish to find similar users. To model similarity, we assume the existence of a set of queries, and two users are deemed similar if their answers to these queries are (mostly) identical. Technically, each user has a vector of preferences (answers to queries), and two users are similar if their preference vectors differ in only a few coordinates. The preferences are unknown to the system initially, and the goal of the algorithm is to classify the users into classes of roughly the same preferences by asking each user to answer the least possible number of queries. We prove nearly matching lower and upper bounds on the maximal number of queries required to solve the problem. Specifically, we present an “anytime” algorithm that asks each user at most one query in each round, while maintaining a partition of the users. The quality of the partition improves over time: for n users and time T, groups of [(O)\tilde](n/T)\tilde{O}(n/T) users with the same preferences will be separated (with high probability) if they differ in sufficiently many queries. We present a lower bound that matches the upper bound, up to a constant factor, for nearly all possible distances between user groups.     

Existence theory for a stochastic differential equation

A non-linear function stochastic differential equation was studied where t𝛆R₊={t;t ? 0},ω𝛆 Ω, Ω being the underlying sot of a complete probability measure space ( Ω,A,P) The random process x(t;ω) is the unknown stochastic function defined on R+ × Ω h(t, x;ω ) ) is the stochastic term defined for t𝛆 R+ and x ( t;ω)εG(a Branch Space); and n(t, x ω) is a random variable defined for tε R+ω 𝛆 Ω, and x 𝛆 F{Grcub; (a Frcchet space). The purpose of this paper is to develop sufficient conditions for the existence of random solutions, second order stochastic processes, for the above equation and to place bounds upon these random solutions. Several examples are also presented which illustrate the usefulness of the theoretical findings.     

Efficient Range Query Processing in Peer-to-Peer Systems

With the increasing popularity of the peer-to-peer (P2P) computing paradigm, many general range query schemes for distributed hash table (DHT)-based P2P systems have been proposed in recent years. Although those schemes can provide range query capability without modifying the underlying DHTs, they have the query delay depending on both the scale of the system and the size of the query space or the specific query, and thus cannot guarantee to return the query results in a bounded delay. In this paper, we propose Armada, an efficient range query processing scheme to support delay-bounded single-attribute and multiple-attribute range queries. It is the first delay-bounded general range query scheme on constant-degree DHTs, and can return the results for any range query within 2logN hops in a P2P system with N peers. Results of analysis and simulations show that the average delay in Armada is less than logN, and the average message cost of single-attribute range queries is about logN+2n 2 (n is the number of peers that intersect with the query). These results are very close to the lower bounds on delay and message cost of range queries over constant-degree DHTs.     

A parametric solution to the pole assignment problem using dynamicoutput-feedback

A technique is presented for pole placement of linear time-invariant systems using dynamic feedback. A previously developed method for partial pole assignment using constant feedback is generalized to the dynamic output-feedback case. Subject to a mild assumption on the number of complex conjugate poles to be assigned, it is almost always possible to arbitrarily assign all the closed-loop system poles using a compensator of order [(n-φ)/max(m,l)] using this new method. Here, n, m, and l are the order of the system, and the number of inputs and outputs, respectively, and φ Δ/=max(m,l)+[max(m,l)/2]+…+[max(m,l)/min(m,l)] where [x] denotes the nearest integer lower than or equal to x (i.e., floor (x)), and [x] denotes the nearest integer greater than or equal to x (i.e., ceiling (x)). An equivalent result is that using a compensator of order q, it is almost always possible to arbitrarily assign min(n+q,(max(m,l)+1)q+φ) closed-loop system poles. Only the normal procedures of linear algebra are required to implement the technique. Note that φ⩾l+m-1 and, therefore, the result is stronger than previous exact pole assignment results. Since it does not involve iteration or any other numerical techniques, it is possible to implement the method symbolically and, therefore, to obtain general parametric solutions to the pole assignment problem. The freedom in this design approach can also often be used to guarantee the internal stability and/or robustness of the resulting closed-loop system     

Improved upper bounds for the mixed structured singular value

In this paper, we take a new look at the mixed structured singular value problem, a problem of finding important applications in robust stability analysis. Several new upper bounds are proposed using a very simple approach which we call the multiplier approach. These new bounds are convex and computable by using linear matrix inequality (LMI) techniques. We show, most importantly, that these upper bounds are actually lower bounds of a well-known upper bound which involves the so-called D-scaling (for complex perturbations) and G-scaling (for real perturbations)     

Towards lower bounds on locally testable codes via density arguments

The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs, and to resolve this question, it suffices to consider the case of query complexity 3. We argue that to refute the existence of such an asymptotically good family, it is sufficient to prove that the number of dual codewords of weight at most 3 is super-linear in the blocklength of the code and they are distributed ??naturally??. The main technical contribution of this paper is an improvement of the combinatorial lemma of Goldreich et?al. (Comput Complex 15(3):263?C296, 2006) which bounds the rate of 2-query locally decodable codes (LDCs) and is used in state-of-the-art rate bounds for linear LDCs. The lemma of Goldreich et?al. bounds the rate of 2-query LDCs of blocklength n in terms of the corruption parameter ??(n)??this is the maximal fraction of corrupted codeword bits for which a (2-query) decoder can recover correctly every message bit (with high probability). Our combinatorial lemma gives non-trivial rate bounds for any corruption parameter ??(n) such that ??(n) · n =???(1), whereas the previous lemma works only for corruption parameter ??(n) such that ??(n) · n ???log n. The study of LDCs with sublinear corruption parameter is also motivated by Dvir??s (IEEE conference on computational complexity. IEEE Computer Society, pp 291?C298, 2010) observation that sufficiently strong bounds on the rate of such LDCs imply explicit constructions of rigid matrices.     

Lower bounds for monotone span programs

Span programs provide a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for formula size, symmetric branching programs, and contact schemes. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. We prove a lower bound of (m ^2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.     

On the rank of certain finite fields

In the present paper we shall show that the rank of the finite field regarded as an -algebra has one of the two values 2n or 2n+1 ifn satisfies 1/2q+1<n<1/2(m(q)–2). Herem(q) denotes the maximum number of -rational points of an algebraic curve of genus 2 over . Using results of Davenport-Hasse, Honda and Rück we shall give lower bounds form(q) which are close to the Hasse-Weil bound . For specialq we shall further show thatm(q) is equal to the Hasse-Weil bound.     

The query complexity of learning DFA

It is known that the class of deterministic finite automata is polynomial time learnable by using membership and equivalence queries. We investigate the query complexity of learning deterministic finite automata, i.e., the number of membership and equivalence queries made during the process of learning. We extend a known lower bound on membership queries to the case of randomized learning algorithms, and prove lower bounds on the number of alternations between membership and equivalence queries. We also show that a trade-off exists, allowing us to reduce the number of equivalence queries at the price of increasing the number of membership queries.     

A Microchoice Bound for Continuous-Space Classification Algorithms

Classifiers are often constructed iteratively by introducing changes sequentially to an initial classifier. Langford and Blum (COLT'99: Proceedings of the 12th Annual Conference on Computational Learning Theory, 1999, San Mateo, CA: Morgan Kaufmann, pp. 209–214) take advantage of this structure (the microchoice structure), to obtain bounds for the generalization ability of such algorithms. These bounds can be sharper than more general bounds. This paper extends the applicability of the microchoice approach to the more realistic case where the classifier space is continuous and the sequence of changes is not restricted to a pre-fixed finite set.Proving the microchoice bound in the continuous case relies on a conditioning technique that is often used in proving VC results. It is shown how this technique can be used to convert any learning algorithm over a continuous space into a family of algorithms over discrete spaces.The new continuous microchoice result is applied to obtain a bound for the generalization ability of the perceptron algorithm. The greedy nature of the perceptron algorithm, which generates new classifiers by introducing corrections based on misclassified points, is exploited to obtain a generalization bound that has an asymptotic form of O( ), where n is the training set size.     

Finding all periods and initial palindromes of a string in parallel

An optimalO(log logn)-time CRCW-PRAM algorithm for computing all period lengths of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. The algorithm can be used to find all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We derive a lower bound for finding initial palindromes by modifying a known lower bound for finding the period length of a string [9]. Whenp processors are available the bounds become (n/p+log_1+p/n2p).This work was partially supported by NSF Grant CCR-90-14605. D. Breslauer was partially supported by an IBM Graduate Fellowship while studying at Columbia University and by a European Research Consortium for Informatics and Mathematics postdoctoral fellowship.     

Polynomial certificates for propositional classes

This paper studies the complexity of learning classes of expressions in propositional logic from equivalence queries and membership queries. In particular, we focus on bounding the number of queries that are required to learn the class ignoring computational complexity. This quantity is known to be captured by a combinatorial measure of concept classes known as the certificate complexity. The paper gives new constructions of polynomial size certificates for monotone expressions in conjunctive normal form (CNF), for unate CNF functions where each variable affects the function either positively or negatively but not both ways, and for Horn CNF functions. Lower bounds on certificate size for these classes are derived showing that for some parameter settings the new certificate constructions are optimal. Finally, the paper gives an exponential lower bound on the certificate size for a natural generalization of these classes known as renamable Horn CNF functions, thus implying that the class is not learnable from a polynomial number of queries.     

Optimal Reconstruction of Graphs under the Additive Model

We study the problem of reconstructing unknown graphs under the additive combinatorial search model. The main result concerns the reconstruction of bounded degree graphs, i.e., graphs with the degree of all vertices bounded by a constant d . We show that such graphs can be reconstructed in O(dn) nonadaptive queries, which matches the information-theoretic lower bound. The proof is based on the technique of separating matrices. A central result here is a new upper bound for a general class of separating matrices. As a particular case, we obtain a tight upper bound for the class of d -separating matrices, which settles an open question stated by Lindstr?m in [20]. Finally, we consider several particular classes of graphs. We show how an optimal nonadaptive solution of O(n ² / log n) queries for general graphs can be obtained. We also prove that trees with unbounded vertex degree can be reconstructed in a linear number of queries by a nonadaptive algorithm. Received August 1997; revised January 1999.     

Neural networks with local receptive fields and superlinear VC dimension

Local receptive field neurons comprise such well-known and widely used unit types as radial basis function (RBF) neurons and neurons with center-surround receptive field. We study the Vapnik-Chervonenkis (VC) dimension of feedforward neural networks with one hidden layer of these units. For several variants of local receptive field neurons, we show that the VC dimension of these networks is superlinear. In particular, we establish the bound Omega(W log k) for any reasonably sized network with W parameters and k hidden nodes. This bound is shown to hold for discrete center-surround receptive field neurons, which are physiologically relevant models of cells in the mammalian visual system, for neurons computing a difference of gaussians, which are popular in computational vision, and for standard RBF neurons, a major alternative to sigmoidal neurons in artificial neural networks. The result for RBF neural networks is of particular interest since it answers a question that has been open for several years. The results also give rise to lower bounds for networks with fixed input dimension. Regarding constants, all bounds are larger than those known thus far for similar architectures with sigmoidal neurons. The superlinear lower bounds contrast with linear upper bounds for single local receptive field neurons also derived here.