A constrained nonlinear 0–1 program for data allocation

This paper analyzes the problem of allocating copies of relations from a global database to the sites of a geographically distributed communication network. The objective of the allocation is to minimize the total cost due to transmissions generated by queries from the various sites, including queries that access multiple relations. This allocation problem is modeled as a constrained nonlinear 0–1 subproblems generated during subgradient optimization are solved as optimization. Some of the unconstrained quadratic 0–1 subproblems generated during subgradient optimization are solved as maximum flow problems, while the others require implicit enumeration, depending on the nature of the objective function coefficients of the subproblems. Our solution approach is tested extensively on data allocation problems with as many as 100 sites and 20 relations. On a set of randomly generated test problems our approach was close to two orders of magnitude faster than the general purpose integer programming code OSL.     

On the complexity of the multivariate Sturm–Liouville eigenvalue problem

We study the complexity of approximating the smallest eigenvalue of -Δ+q with Dirichlet boundary conditions on the d-dimensional unit cube. Here Δ is the Laplacian, and the function q is non-negative and has continuous first order partial derivatives. We consider deterministic and randomized classical algorithms, as well as quantum algorithms using quantum queries of two types: bit queries and power queries. We seek algorithms that solve the problem with accuracy . We exhibit lower and upper bounds for the problem complexity. The upper bounds follow from the cost of particular algorithms. The classical deterministic algorithm is optimal. Optimality is understood modulo constant factors that depend on d. The randomized algorithm uses an optimal number of function evaluations of q when d≤2. The classical algorithms have cost exponential in d since they need to solve an eigenvalue problem involving a matrix with size exponential in d. We show that the cost of quantum algorithms is not exponential in d, regardless of the type of queries they use. Power queries enjoy a clear advantage over bit queries and lead to an optimal complexity algorithm.     

MultidimensionalB-trees: Analysis of dynamic behavior

The MultidimensionalB-tree (MDBT) is a new method for multiple attribute indexing which uses B-trees to maintain the filial sets at each level and imposes an ordering on these filial sets in order to ensure efficient searching for various associative queries. In this paper, we show that the MDBT provides an attractive alternative to other indexing structures when frequent changes to the database occur. We present algorithms for maintaining the MDBT structure when insertions or deletions are posted which also account for some storage reclamation. Procedures for evaluating the average and worst-case times of our algorithms are given, showing that the maintenance of the MDBT structure can be done at a relatively low cost.     

A limit field for orthogonal range searches in two-dimensional random point search trees

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle. We prove that, when suitably shifted and rescaled, the random cost function converges uniformly in probability towards a random field that is characterized as the unique solution to a distributional fixed-point equation. We also state similar results for 2-d trees. Our results imply for instance that the worst case query satisfies the same asymptotic estimates as a typical query, and thereby resolve an open question of Chanzy et al. (2001).     

Optimal dynamic multi-attribute hashing for range queries

This paper examines a partial match retrieval scheme which supports range queries for highly dynamic databases. The scheme relies on order preserving multi-attribute hashing. In general, designing optimal indexes is NP-hard. Greedy algorithms used to determine the optimal indexes for simple partial match queries are not directly applicable because there are a larger number of queries to consider in determining the optimal indexes. In this paper we present heuristic algorithms which provide near-optimal solutions. The optimisation scheme we propose can be used to design other dynamic file structures such as the grid file, BANG file and multilevel grid file to further enhance their retrieval performance taking into consideration the query distribution.     

Scheduling programs with repetitive projects: A comparison of a simulated annealing,a genetic and a pair-wise swap algorithm

We address the problem of scheduling in programs involving the production of multiple units of the same product. Our study was motivated by a construction program for fast naval patrol boats. Other applications of this problem include procurement of multiple copies of aircraft, spacecraft, and weapon systems. In this problem we must decide how many units of the product to assign to each of a number of available crews (individuals, teams, subcontractors, etc.). These types of problems are characterized by two potentially conflicting considerations: 1) the need to complete each unit by its contractual due date, and 2) learning effects. Because of the first consideration, there is a tendency to use multiple crews for simultaneous production, so that meeting due dates is assured. However, the second consideration encourages assigning many units to a single crew so that learning effects are maximized. We study this scheduling problem with two different penalty cost structures and develop models for both versions. The models trade-off the penalty associated with late deliveries and the savings due to learning (and possibly incentive payments for early completion). We discuss different heuristic algorithms — simulated annealing, a genetic algorithm, and a pair-wise swap heuristic — as well as an exhaustive search to determine a baseline for comparisons. Our computational results show that the pair-wise swap algorithm is the most efficient solution procedure for these models.     

On boolean decision trees with faulty nodes

We consider the problem of computing with faulty components in the context of the Boolean decision tree model, in which cost is measured by the number of input bits queried, and the responses to queries are faulty with a fixed probability. We show that if f can be represented in k-DNF form and in j-CNF form, then O(n log(min(k, j)/q)) queries suffice to compute f with error probability less than q, where n is the number of input bits. © 1994 John Wiley & Sons, Inc.     

Dynamic programming for optimization of system throughput with application to selective-repeat ARQ protocols over broadcast channels

This paper studies packet network data link layer error control protocols suitable for point-to-multipoint communication. We optimize the throughput performance of two new selective-repeat protocols which differ in the way the sender uses the outcomes of the previous transmission. In both protocols, multiple copies of a data frame are sent (instead of just a single copy). The optimum number of copies is determined based on how many receivers have not yet received the data frame. A dynamic programming technique is used to solve this optimization problem. The results show that by sending the optimum number of copies of a data frame instead of just a single copy, the throughput will be significantly improved.     

Application of principal component analysis to multi-disk concurrent accessing

This paper is concerned with the allocation of multi-attribute records on several disks so as to achieve high degree of concurrency of disk access when responding to partial match queries.An algorithm to distribute a set of multi-attribute records onto different disks is presented. Since our allocation method will use the principal component analysis, this concept is first introduced. We then use it to generate a set of real numbers which are the projections on the first principal component direction and can be viewed as hashing addresses.Then we propose an algorithm based upon these hashing addresses to allocate multi-attribute records onto different disks. Some experimental results show that our method can indeed be used to solve the multi-disk data allocation problem for concurrent accessing.     

Approximating average parameters of graphs

Inspired by Feige (36th STOC, 2004), we initiate a study of sublinear randomized algorithms for approximating average parameters of a graph. Specifically, we consider the average degree of a graph and the average distance between pairs of vertices in a graph. Since our focus is on sublinear algorithms, these algorithms access the input graph via queries to an adequate oracle. We consider two types of queries. The first type is standard neighborhood queries (i.e., what is the ith neighbor of vertex v?), whereas the second type are queries regarding the quantities that we need to find the average of (i.e., what is the degree of vertex v? and what is the distance between u and v?, respectively). Loosely speaking, our results indicate a difference between the two problems: For approximating the average degree, the standard neighbor queries suffice and in fact are preferable to degree queries. In contrast, for approximating average distances, the standard neighbor queries are of little help whereas distance queries are crucial. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Succinct data structures for flexible text retrieval systems

We propose succinct data structures for text retrieval systems supporting document listing queries and ranking queries based on the tf*idf (term frequency times inverse document frequency) scores of documents. Traditional data structures for these problems support queries only for some predetermined keywords. Recently Muthukrishnan proposed a data structure for document listing queries for arbitrary patterns at the cost of data structure size. For computing the tf*idf scores there has been no efficient data structures for arbitrary patterns.Our new data structures support these queries using small space. The space is only 2/ times the size of compressed documents plus 10n bits for a document collection of length n, for any 0<1. This is much smaller than the previous O(nlogn) bit data structures. Query time is O(m+qlogn) for listing and computing tf*idf scores for all q documents containing a given pattern of length m. Our data structures are flexible in a sense that they support queries for arbitrary patterns.     

Approximate similarity search: A multi-faceted problem

We review the major paradigms for approximate similarity queries and propose a classification schema that easily allows existing approaches to be compared along several independent coordinates. Then, we discuss the impact that scheduling of index nodes can have on performance and show that, unlike exact similarity queries, no provable optimal scheduling strategy exists for approximate queries. On the positive side, we show that optimal-on-the-average schedules are well-defined and that their performance is indeed the best among practical schedules.     

On the number of range queries in k-space

A range query on a set of points in a k-dimensions coordinate space asks for all points lying within a hyper-rectangle specified by ranges of permissible values for each of the coordinates. In this paper we regard as identical any two range queries which return the same set of points. We then investigate the number of range queries possible on a set—given a set of N points in k-space, what is the maximum number of distinct subsets that may be specified by giving bounding hyper-rectangles? The bounds we find for this number (as a function of N and k) are substantial improvements over previous results, and tighten a lower bound on the computational time required to process range queries. We also report some results concerning the expected number of range queries on random distributions of points.     

On the deductive security of queries to confidential databases in cloud computing systems

We study certain simple models of confidential databases in cloud computing systems. In the framework of these models we introduce a concept of deductive security for queries to such databases, find necessary and sufficient conditions of deductive security, and describe some classes of queries which satisfy these requirements.     

On R-trees with low query complexity

The R-tree is a well-known bounding-volume hierarchy that is suitable for storing geometric data on secondary memory. Unfortunately, no good analysis of its query time exists. We describe a new algorithm to construct an R-tree for a set of planar objects that has provably good query complexity for point location queries and range queries with ranges of small width. For certain important special cases, our bounds are optimal. We also show how to update the structure dynamically, and we generalize our results to higher-dimensional spaces.     

Strict and tolerant antidivision queries with ordinal layered preferences

In this paper, we are interested in taking preferences into account for a family of queries inspired by the antidivision. An antidivision query aims at retrieving the elements associated with none of the elements of a specified set of values. We suggest the introduction of preferences inside such queries with the following specificities: (i) the user gives his/her preferences in an ordinal way and (ii) the preferences apply to the divisor which is defined as a hierarchy of sets. Different uses of the hierarchy are investigated, which leads to queries conveying different semantics and the property of the result delivered is characterized. Furthermore, the case where a conjunctive stratified antidivision query returns an empty set of answers is dealt with, and an approach aimed at relaxing such queries is proposed.     

Cost prediction for ray shooting in octrees

The ray shooting problem arises in many different contexts and is a bottleneck of ray tracing in computer graphics. Unfortunately, theoretical solutions to the problem are not very practical, while practical methods offer few provable guarantees on performance.

Attempting to combine practicality with theoretical soundness, we show how to provably measure the average performance of any ray-shooting method based on traversing a bounded-degree spatial decomposition, where the average is taken to mean the expectation over a uniform ray distribution. An approximation yields a simple, easy-to-compute cost predictor that estimates the average performance of ray shooting without running the actual algorithm.

We experimentally show that this predictor provides an accurate estimate of the efficiency of executing ray-shooting queries in octree-induced decompositions, irrespective of whether or not the bounded-degree requirement is enforced, and of the criteria used to construct the octrees. We show similar guarantees for decompositions induced by kd-trees and uniform grids. We also confirm that the performance of an octree while ray tracing or running a radio-propagation simulation is accurately captured by our cost predictor, for ray distributions arising from realistic data.     

灾后运输网络中的最短路修复合作博弈

在最短路修复合作博弈中,当灾后运输网络规模较大时,最优成本分摊问题难以直接求解。基于拉格朗日松弛理论,提出了一种最短路修复合作博弈成本分摊算法。该算法将最短路修复合作博弈分解为两个具有特殊结构的子博弈,进而利用两个子博弈的结构特性,可以{高效地}求解出二者的最优成本分摊,将这两个成本分摊相加,可以获得原博弈的一个近乎最优的稳定成本分摊。结果部分既包含运输网络的随机仿真,也包含玉树地震灾区的现实模拟,无论数据来源于仿真还是现实,该算法都能在短时间内为最短路修复合作博弈提供稳定的成本分摊方案。     

Multidimensional digital searching—alternative data structures

We analyze the average cost of partial match queries in M-dimensional Digital Search Trees and Patricia Tries. Our results allow a precise comparison of the average behavior of these data structures with the M-dimensional Tries studied by Flajolet and Puech [J. Assoc. Comput. Mach., 33 , 371–407 (1986)]. It turns out that Patricia is superior to Digital Search Tres, the latter ones being superior to Tries. © 1994 John Wiley & Sons, Inc.     

Learning read once functions using subcube parity queries

The article considers the problem of constructing a conditional diagnostic test (the exact identification problem) on the set of all read-once functions essentially dependent on the specified variables in an arbitrary hereditary basis. We use standard queries on function values at points and also parity queries on the number of ones in subfunctions obtained by substituting constants for variables (subcube parity queries return the modulo-2 sum of the function values on a subcube of the Boolean cube). For the elementary basis consisting of conjunction, disjunction, and negation, we prove the existence of a conditional diagnostic test with a quadratic (in the number of variables) number of queries. For bases that allow read-once expression of all elementary-basis functions (containing at least one nonmonotone and at least one nonlinear function) and are essentially different from the elementary basis, we prove the necessity of using an exponential (in the number of variables) number of queries in the worst case. Our analysis thus establishes the boundary between polynomial and exponential complexity problems.