In this paper we study the following question posed by H. S. Wilf: What is, asymptotically as n ! 1, the probablility that a randomly chosen part size in a random composition of an integer n has multiplicity m ? More specifically, given positive integers n and m, suppose that a composition of n is selected uniformly at random and then, out of the set of part sizes in , a part size j is chosen uniformly at random. Let P(A (m) n ) be the probability that j has multiplicity m. We show that for fixed m, P(A (m) n ) goes to 0 at the rate 1= ln n. A more careful analysis uncovers an unexpected result: (ln n)P(A (m) n ) does not have a limit but instead oscillates around the value 1=m as n !1. This work is a counterpart of a recent paper of Corteel, Pittel, Savage and Wilf who studied the same problem in the case of partitions rather than compositions. 1 Introduction In this paper we consider the multiplicity of a randomly chosen part size in a random composition of an integer n. L...

The object-relational database management system (ORDBMS) offers many potential benefits for scientific, multimedia and financial applications. However, work remains in the integration of domain-specific class libraries into ORDBMS query processing. A major problem is that the standard mechanisms for query selectivity estimation, taken from relational database systems, rely on properties specific to the standard data types; creation of new mechanisms remains extremely difficult because the software interfaces provided by vendors are relatively low-level. In this paper, we discuss extensions of the generalized search tree, or GiST, to support a higher-level but less type-specific approach. Specifically, we discuss the computation of selectivity estimates with confidence intervals using a variety of index-based approaches and present results from an experimental comparison of these methods with several estimators from the literature. 1.

this paper, we study the problem of sorting permutations and circular permutations using as few fixed-length reversals as possible. Our problem is implicit in the popular TOP-SPIN

Michael A. Bender y Dongdong Ge Simai He Haodong Hu Ron Y. Pinter Steven Skiena Firas Swidan Abstract We study the problem of sorting integer sequences and permutations by length-weighted reversals. We consider a wide class of cost functions, namely f(`) = ` for all 0, where ` is the length of the reversed subsequence. We present tight or nearly tight upper and lower bounds on the worst-case cost of sorting by reversals. Then we develop algorithms to approximate the optimal cost to sort a given input. Furthermore, we give polynomial-time algorithms to determine the optimal reversal sequence for a restricted but interesting class of sequences and cost functions. Our results have direct application in computational biology to the eld of comparative genomics.

Until recently, Internet routers and ATM switches were generally built around a central pool of shared memory buffers and a fast, shared-bus backplane. However, limitations in both memory and bus bandwidth have led to the use of input queues and switched backplanes. Input queues relieve the bottleneck by distributing the memory over each switch input; and a switched backplane allows packet transfers to take place simultaneously. This thesis focuses on the design of switched backplanes with input queues. In particular, we focus on the design of schedulers for switched backplanes. The scheduler decides the order in which packets, or cells, may traverse the backplane. Studies have shown that existing scheduling algorithms are either too complex to operate at high speed or lack the intelligence to perform well over a wide range of traffic patterns. In this thesis, we present two new algorithms that are fast, simple and efficient. Using the methods of Lyapunov, we prove that both algorithms can achieve 100% throughput for all traffic patterns with independent arrivals. We also demonstrate heuristics that can be implemented in fast and relatively simple hardware. Our exploratory design work shows that the heuristics can make a scheduling decision within 10-20 nanoseconds when implemented using 0.25 CMOS technology. At this scheduling speed, it is possible to design switches or routers with more than one terabit per second of aggregate bandwidth. m v Acknowledgments This thesis would not have been possible without the help of many people. First and foremost, among these are my parents who I would like to thank for their utmost dedication to my education. Importantly, I would like to thank my adviser, Professor Nick McKeown, for his unparalleled support and guidance in both ...

A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinatorial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising "boxes," where starting points for the local minimizer are generated. In order to cover a wide spectrum of possible applications with no user intervention, the method is designed with adaptive mechanisms: the box size is adapted to the local structure of the function to be optimized, the search parameters are adapted to obtain a proper balance of diversification and intensification. The algorithm is compared with some existing algorithms, and the experimental results are presented for a suite of benchmark tasks.

The problem of selecting actions in environments that are dynamic and not completely predictable or observable is a central problem in intelligent behavior. In AI, this translates into the problem of designing controllers that can map sequences of observations into actions so that certain goals are achieved. Three main approaches have been used in AI for designing such controllers: the programming approach, where the controller is programmed by hand in a suitable high-level procedural language, the planning approach, where the control is automatically derived from a suitable description of actions and goals, and the learning approach, where the control is derived from a collection of experiences. The three approaches can exhibit successes and limitations. The focus of this paper is on the planning approach. More specifically, we present an approach to planning based on various state models that can handle various types of action dynamics (deterministic and probabilistic) ...

Despite the steady decrease in secondary storage prices and continuous, sometimes drastic, improvements in storage density, the data storage requirements of many organizations cannot be met economically using secondary storage alone. Tertiary storage solutions, especially automated magnetic tape libraries, o er a much lower storage cost at a level of functionality that satis es the needs of many application types. Database management systems (DBMS) typically do not incorporate tertiary storage devices such as magnetic tapes and optical disks as a rst-class citizen in the storage hierarchy. The typical solution in bringing tertiary-resident data under the control of a DBMS is to use operating system facilities to copy the data to secondary storage, and then to perform query optimization and execution as if the data had been in secondary storage all along. This approach fails to recognize the opportunities for saving execution time and storage space if the data were accessed on tertiary devices directly and in parallel with other I/Os. In this paper we examine ways of joining two relations stored on magnetic tapes. Our earlier work has shown that when one relation is stored on tape and the other on disk, a parallel I/O variant of Nested Block Join performs quite well, given su cient main memory space. Work presented in this paper extends by considering the case where both relations are larger than available disk space. To tackle main memory size limitations, we focus on hashing-based solutions. We modi ed Grace Hash Join to handle a range of tape relation sizes and to exploit parallelism between disk and tape I/Os. We showhow disk and main memory space a ect the performance of tertiary joins and demonstrate how parallel I/O helps these methods save execution time as well as memory and disk space.

This note provides exact formulae for the mean and variance of the cost of top-down recursive mergesort. These formulae improve upon earlier results of Flajolet and Golin. Key words. analysis of algorithms, mergesort, Dirichlet series, asymptotic expansions.

Lopsided trees are rooted, ordered, trees in which the length of an edge from a node to its i th child depends upon the value of i: These trees model a variety of problems and have therefore been extensively studied. In this paper we combine analytic and combinatorial techniques to address three open problems on such trees: ffl Given n, efficiently construct a lopsided tree with n leaves that has minimal external-path-length. ffl Express the cost of the minimal external-path-length tree as a function of n: ffl Calculate exactly how many nodes of depth x exist in the infinite lopsided tree. Lopsided trees model Varn codes, prefix free codes in which the letters of the encoding alphabet can have different lengths. The solutions to the first and second problems above solve corresponding open problems on Varn codes. The solution to the third problem can be used to model the performance of broadcasting algorithms in the postal model of communication. Finding these solutions requires g...