This paper aims to improve the accuracy of query result-size estimations in query optimizers by leveraging the dynamic feedback obtained from observations on the executed query workload. To this end, an approximate "synopsis" of data-value distributions is devised that combines histograms with parametric curve fitting, leading to a specific class of linear splines. The approach reconciles the benefits of histograms, simplicity and versatility, with those of parametric techniques especially the adaptivity to statistically biased and dynamically evolving query workloads. The paper

Dynamic programming is an important algorithm design technique. It is used for solving problems whose solutions involve recursively solving subproblems that share subsubproblems. While a straightforward recursive program solves common subsubproblems repeatedly and often takes exponential time, a dynamic programming algorithm solves every subsubproblem just once, saves the result, reuses it when the subsubproblem is encountered again, and takes polynomial time. This paper describes a systematic method for transforming programs written as straightforward recursions into programs that use dynamic programming. The method extends the original program to cache all possibly computed values, incrementalizes the extended program with respect to an input increment to use and maintain all cached results, prunes out cached results that are not used in the incremental computation, and uses the resulting incremental program to form an optimized new program. Incrementalization statically exploits semantics of both control structures and data structures and maintains as invariants equalities characterizing cached results. The principle underlying incrementalization is general for achieving drastic program speedups. Compared with previous methods that perform memoization or tabulation, the method based on incrementalization is more powerful and systematic. It has been implemented and applied to numerous problems and succeeded on all of them. 1

Abstract. Dynamic programming is a classical programming technique, applicable in a wide variety of domains such as stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing of ambiguous languages, and biosequence analysis. Little methodology has hitherto been available to guide the design of such algorithms. The matrix recurrences that typically describe a dynamic programming algorithm are difficult to construct, error-prone to implement, and, in nontrivial applications, almost impossible to debug completely. This article introduces a discipline designed to alleviate this problem. We describe an algebraic style of dynamic programming over sequence data. We define its formal framework, based on a combination of grammars and algebras, and including a formalization of Bellman’s Principle. We suggest a language used for algorithm design on a convenient level of abstraction. We outline three ways of implementing this language, including an embedding in a lazy functional language. The workings of the

We present efficient cache-oblivious algorithms for several fundamental dynamic programs. These include new algorithms with improved cache performance for longest common subsequence (LCS), edit distance, gap (i.e., edit distance with gaps), and least weight subsequence. We present a new cache-oblivious framework called the Gaussian Elimination Paradigm (GEP) for Gaussian elimination without pivoting that also gives cache-oblivious algorithms for Floyd-Warshall all-pairs shortest paths in graphs and ‘simple DP’, among other problems. 1

ABSTRACT: A common model for computing the similarity of two stringsXandYof lengthsm andnrespectively, withmn, is to transformXintoYthrough a sequence of edit operations, called an edit sequence. The edit operations are of three types: insertion, deletion, and substitution. A given cost function assigns a weight to each edit operation. The amortized weight for a given edit sequence is the ratio of its weight to its length, and the minimum of this ratio over all edit sequences is the normalized edit distance. Existing algorithms for normalized edit distance computation with proven complexity bounds requireO(mn2)time in the worst-case. We give provably better algorithms: anO(mnlogn)-time algorithm when the cost function is uniform, i.e, the weights of edit operations depend only on the type but not on the individual symbols involved, and anO(mnlogm)-time algorithm when the weights are rational.

A common model for computing the similarity of two strings X and Y of lengths m, and n respectively with m n, is to transform X into Y through a sequence of three types of edit operations: insertion, deletion, and substitution. The model assumes a given cost function which assigns a non-negative real weight to each edit operation. The amortized weight for a given edit sequence is the ratio of its weight to its length, and the minimum of this ratio over all edit sequences is the normalized edit distance. Existing algorithms for normalized edit distance computation with proven complexity bounds require O(mn

Abstract. In this paper a parametric description for the state space of an arbitrary TPN is given. An enumerative procedure for reducing the state space is introduced. The reduction is defined as a truncated multistage decision problem and solved recursively. A reachability graph is defined in a discrete way by using the reachable integer-states of the TPN.

Games offer OR/MS lecturers and students important educational resources. However, for various reasons the OR/MS literature in general- and introductory textbooks in particular- scarcely make use of this treasure. In this discussion we suggest that it is time to reconsider this position and regard games as a valuable source for developing educationally rich material for OR/MS courses. Hopefully this will initiate a constructive discussion on this topic that will eventually facilitate the identification and development of good OR/MS educational resources and stimulate the development of new exciting ways to make OR/MS tools more accessible to students and the public at large. 1.

Decision makers often want to see a diverse collection of good solutions in addition to a solution that is in some mathematical sense an optimal solution to a problem. The purpose of the objective function is to quantify the notion “good ” while the purpose of this paper is to exhibit a suitable function for quantifying the notion “diverse.” We focus on the case where important aspects of the solutions are best represented as matrices or sets of vectors, such as when the solution involves selections. We establish a distance function and its connections with related distance functions used in optimization and psychology. A real-world application illustrates its use for decision support.

In this discussion we examine the famous Towers of Hanoi puzzle from an OR/MS perspective, focusing on its educational content. We show that this puzzle provides an excellent environment for illustrating a number of fundamental OR/MS problem-solving concepts in general and dynamic programming concepts in particular. In addition to the popular 'min' version of the problem, we also present an interesting but rather neglected 'max ' version. On-line interactive modules are included.