Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems --- Sorting and Searching; E.5 [Data]: Files --- Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics --- Probabilistic algorithms; E.2 [Data Storage Representation]: Composite structures, linked representations. General Terms: Algorithms, Theory. Additional Key Words and Phrases: Adaptive sorting algorithms, Comparison trees, Measures of disorder, Nearly sorted sequences, Randomized algorithms. A Survey of Adaptive Sorting Algorithms 2 CONTENTS INTRODUCTION I.1 Optimal adaptivity I.2 Measures of disorder I.3 Organization of the paper 1.WORST-CASE ADAPTIVE (INTERNAL) SORTING ALGORITHMS 1.1 Generic Sort 1.2 Cook--Kim division 1.3 Partition Sort 1.4 Exponential Search 1.5 Adaptive Merging 2.EXPECTED-CASE ADAPTIV

Abstract-In this paper, we present an algorithm for hidden surface removal for a class of poly-hedral surfaces which have a property that they can be ordered relatively quickly. For example, our results apply directly to terrain maps. A distinguishing feature of our algorithm is that its running time is sensitive to the actual size of the visible image, rather than the total number of intersections in the image plaue which can be much larger than the visible image. The time complexity of this algorithm is O((k + n) log ’ n) where n and /c are, respectively, the input and the output sizes. Thus, in a significant number of situations this will be faster than the worst case optimal algorithms which have running time of n(n’) irrespective of the output size.

LEDA (Library of Efficient Data Types and Algorithms) is an ongoing project which aims to build a library of the efficient data structures and algorithms used in combinatorial computing [12]. We discuss three recent aspects of the project: The cost of flexibility, implementation parameters, and augmented trees. Keyword Codes: D.2.0; D.1.5; F.2.2 Keywords: Software Engineering, General; object-oriented Programming; Nonnumerical Algorithms and Problems 1 Introduction We will treat the topic on the basis of a concrete example: the LEDA (Library of Efficient Data Types and Algorithms) software library. The authors started the LEDA project in 1989 as an attempt to narrow the gap between algorithm research, teaching and implementation. The project aims to build a library of the efficient data structures and algorithms used in combinatorial computing. The rationale of the project is given in [12] and briefly reviewed in section 2. LEDA is freely available by anonymous ftp for education...

Given a k-character query string and an array of n strings arranged in lexicographical order, computing the rank of the query string among the n strings or deciding whether it occurs in the array requires the inspection of 1

Abstract — Hash tables are a fundamental data structure in many network applications, including route lookups, packet classification and monitoring. Often a part of the data path, they need to operate at wire-speed. However, several associative memory accesses are needed to resolve collisions, making them slower than required. This motivates us to consider minimal perfect hashing schemes, which reduce the number of memory accesses to just 1 and are also space-efficient. Existing perfect hashing algorithms are not tailored for network applications because they take too long to construct and are hard to implement in hardware. This paper introduces a hardware-friendly scheme for minimal perfect hashing, with space requirement approaching 3.7 times the information theoretic lower bound. Our construction is several orders faster than existing perfect hashing schemes. Instead of using the traditional mapping-partitioning-searching methodology, our scheme employs a Bloom filter, which is known for its simplicity and speed. We extend our scheme to the dynamic setting, thus handling insertions and deletions. I.

First we present a new variant of Merge-sort, which needs only 1.25n space, because it uses space again, which becomes available within the current stage. It does not need more comparisons than classical Merge-sort. The main result is an easy to implement method of iterating the procedure in-place starting to sort 4/5 of the elements. Hereby we can keep the additional transport costs linear and only very few comparisons get lost, so that n log n − 0.8n comparisons are needed. We show that we can improve the number of comparisons if we sort blocks of constant length with Merge-Insertion, before starting the algorithm. Another improvement is to start the iteration with a better version, which needs only (1+ε)n space and again additional O(n) transports. The result is, that we can improve this theoretically up to n log n − 1.3289n comparisons in the worst case. This is close to the theoretical lower bound of n log n − 1.443n. The total number of transports in all these versions can be reduced to ε n log n+O(1) for any ε> 0. 1

: We describe a sorting algorithm that is optimally adaptive with respect to several important measures of presortedness. In particular, the algorithm requires O(n+k log k) time on n-sequences X that have a longest ascending subsequence of length n \Gamma k and for which Rem(X) = k; O(n log(k=n)) time on sequences with k inversions; and O(n log k) time on sequences that can be decomposed into k monotone shuffles. The algorithm makes use of an adaptive merging operation that can be implemented using finger search trees. 1 Introduction An adaptive algorithm is one which requires fewer resources to solve `easy' problem instances than it does to solve `hard'. For sorting an adaptive algorithm should run in O(n) time if presented with a sorted n-sequence, and in O(n log n) time for all n- sequences, with the time for any particular sequence depending upon the `nearness' of the sequence to being sorted. Mannila [7] established the notion of a measure of presortedness to quantify the disord...

Median smoothing of a series of data values is considered. Naive programming of such an algorithm would result in large amount of computation, especially when the series of data values is long. By maintaining a heap structure that we update when moving along the data we obtain an optimal median smoothing algorithm.

An efficient contact search for dynamic explicit finite element (FE) simulations with several moving bodies is essential to avoid unacceptable costs. The time spent for contact algorithms is mainly determined by the cost of the search phase. We present a variant of the position code algorithm for efficient global contact search. Instead of a row-wise ordering we propose a numbering that follows a space filling curve. An analysis proves that the new ordering is more efficient in case of long surface segments. The two variants of the position code algorithm and another widely used algorithm, which is based on a hierarchical ordering, are implemented in an industrial FE code and applied to problems in fastening and demolition technology. Experimental results show that the presented method is well suited for all types of meshes and meets the great demands on e#ciency for the mentioned field while the other algorithms show disadvantages in some cases. Key words: finite elements, contact ...

Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The Worst--Case Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc