It is shown that there are # 2n n # - # n-1 m=0 2 n-m-1 # 2m m # permutations which are the union of an increasing sequence and a decreasing sequence. 1991 Mathematics Subject Classification 05A15 Submitted: December 1, 1997; Accepted: January 10, 1998 1 Introduction Merge permutations, permutations which are the union of two increasing subsequences, have been studied for many years [3]. It is known that they are characterised by the property of having no decreasing subsequence of length 3 and that there are # 2n n # /(n + 1) such permutations of length n. Recently there has been some interest in permutations which are the union of an increasing subsequence with a decreasing subsequence. We call such permutations skew-merged. Stankova [4] proved that a permutation is skewmerged if and only if it has no subsequence abcd orderedinthesamewayas 2143 or 3412. In [1, 2] the more general problem of partitioning a permutation into given numbers of increasing and decreasing ...

We study the eects of caches on basic graph and hashing algorithms and show how cache eects inuence the best solutions to these problems. We study the performance of basic data structures for storing lists of values and use these results to design and evaluate algorithms for hashing, Breadth-First-Search (BFS) and Depth-First-Search (DFS).

We study the problem of finding a longest common increasing subsequence (LCIS) of multiple sequences of numbers. The LCIS problem is a fundamental issue in various application areas, including the whole genome alignment. In this paper we give an efficient algorithm to find the LCIS of two sequences in O(min(r log ℓ, nℓ+r) log log n+Sort(n)) time where n is the length of each sequence and r is the number of ordered pairs of positions at which the two sequences match, ℓ is the length of the LCIS, and Sort(n) is the time to sort n numbers. For m sequences where m ≥ 3, we find the LCIS in O(min(mr 2, r log ℓ log m r)+m·Sort(n)) time where r is the total number of m-tuples of positions at which the m sequences match. The previous results find the LCIS of two sequences in O(n 2) and O(nℓ log log n+Sort(n)) time. Our algorithm is faster when r is relatively small, e.g., for r < min(n 2 /(log ℓ log log n), nℓ / log ℓ). 1

: This paper investigates the performance of hashing algorithms by both an experimental and an analytical approach. We examine the performance of three classical hashing algorithms: chaining, double hashing and linear probing. Our experimental results show that, despite the theoretical superiority of chaining and double hashing, linear probing outperforms both for random lookups. We explore variations on the data structures used by these traditional algorithms to improve their spatial locality and hence cache performance. Our results also help determine the optimal table size for a given key set size. In addition to time, we also study the average number of probes and cache misses incurred by these algorithms. For most of the algorithms studied in this paper, our analysis agrees with the experimental results. As a supplementary result, we examine the behavior of random lookups to a hash table. This provides a simple way to estimate the cache miss penalties of different machines. Two c...

Functional programming is largely untested in the industrial environment. This paper summarises the results of a study into the suitability of Haskell in the area of text compression, an area with definite commercial interest. Our program initially performs very poorly in comparison with a version written in C. Experiments reveal the cause of this to be the large disparity in the relative speed of I/O and bit--level operations and also a space leak inherent in the Haskell definition. 1 Introduction Claims for the advantages of functional programming languages abound [1] but industrial take--up of the paradigm has been almost non--existent. Two of the main reasons for this are: ffl lack of proof that the advantages apply to large--scale developments; ffl lack of industry--strength compilers and environments, particularly for high speed computation. The FLARE project, managed by BT, sets out to address these issues: "The effectiveness of functional programming has been amply ...

A priority queue transforms an input permutation p 1 of a totally ordered set of size n into an output permutation p 2 . Atkinson and Thiyagarajah showed that the number of such pairs (p 1 ; p 2 ) is (n+1) n\Gamma1 , which is well known to be the number of labeled trees on n + 1 vertices. We give a new proof of this result by finding a bijection from such pairs of permutations to labeled trees.