Catherine C. McGeoch

Amortized analyses of self-organizing sequential search heuristics

The performance of sequential search can be enhanced by the use of heuristics that move elements closer to the front of the list as they are found. Previous analyses have characterized the performance of such heuristics probabilistically. In this article, we use amortization to analyze the heuristics in a worst-case sense; the relative merit of the heuristics in this analysis is different in the probabilistic analyses. Experiments show that the behavior of the heuristics on real data is more closely described by the amortized analyses than by the probabilistic analyses.

Analyzing algorithms by simulation: variance reduction techniques and simulation speedups

Although experimental studies have been widely applied to the investigation of algorithm performance, very little attention has been given to experimental method in this area. This is unfortunate, since much can be done to improve the quality of the data obtained; often, much improvement may be needed for the data to be useful. This paper gives a tutorial discussion of two aspects of good experimental technique: the use of <italic>variance reduction techniques</italic> and <italic>simulation speedups</italic> in algorithm studies. In an illustrative study, application of variance reduction techniques produces a decrease in variance by a factor 1000 in one case, giving a dramatic improvement in the precision of experimental results. Furthermore, the complexity of the simulation program is improved from &THgr;<italic>mn</italic>/H<italic><subscrpt>n</subscrpt></italic>) to &THgr;(<italic>m</italic> + <italic>n</italic> log <italic>n</italic>) (where <italic>m</italic> is typically much larger than <italic>n</italic>), giving a much faster simulation program and therefore more data per unit of computation time. The general application of variance reduction techniques is also discussed for a variety of algorithm problem domains.

Experimental evaluation of an adiabiatic quantum system for combinatorial optimization

This paper describes an experimental study of a novel computing system (algorithm plus platform) that carries out quantum annealing, a type of adiabatic quantum computation, to solve optimization problems. We compare this system to three conventional software solvers, using instances from three NP-hard problem domains. We also describe experiments to learn how performance of the quantum annealing algorithm depends on input.

Some unexpected expected behavior results for bin packing

We study the asymptotic expected behavior of the First Fit and First Fit Decreasing bin packing algorithms applied to items chosen uniformly from the interval (0,u], u ≤ 1. Our results indicate that the algorithms perform even better than previously expected.

Experimental algorithmics

Theoretical questions and motivations, combined with empirical research methods, produce insights into algorithm and program performance.

All-pairs shortest paths and the essential subgraph

The essential subgraph H of a weighted graph or digraphG contains an edge (v, w) if that edge is uniquely the least-cost path between its vertices. Let s denote the number of edges ofH. This paper presents an algorithm for solving all-pairs shortest paths onG that requires O(ns+n2 logn) worst-case running time. In general the time is equivalent to that of solvingn single-source problems using only edges inH. For general models of random graphs and digraphsG, s=0(n logn) almost surely. The subgraphH is optimal in the sense that it is the smallest subgraph sufficient for solving shortest-path problems inG. Lower bounds on the largest-cost edge ofH and on the diameter ofH andG are obtained for general randomly weighted graphs. Experimental results produce some new conjectures about essential subgraphs and distances in graphs with uniform edge costs.

Optimal sampling strategies for quicksort

A well-known improvement on the basic Quicksort algorithm is to sample from the subarray at each recursive stage and to use the sample median as the partition element. General sampling strategies, which allow sample size to vary as a function of subarray size, are analyzed here in terms of the total cost of comparisons required for sorting plus those required for median selection. Both this generalization and this cost measure are new to the analysis of Quicksort. A square-root strategy, which takes a sample of size Φ(√n) for a subarray of size n, is shown to be optimal over a large class of strategies. The square-root strategy has O(n1,5) worst-case cost. The exact optimal strategy for a standard implementation of Quicksort is found computationally for n below 3000.

Does Anybody Really Know What Time It Is

veryone jokes about African time, but I think the North American concept of time is a big joke. Have you ever noticed how often you hear the word ‘busy’ in a day? Being busy in North American culture is highly valued. By contrast, African culture does not value being busy. If you ask someone if they are busy, they look at you strangely. Don’t even try to ask someone what time it is. They don’t have watches. This culture values spending time with friends and family, and helping each other.

Emerging opportunities for theoretical computer science

The principles underlying this report can be summarized as follows:1. A strong theoretical foundation is vital to computer science.2. Theory can be enriched by practice.3. Practice can be enriched by theory.4. If we are guided by (2) and (3), the value, impact, and funding of theory will be enhanced.In order to achieve a greater synergy between theory and application, and to sustain and expand on the remarkable successes of Theory of Computing (TOC), we consider it essential to increase the impact of theory on key application areas. This requires additional financial resources in support of theory, and closer interaction between theoreticians and researchers in other areas of computer science and in other disciplines.The report does not make a detailed assessment of the overall state of theoretical computer science or fully chronicle the achievements of this field. Instead, it has the specific objective of recommending ways to harness these remarkable achievements for the solution of challenging problems emerging from new developments such as the information superhighway.Section 1 describes the events leading up to this report and delineates the reports objectives. Section 2 establishes the context for the report. It traces the history of TOC, describes the impact that TOC has achieved in the areas of core theory and fundamental algorithms, points out the differences between these areas and application-oriented theory, and calls for an intensified effort to bring the methods of TOC to bear on applications. It then goes on to define the four main categories into which our recommen- dations fall: building bridges between theory and applications, algorithm engineering, communication, and education. Section 3 discusses some specific opportunities for stimulating interactions between TOC and applied areas. Section 4 proposes an applied research initiative, Information Access in a Globally Distributed Environment, which identifies an exciting current technological area that we believe presents challenging opportunities for excellent theoretical work. Section 5 proposes a second applied research initiative, The Algorithmic Stockroom, that would exploit and extend the body of theoretical knowledge in the field of algorithms. Section 6 proposes a broadening in graduate education with two purposes in mind: to better prepare theoreticians to interact creatively with practitioners, and to provide future practitioners with the background they will need to benefit from this exchange.

How to Find Big-Oh in Your Data Set (and How Not to)

The empirical curve bounding problem is defined as follows. Suppose data vectors X, Y are presented such that E(Y[i])=f(X[i]) where f(x) is an unknown function. The problem is to analyze X, Y and obtain complexity bounds O(g u (x)) and Ω(g i (x)) on the function −f(x). As no algorithm for empirical curve bounding can be guaranteed correct, we consider heuristics. Five heuristic algorithms are presented here, together with analytical results guaranteeing correctness for certain families of functions. Experimental evaluations of the correctness and tightness of bounds obtained by the rules for several constructed functions f(x) and real datasets are described. A hybrid method is shown to have very good performance on some kinds of functions, suggesting a general, iterative refinement procedure in which diagnostic features of the results of applying particular methods can be used to select additional methods.