41531267
A linear time algorithm for approximate 2-means clustering
Matousek [Discrete Comput. Geom. 24 (1) (2000) 61-84] designed an O(nlogn) deterministic algorithm for the approximate 2-means clustering problem for points in fixed dimensional Euclidean space which had left open the possibility of a linear time algorithm. In this paper, we present a simple randomized algorithm to determine an approximate 2-means clustering of a given set of points in fixed dimensional Euclidean space, with constant probability, in linear time.We first approximate the mean of the larger cluster using random sampling. We then show that the problem can be reduced to a set of lines, on which it can be solved by carefully pruning away points of the larger cluster and randomly sampling on the remaining points to obtain an approximate to the mean of the smaller cluster.
32334601
Finding an Approximate Median with High Probability in Constant Parallel Time
Given n elements from a totally ordered set we outline a method for choosing an element whose rank is γn for some 0 0.
9302549
Planar Graph Blocking for External Searching

AbstractWe present a new scheme for storing a planar graph in external memory so that any online path can be traversed in an I-O efficient way. Our storage scheme significantly improves the previous results for planar graphs with bounded face size. We also prove an upper bound on I-O efficiency of any storage scheme for well-shaped triangulated meshes. For these meshes, our storage scheme achieves optimal performance.

11169442
Linear Time Algorithms for Clustering Problems in Any Dimensions
We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2(k/e)O(1)dn) time (1+e)-approximation algorithms for these problems. These are the first algorithms for these problems linear in the size of the input (nd for n points in d dimensions), independent of dimensions in the exponent, assuming k and e to be fixed. A key ingredient of the k-median result is a (1+e)-approximation algorithm for the 1-median problem which has running time O(2(1/e)O(1)d). The previous best known algorithm for this problem had linear running time.
10562059
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.(MATH) For the problem of transitive closure, the previous best known algorithms, for achieving O(1) query time, require O(\min(m, \frac{n^3}{m}))$ amortized update time, implying an upper bound of O(n^{\frac{3}{2}})$ on update time per edge-deletion. We present an algorithm that achieves $O(1)$ query time and O(n \log^2n + \frac{n^2}{\sqrt{m}}{\sqrt{\log n}})$ update time per edge-deletion, thus improving the upper bound to O(n^{\frac{4}{3}}\sqrt[3]{\log n})$.(MATH) For the problem of maintaining all-pairs shortest distances in unweighted digraph under deletion of edges, we present an algorithm that requires O(\frac{n^3}{m} \log^2 n)$ amortized update time and answers a distance query in O(1) time. This improves the previous best known update bound by a factor of log n. For maintaining all-pairs shortest paths, we present an algorithm that achieves O(\min(n^{\frac{3}{2}} \sqrt{\log n}, \frac{n^3}{m} \log ^2n))$ amortized update time and reports a shortest path in optimal time (proportional to the length of the path). For the latter problem we improve the worst amortized update time bound by a factor of O(\sqrt{\frac{n}{\log n}})$.(MATH) We also present the first decremental algorithm for maintaining all-pairs (1+ε) approximate shortest paths/distances, for any ε > 0, that achieves a sub-quadratic update time of O(n log2n + \frac{n^2}{\sqrt{\epsilon m}}\sqrt{\log n})$ and optimal query time.Our algorithms are randomized and have one-sided error for query (with probability O(1/nc) for any constant c).
1068367
An Efficient Output-Size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains
Abstract. We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log 4 n) steps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data structures is somewhat novel in the context of parallel algorithms.
14600509
A Genetic Prototype Learner
Supervised classification problems have received considerable attention from the machine learning community. We propose a novel genetic algorithm based prototype learning system, PLEASE, for this class of problems. Given a set of prototypes for each of the possible classes, the class of an input instance is determined by the prototype nearest to this instance. We assume ordinal attributes and prototypes are represented as sets of feature-value pairs. A genetic algorithm is used to evolve the number of prototypes per class and their positions on the input space as determined by corresponding feature-value pairs. Comparisons with C4.5 on a set of artificial problems of controlled complexity demonstrate the effectiveness of the proposed system.
2777534
Towards a pareto-optimal solution in general-sum games
Multiagent learning literature has investigated iterated two-player games to develop mechanisms that allow agents to learn to converge on Nash Equilibrium strategy profiles. Such equilibrium configuration implies that there is no motivation for one player to change its strategy if the other does not. Often, in general sum games, a higher payoff can be obtained by both players if one chooses not to respond optimally to the other player. By developing mutual trust, agents can avoid iterated best responses that will lead to a lesser payoff Nash Equilibrium. In this paper we work with agents who select actions based on expected utility calculations that incorporates the observed frequencies of the actions of the opponent(s). We augment this stochastically-greedy agents with an interesting action revelation strategy that involves strategic revealing of one's action to avoid worst-case, pessimistic moves. We argue that in certain situations, such apparently risky revealing can indeed produce better payoff than a non-revealing approach. In particular, it is possible to obtain Pareto-optimal solutions that dominate Nash Equilibrium. We present results over a large number of randomly generated payoff matrices of varying sizes and compare the payoffs of strategically revealing learners to payoffs at Nash equilibrium.
7580001
Evolutionary Tournament-Based Comparison of Learning and Non-Learning Strategies for Iterated Games
Evolutionary tournaments have been used as a tool for comparing strategies. For instance, in the late 1970’s, Axelro d organized tournaments to compare strategies for playing th e iterated prisoner’s dilemma (PD) game. While these tournaments and later research have provided us with a better understanding of successful strategies for iterated PD, ou r understanding is less clear about strategies for playing it erated versions of arbitrary single-stage games. While solut ion concepts like Nash equilibria has been proposed for general sum games, learning strategies like fictitious play may be pr eferred for playing against sub-rational players. In this pa per, we discuss the relative performance of both learning and non learning strategies that embody some of the above approache s on an experimental testbed of all possible structurally dis tinct 2x2 conflicted games with ordinal payoffs. This set of bimatrices provides a baseline, neutral testbed for comparin g strategies. We discuss the testbed, our choice of represent ative learning and non-learning strategies and relative ran kings of these strategies ranked by cumulative score in tournamen ts. We also study the performance of the strategies in an evolutionary tournament. Finally, we provide some analysis of th e observed results to highlight the advantage of learning str ategies.
9417710
Using real-valued genetic algorithms to evolve rule sets for classification
In this paper, we use a genetic algorithm to evolve a set of classification rules with real-valued attributes. We show how real-valued attribute ranges could be encoded with real-valued genes and present a new uniform method for representing don't cares in the rules. We view supervised classification as an optimization problem, and evolve rule sets that maximize the number of correct classifications of input instances. We use a variant of the Pitt approach to genetic-based machine learning system with a novel conflict resolution mechanism between competing rules within the same rule set. Experimental results demonstrate the effectiveness of our proposed approach on a benchmark wine classifier system.<<ETX>>
16671606
Individual learning of coordination knowledge
Abstract. Social agents, both human and computational, inhabiting a world containing multiple active agents, need to coordinate their activities. This is because agents share resources, and without proper coordination or ‘rules of the road’, everybody will be interfering with the plans of others. As such, we need coordination schemes that allow agents to effectively achieve local goals without adversely affecting the problem-solving capabilities of other agents. Researchers in the field of Distributed Artificial Intelligence (DAI) have developed a variety of coordination schemes under different assumptions about agent capabilities and relationships. Whereas some of these researchers have been motivated by human cognitive biases, others have approached it as an engineering problem of designing the most effective coordination architecture or protocol. We evaluate individual and concurrent learning by multiple, autonomous agents as a means for acquiring coordination knowledge. We show that a uniform reinforc...