Exploring NK Fitness Landscapes Using Imitative Learning

The idea that a group of cooperating agents can solve problems more efficiently than when those agents work independently is hardly controversial, despite our obliviousness of the conditions that make cooperation a successful problem solving strategy. Here we investigate the performance of a group of agents in locating the global maxima of NK fitness landscapes with varying degrees of ruggedness. Cooperation is taken into account through imitative learning and the broadcasting of messages informing on the fitness of each agent. We find a trade-off between the group size and the frequency of imitation: for rugged landscapes, too much imitation or too large a group yield a performance poorer than that of independent agents. By decreasing the diversity of the group, imitative learning may lead to duplication of work and hence to a decrease of its effective size. However, when the parameters are set to optimal values the cooperative group substantially outperforms the independent agents

Minimum Coresets for Maxima Representation of Multidimensional Data

Coresets are succinct summaries of large datasets such that, for a given problem, the solution obtained from a coreset is provably competitive with the solution obtained from the full dataset. As such, coreset-based data summarization techniques have been successfully applied to various problems, e.g., geometric optimization, clustering, and approximate query processing, for scaling them up to massive data. In this paper, we study coresets for the maxima representation of multidimensional data: Given a set P of points in R^d , where d is a small constant, and an error parameter ε ∈ (0, 1), a subset Q ⊆ P is an ε-coreset for the maxima representation of P iff the maximum of Q is an ε-approximation of the maximum of P for any vector u ∈ R^d , where the maximum is taken over the inner products between the set of points (P or Q) and u. We define a novel minimum ε-coreset problem that asks for an ε-coreset of the smallest size for the maxima representation of a point set. For the two-dimensional case, we develop an optimal polynomial-time algorithm for the minimum ε-coreset problem by transforming it into the shortest-cycle problem in a directed graph. Then, we prove that this problem is NP-hard in three or higher dimensions and present polynomial-time approximation algorithms in an arbitrary fixed dimension. Finally, we provide extensive experimental results on both real and synthetic datasets to demonstrate the superior performance of our proposed algorithms.Peer reviewe