The Maximum Traveling Salesman Problem with Submodular Rewards

In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $\kappa$, of the edges in the tour. This problem is known to be NP-hard. We analyze two simple algorithms for finding an approximate solution. Both algorithms require $O(|V|^3)$ oracle calls to the submodular function. The approximation factors are shown to be $\frac{1}{2+\kappa}$ and $\max\set{\frac{2}{3(2+\kappa)},2/3(1-\kappa)}$, respectively; so the second method has better bounds for low values of $\kappa$. We also look at how these algorithms perform for a directed graph and investigate a method to consider edge costs in addition to rewards. The problem has direct applications in monitoring an environment using autonomous mobile sensors where the sensing reward depends on the path taken. We provide simulation results to empirically evaluate the performance of the algorithms.Comment: Extended version of ACC 2013 submission (including p-system greedy bound with curvature

Orthogonal simple component analysis: A new, exploratory approach

Combining principles with pragmatism, a new approach and accompanying algorithm are presented to a longstanding problem in applied statistics: the interpretation of principal components. Following Rousson and Gasser [53 (2004) 539--555] @p250pt@ the ultimate goal is not to propose a method that leads automatically to a unique solution, but rather to develop tools for assisting the user in his or her choice of an interpretable solution. Accordingly, our approach is essentially exploratory. Calling a vector 'simple' if it has small integer elements, it poses the open question: @p250pt@ What sets of simply interpretable orthogonal axes---if any---are angle-close to the principal components of interest? its answer being presented in summary form as an automated visual display of the solutions found, ordered in terms of overall measures of simplicity, accuracy and star quality, from which the user may choose. Here, 'star quality' refers to striking overall patterns in the sets of axes found, deserving to be especially drawn to the user's attention precisely because they have emerged from the data, rather than being imposed on it by (implicitly) adopting a model. Indeed, other things being equal, explicit models can be checked by seeing if their fits occur in our exploratory analysis, as we illustrate. Requiring orthogonality, attractive visualization and dimension reduction features of principal component analysis are retained.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS374 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A storage and access architecture for efficient query processing in spatial database systems

Due to the high complexity of objects and queries and also due to extremely large data volumes, geographic database systems impose stringent requirements on their storage and access architecture with respect to efficient query processing. Performance improving concepts such as spatial storage and access structures, approximations, object decompositions and multi-phase query processing have been suggested and analyzed as single building blocks. In this paper, we describe a storage and access architecture which is composed from the above building blocks in a modular fashion. Additionally, we incorporate into our architecture a new ingredient, the scene organization, for efficiently supporting set-oriented access of large-area region queries. An experimental performance comparison demonstrates that the concept of scene organization leads to considerable performance improvements for large-area region queries by a factor of up to 150

Improved approximation of arbitrary shapes in dem simulations with multi-spheres

DEM simulations are originally made for spherical particles only. But most of real particles are anything but not spherical. Due to this problem, the multi-sphere method was invented. It provides the possibility to clump several spheres together to create complex shape structures. The proposed algorithm offers a novel method to create multi-sphere clumps for the given arbitrary shapes. Especially the use of modern clustering algorithms, from the field of computational intelligence, achieve satisfactory results. The clustering is embedded into an optimisation algorithm which uses a pre-defined criterion. A mostly unaided algorithm with only a few input and hyperparameters is able to approximate arbitrary shapes