Dynamic Facility Location via Exponential Clocks

The \emph{dynamic facility location problem} is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: there is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities, and connect every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use \emph{no clustering} and we allow clients to connect through paths of \emph{arbitrary lengths}. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem

Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems

Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments in information theory, however, suggest quantifying collective organization in a system- and phenomenon-agnostic way: decompose the system's thermodynamic entropy density into a localized entropy, that solely contained in the dynamics at a single location, and a bound entropy, that stored in space as domains, clusters, excitations, or other emergent structures. We compute this decomposition and related quantities explicitly for the nearest-neighbor Ising model on the 1D chain, the Bethe lattice with coordination number k=3, and the 2D square lattice, illustrating its generality and the functional insights it gives near and away from phase transitions. In particular, we consider the roles that different spin motifs play (in cluster bulk, cluster edges, and the like) and how these affect the dependencies between spins.Comment: 12 pages, 8 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ising_bmu.ht

A strongly polynomial algorithm for generalized flow maximization

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.Comment: minor correction

Innovative method for cutting edge preparation with flexible diamond tools

The micro geometry of the cutting edge is of central importance for the performance of cutting tools. It influences all essential parameters in the machining process: chip formation, thermal and mechanical load on the tool and the workpiece, tool wear and the resulting workpiece quality. The effect depends on the size and shape of the cutting edge rounding. Depending on the machining process, asymmetrical roundings often show the greatest potential. In addition to increasing tool life, the quality of the surfaces produced can be improved by a specifically designed asymmetrical rounding. For edge preparation, blasting, brushing and drag finishing are used in industrial applications. However, an economic production of asymmetrical cutting edge geometries on cutting tools with complicated cutting edge geometry, such as solid carbide tools with helical cutting edge, cannot be achieved with these methods. Therefore, a novel method for preparation of the cutting edge rounding using flexible bond diamond polishing tools is introduced. Hence, the conducted research in this study analyzes the basic mechanisms and influencing factors using the new preparation method. For this purpose, polishing tests are carried out on carbide indexable inserts. The results show that the polishing tools can be used to create both asymmetrical and symmetrical roundings in an industrially relevant dimension. © 2019 The Authors. Published by Elsevier B.V