An Improved Upper Bound for the Ring Loading Problem

The Ring Loading Problem emerged in the 1990s to model an important special case of telecommunication networks (SONET rings) which gained attention from practitioners and theorists alike. Given an undirected cycle on $n$ nodes together with non-negative demands between any pair of nodes, the Ring Loading Problem asks for an unsplittable routing of the demands such that the maximum cumulated demand on any edge is minimized. Let $L$ be the value of such a solution. In the relaxed version of the problem, each demand can be split into two parts where the first part is routed clockwise while the second part is routed counter-clockwise. Denote with $L^*$ the maximum load of a minimum split routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98] showed that $L \leq L^* + 1.5D$, where $D$ is the maximum demand value. They also found (implicitly) an instance of the Ring Loading Problem with $L = L^* + 1.01D$. Recently, Skutella [Sku16] improved these bounds by showing that $L \leq L^* + \frac{19}{14}D$, and there exists an instance with $L = L^* + 1.1D$. We contribute to this line of research by showing that $L \leq L^* + 1.3D$. We also take a first step towards lower and upper bounds for small instances

Partitioning problems in parallel, pipelined and distributed computing

The problem of optimally assigning the modules of a parallel program over the processors of a multiple computer system is addressed. A Sum-Bottleneck path algorithm is developed that permits the efficient solution of many variants of this problem under some constraints on the structure of the partitions. In particular, the following problems are solved optimally for a single-host, multiple satellite system: partitioning multiple chain structured parallel programs, multiple arbitrarily structured serial programs and single tree structured parallel programs. In addition, the problems of partitioning chain structured parallel programs across chain connected systems and across shared memory (or shared bus) systems are also solved under certain constraints. All solutions for parallel programs are equally applicable to pipelined programs. These results extend prior research in this area by explicitly taking concurrency into account and permit the efficient utilization of multiple computer architectures for a wide range of problems of practical interest

The radiating part of circular sources

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is limited, with the limit fixed by the wavenumber of source multiplied by the source radius (Helmholtz number). The acoustic field is found in terms of the elementary fields generated by a set of line sources whose form is given by Chebyshev polynomials of the second kind, and whose amplitude is found to be given by weighted integrals of the radial source term. The analysis is developed for tonal sources, such as rotors, and, for Helmholtz number less than two, for random disk sources. In this case, the analysis yields the cross-spectrum between two points in the acoustic field. The analysis is applied to the problems of tonal radiation, random source radiation as a model problem for jet noise, and to noise cancellation, as in active control of noise from rotors. It is found that the approach gives an accurate model for the radiation problem and explicitly identifies those parts of a source which radiate.Comment: Submitted to Journal of the Acoustical Society of Americ

Analysis of Flexural Strength and Contact Pressure After Simulated Chairside Adjustment of Pressed Lithium Disilicate Glass-Ceramic

Statement of problem Research evaluating load-to-failure of pressed lithium disilicate glass-ceramic (LDGC) with a clinically validated test after adjustment and repair procedures is scarce. Purpose The purpose of this in vitro study was to investigate the effect of the simulated chairside adjustment of the intaglio surface of monolithic pressed LDGC and procedures intended to repair damage. Material and methods A total of 423 IPS e.max Press (Ivoclar Vivadent AG) disks (15 mm diameter, 1 mm height) were used in the study. The material was tested by using an equibiaxial loading arrangement (n≥30/group) and a contact pressure test (n≥20/group). Specimens were assigned to 1 of 14 groups. One-half was assigned to the equibiaxial load test and the other half underwent contact pressure testing. Testing was performed in 2 parts, before glazing and after glazing. Before-glazing specimens were devested and entered in the test protocol, while after-glazing specimens were devested and glazed before entering the test protocol. Equibiaxial flexure test specimens were placed on a ring-on-ring apparatus and loaded until failure. Contact pressure specimens were cemented to epoxy resin blocks with a resin cement and loaded with a 50-mm diameter hemisphere until failure. Tests were performed on a universal testing machine with a crosshead speed of 0.5 mm/min. Weibull statistics and likelihood ratio contour plots determined intergroup differences (95% confidence bounds). Results Before glazing, the equibiaxial flexural strength test and the Weibull and likelihood ratio contour plots demonstrated a significantly higher failure strength for 1EC (188 MPa) than that of the damaged and/or repaired groups. Glazing following diamond-adjustment (1EGG) was the most beneficial post-damage procedure (176 MPa). Regarding the contact pressure test, the Weibull and likelihood ratio contour plots revealed no significant difference between the 1PC (98 MPa) and 1PGG (98 MPa) groups. Diamond-adjustment, without glazing (1EG and 1PG), resulted in the next-to-lowest equibiaxial flexure strength and the lowest contact pressure. After glazing, the strength of all the groups, when subjected to glazing following devesting, increased in comparison with corresponding groups in the before-glazing part of the study. Conclusions A glazing treatment improved the mechanical properties of diamond-adjusted IPS e.max Press disks when evaluated by equibiaxial flexure and contact pressure tests. Clinical Implications When adjustments are made on the intaglio surface of a pressed lithium disilicate glass-ceramic, a subsequent glazing treatment is recommended to improve strength

The Price of Anarchy for Selfish Ring Routing is Two

We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page

Main rotor-tail rotor intraction and its implications for helicopter directional control

Aerodynamic interference between the main and tail rotor can have a strong negative influence on the flight mechanics of a conventional helicopter. Significant unsteadiness in the tail rotor loading is encountered under certain flight conditions, but the character of the unsteadiness can depend on the direction of rotation of the tail rotor. Numerical simulations, using Brown's vorticity transport model, of the aerodynamic interaction between the main and tail rotors of a helicopter are presented for a range of forward and lateral flight trajectories. Distinct differences are predicted in the behavior of the system in left and right sideward flight that are consistent with flight experience that the greatest fluctuations in loading or control input are required in left sideways flight (for a counterclockwise rotating main rotor). These fluctuations are generally more extreme for a system with tail rotor rotating top-forward than top-aft. Differences are also exposed in the character of the lateral excitation of the system as forward flight speed is varied. The observed behavior appears to originate in the disruption of the tail rotor wake that is induced by its entrainment into the wake of the main rotor. The extent of the disruption is dependent on flight condition, and the unsteadiness of the process depends on the direction of rotation of the tail rotor. In intermediate-speed forward flight and right sideward flight, the free stream delays the entrainment of the tail rotor wake far enough downstream for the perturbations to the rotor loading to be slight. Conversely, in left sideward and quartering flight, the free stream confines the entrainment process close to the rotors, where it causes significant unsteadiness in the loads produced by the system