Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments

Circulation around a thin zonal island

Author Posting. © Cambridge University Press, 2001. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 437 (2001): 301-323, doi:10.1017/S0022112001004402.Laboratory and numerical experiments are used to study flow of a uniform-density fluid on the [beta]-plane around a thin zonally elongated island (or ridge segment in the abyss). This orientation is chosen specifically to highlight the roles of the zonal boundary layer dynamics in controlling the circulation around the island. There are examples of deep ocean topography that fall into this category which make the work directly applicable to oceanic flows. Linear theory for the transport around the island and the flow structure is based on a modification of the Island Rule (Pedlosky et al. 1997; Pratt & Pedlosky 1999). The linear solution gives a north–south symmetric flow around the island with novel features, including stagnation points which divide the zonal boundary layers into eastward and westward flowing zones, and a western boundary layer of vanishing length, and zonal jets. Laboratory experiments agree with the linear theory for small degrees of nonlinearity, as measured by the ratio of the inertial to Munk boundary layer scales. With increasing nonlinearity the north–south symmetry is broken. The southern stagnation point (for anticyclonic forcing) moves to the eastern tip of the island. The flow rounding the eastern tip from the northern side of the island now separates from the island. Time-dependence emerges and recirculation cells develop on the northern side of the island. Mean transport around the island is relatively unaffected by nonlinearity and given to within 20% by the modified Island Rule. Numerical solutions of the shallow water equations are in close agreement with the laboratory results. The transition from zonal to meridional island orientation occurs for island inclinations from zonal greater than about 20°.This work was supported by the National Science Foundation (Grant Number OCE96-16949)

Hot wire anemometer measurements in the unheated air flow tests of the SRB nozzle-to-case joint

Hot-Wire Anemometer measurements made in the Solid Rocket Booster (SRB) nozzle-to-case joint are discussed. The study was undertaken to glean additional information on the circumferential flow induced in the SRB nozzle joint and the effect of this flow on the insulation bonding flaws. The tests were conducted on a full-scale, 2-D representation of a 65-in long segment of the SRB nozzle joint, with unheated air as the working fluid. Both the flight Mach number and Reynolds number were matched simultaneously and different pressure gradients imposed along the joint face were investigated. Hot-wire anemometers were used to obtain velocity data for different joint gaps and debond configurations. The procedure adopted for hot-wire calibration and use is outlined and the results from the tests summarized

The Laplacian Paradigm in Deterministic Congested Clique

In this paper, we bring the techniques of the Laplacian paradigm to the congested clique, while further restricting ourselves to deterministic algorithms. In particular, we show how to solve a Laplacian system up to precision $\epsilon$ in $n^{o(1)}\log(1/\epsilon)$ rounds. We show how to leverage this result within existing interior point methods for solving flow problems. We obtain an $m^{3/7+o(1)}U^{1/7}$ round algorithm for maximum flow on a weighted directed graph with maximum weight $U$, and we obtain an $\tilde{O}(m^{3/7}(n^{0.158}+n^{o(1)}\text{poly}\log W))$ round algorithm for unit capacity minimum cost flow on a directed graph with maximum cost $W$. Hereto, we give a novel routine for computing Eulerian orientations in $O(\log n \log^* n)$ rounds, which we believe may be of separate interest.Comment: To be presented at the 42nd ACM Symposium on Principles of Distributed Computing (PODC 2023) as brief announcemen

Efficient Approximation Algorithms for Multi-Antennae Largest Weight Data Retrieval

In a mobile network, wireless data broadcast over $m$ channels (frequencies) is a powerful means for distributed dissemination of data to clients who access the channels through multi-antennae equipped on their mobile devices. The $\delta$-antennae largest weight data retrieval ($\delta$ALWDR) problem is to compute a schedule for downloading a subset of data items that has a maximum total weight using $\delta$ antennae in a given time interval. In this paper, we propose a ratio $1-\frac{1}{e}-\epsilon$ approximation algorithm for the $\delta$-antennae largest weight data retrieval ($\delta$ALWDR) problem that has the same ratio as the known result but a significantly improved time complexity of $O(2^{\frac{1}{\epsilon}}\frac{1}{\epsilon}m^{7}T^{3.5}L)$ from $O(\epsilon^{3.5}m^{\frac{3.5}{\epsilon}}T^{3.5}L)$ when $\delta=1$ \cite{lu2014data}. To our knowledge, our algorithm represents the first ratio $1-\frac{1}{e}-\epsilon$ approximation solution to $\delta$ALWDR for the general case of arbitrary $\delta$. To achieve this, we first give a ratio $1-\frac{1}{e}$ algorithm for the $\gamma$-separated $\delta$ALWDR ($\delta$A$\gamma$LWDR) with runtime $O(m^{7}T^{3.5}L)$, under the assumption that every data item appears at most once in each segment of $\delta$A$\gamma$LWDR, for any input of maximum length $L$ on $m$ channels in $T$ time slots. Then, we show that we can retain the same ratio for $\delta$A$\gamma$LWDR without this assumption at the cost of increased time complexity to $O(2^{\gamma}m^{7}T^{3.5}L)$. This result immediately yields an approximation solution of same ratio and time complexity for $\delta$ALWDR, presenting a significant improvement of the known time complexity of ratio $1-\frac{1}{e}-\epsilon$ approximation to the problem