Robust capacitated Steiner trees and networks with uniform demands

Synopsis A numerical method, based on ø=0 circular slip analysis, is used to evaluate the ultimate bearing capacity of a normally-consolidated soil, after complete consolidation under a preload. This is compared with the immediate bearing capacity of the same soil to determine the increase in bearing capa- city resulting from consolidation. Cases of complete failure and failure involving part only of the loaded area (edge failure) are both considered. The increase depends on soil properties but is found to be much smaller for edge failure than for complete failure. Case histories are cited of oil tanks on soft soils where water preload has been applied and where incipient edge failure has occurred. Results of analyses are presented in chart form from which the value of preloading as a means of increasing bearing capacity may be assessed for practical cases. On utilise une méthode numérique, basée sur une analyse du glissement circulaire pour ø=O, pour évaluer la portance maximale d'un sol consolidé normalement, aprés sa consolidation complète sous une précharge. On la compare à la portance immédiate du même sol pour determiner l'augmentation de la portance résultant de la consolidation. On considère à la foisdes exemples de rupture complète et des exemples de rupture mettant en jeu une partie seulement de la surface en charge (rupture en coin). L'augmentation dèpend des propriétés du sol, mais on a trouvé qu'elle était beaucoup plus faible pour la rupture en coin que pour la rupture compléte. On donne des exemples pratiques de reservoires d'huile sur des sols mous auxquels on avait appliqué une précharge d'eau, et où l'on avait observe un commencement de rupture en coin. On présente les résultats des analyses sous forme de graphiques à. partir desquels on peut évaluer pour des exemples pratiques la valeur de l'operation de précharge comme moyen d'augmenter la portance.

Designing networks with resiliency to edge failures using two-stage robust optimization

We investigate benefits of backup reprovisioning after network-state updates in survivable mesh networks. Our approach achieves good capacity utilization and network robustness. We study tradeoff between capacity optimization and computation/reconfiguration overhead with different reprovisioning periods.

Robustness of complex networks has attracted much attention in diverse disciplines. Most of previous studies did not consider the attack cost. In this paper, the network robustness is studied with the consideration of attack cost, with different complex network models and different robustness indices. It is found that with different cost function and attack budget, the best attack strategy changes. When the budget is low and attacking hubs costs much more than attacking an unimportant node, then the high-degree attack (HDA) strategy performs worse than the low-degree attack (LDA) strategy. On the contrary, HDA is always a better strategy when the budget is high. Therefore, there is an intersection before and after that different attack strategies perform better. The position of this intersection is affected by the network structure, robustness index, cost function and the budget.

Most studies addressing translucent network design targeted a tradeoff between minimizing the number of deployed regenerators and minimizing the number of regeneration nodes. The latter highly depends on the carrier’s strategy and is motivated by various considerations such as power consumption, maintenance and supervision costs. However, concentrating regenerators into a small number of nodes exposes the network to a high risk of data loss in the eventual case of regenerator pool failure. In this paper, we address the problem of survivable translucent network design taking into account the simultaneous effect of four transmission impairments. We propose an exact approach based on a mathematical formulation to solve the problem of regenerator placement while ensuring the network survivability in the hazardous event of a regenerator pool failure. For this purpose, for each accepted request requiring regeneration, we determine several routing paths along with associated valid wavelengths going through different regeneration nodes. In doing so, we implement an M : N shared regenerator protection scheme. Simulation results highlight the gain obtained by reducing the number of regeneration nodes without sacrificing network survivability.

Spatial data structures form a core ingredient of many geometric algorithms, both in theory and in practice. Many of these data structures, especially the ones used in practice, are based on partitioning the underlying space (examples are binary space partitions and decompositions of polygons) or partitioning the set of objects (examples are bounding-volume hierarchies). The efficiency of such data structures---and, hence, of the algorithms that use them---depends on certain characteristics of the partitioning. For example the performance of many algorithms that use binary space partitions (BSPs) depends on the size of the BSPs. Similarly, the performance of answering range queries using bounding-volume hierarchies (BVHs) depends on the so-called crossing number that can be associated with the partitioning on which the BVH is based. Much research has been done on the problem of computing partitioning whose characteristics are good in the worst case. In this thesis, we studied the problem from a different point of view, namely instance-optimality. In particular, we considered the following question: given a class of geometric partitioning structures---like BSPs, simplicial partitions, polygon triangulations, …---and a cost function---like size or crossing number---can we design an algorithm that computes a structure whose cost is optimal or close to optimal for any input instance (rather than only worst-case optimal). We studied the problem of finding optimal data structures for some of the most important spatial data structures. As an example having a set of n points and an input parameter r, It has been proved that there are input sets for which any simplicial partitions has crossing number ¿(vr). It has also been shown that for any set of n input points and the parameter r one can make a simplicial partition with stabbing number O(vr). However, there are input point sets for which one can make simplicial partition with lower stabbing number. As an example when the points are on a diagonal, one can always make a simplicial partition with stabbing number 1. We started our research by studying BSPs for line segments in the plane, where the cost function is the size of the BSPs. A popular type of BSPs for line segments are the so-called auto-partitions. We proved that finding an optimal auto-partition is NP-hard. In fact, finding out if a set of input segments admits an auto-partition without any cuts is already NP-hard. We also studied the relation between two other types of BSPs, called free and restricted BSPs, and showed that the number of cuts of an optimal restricted BSP for a set of segments in R2 is at most twice the number of cuts of an optimal free BSP for that set. The details are being represented in Chapter 1 of the thesis. Then we turned our attention to so-called rectilinear r-partitions for planar point sets, with the crossing number as cost function. A rectilinear r-partition of a point set P is a partitioning of P into r subsets, each having roughly |P|/r points. The crossing number of the partition is defined using the bounding boxes of the subsets; in particular, it is the maximum number of bounding boxes that can be intersected by any horizontal or vertical line. We performed some theoretical as well as experimental studies on rectilinear r-partitions. On the theoretical side, we proved that computing a rectilinear r-partition with optimal stabbing number for a given set of points and parameter r is NP-hard. We also proposed an exact algorithm for finding optimal rectilinear r-partitions whose running time is polynomial when r is a constant, and a faster 2-approximation algorithm. Our last theoretical result showed that considering only partitions whose bounding boxes are disjoint is not sufficient for finding optimal rectilinear r-partitions. On the experimental side, we performed a comparison between four different heuristics for constructing rectilinear r-partitions. The so-called windmill KD-tree gave the best results. Chapter 2 of the thesis describes all the details of our research on rectilinear r-partitions. We studied another spatial data structure in Chapter 3 of the thesis. Decomposition of the interior of polygons is one of the fundamental problems in computational geometry. In case of a simple polygon one usually wants to make a Steiner triangulation of it, and when we have a rectilinear polygon at hand, one typically wants to make a rectilinear decomposition for it. Due to this reason there are algorithms which make Steiner triangulations and rectangular decompositions with low stabbing number. These algorithms are worst-case optimal. However, similar to the two previous data structures, there are polygons for which one can make decompositions with lower stabbing numbers. In 3 we proposed a 3-approximation for finding an optimal rectangular decomposition of a rectilinear polygon. We also proposed an O(1)-approximation for finding optimal Steiner triangulation of a simple polygon. Finally, in Chapter 4 of the thesis, we considered another optimization problem, namely how to approximate a piecewise-linear function F: R ¿R with another piecewise-linear function with fewer pieces. Here one can distinguish two versions of the problem. The first one is called the min-k problem; the goal is then to approximate the function within a given error e such that the resulting function has the minimum number of links. The second one is called the min-e problem; here the goal is to find an approximation with at most k links (for a given k) such that the error is minimized. These problems have already been studied before. Our contribution is to consider the problem for so-called uncertain functions, where the value of the input function F at its vertices is given as a discrete set of different values, each with an associated probability. We show how to compute an approximation that minimizes the expected error.

Hierarchical approach for survivable network design

An improved approximation algorithm for the partial-terminal Steiner tree problem with edge cost 1 or 2

Modifying edges of a network to obtain short subgraphs

This paper proposes a multiple adaptive notch filter with the p‐th power average of the estimated error E[ep(n)] ‖as the cost function. The adaptive filter consists of a cascade connection of second‐order adaptive notch filters composed of the allpass filters. In general, the elimination bandwidth of the notch filter is desirably small from the practical point of view. However, as the elimination bandwidth is set smaller, the convergence speed of the tap coefficients of the adaptive filter becomes much slower. From the point of view of convergence theory, the radius of the pole of the second‐order allpass filter needs to be close to 1, so that the elimination bandwidth must be extremely small. Convergence speed must be sacrificed due to the practical and theoretical points of view. In this paper, an adaptive notch filter is studied in which the elimination bandwidth of the notch filter is designed small while the gradient of the tap vector of the cost function used in the adaptive algorithm is made effectively equal to the case in which the elimination bandwidth is rather large. In this way, realization of a multiple adaptive notch filter with a high convergence is possible. The absolute value of the transfer function of the notch filter is close to 0 near the elimination frequency while it is close to 1 at other frequencies. Hence, by setting the power of the absolute value larger, the elimination bandwidth becomes larger and the smoothness near the elimination frequency is increased. By means of the gradient algorithm with a cost function E[ep(n)], this property can be utilized so that excellent convergence speed and steady‐state characteristics can be obtained. Finally, verification of the analytical results and comparison with the conventional method are carried out by computer simulation. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(8): 1–8, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10162

The frequency and severity of natural disasters is surging, posing an urgent need for robust communication network infrastructure that is capable of withstanding these events. In this paper, we present a groundbreaking graph-theoretic system designed to evaluate and enhance network resilience in the face of natural disasters. Our solution harnesses the power of topological robustness metrics, integrating real-time weather data, geographic information, detailed network topology data, advanced resilience algorithms, and continuous network monitoring. The proposed scheme considers four major real-world U.S.-based network providers and evaluates their physical topologies against two major hurricanes. Our novel framework quantifies the important characteristics of network infrastructure; for instance, AT&T is identified to have fared better against Hurricane Ivan (57.98 points) than Hurricane Katrina (39.17 points). We not only provide current insights into network infrastructure resilience, but also uncover valuable findings that shed light on the performance of backbone U.S. networks during hurricanes. Furthermore, our findings provide actionable insights to enrich the overall survivability and functionality of communication networks, mitigating the adverse impacts of natural disasters on communication systems and critical services in terms of improving network resiliency via adding additional nodes and link or rewiring.

We consider the least-squares (L2) minimization problems in multiple view geometry for triangulation, homography, camera resectioning and structure-and-motion with known rotation, or known plane. Although optimal algorithms have been given for these problems under an L-infinity cost function, finding optimal least-squares solutions to these problems is difficult, since the cost functions are not convex, and in the worst case may have multiple minima. Iterative methods can be used to find a good solution, but this may be a local minimum. This paper provides a method for verifying whether a local-minimum solution is globally optimal, by providing a simple and rapid test involving the Hessian of the cost function. The basic idea is that by showing that the cost function is convex in a restricted but large enough neighbourhood, a sufficient condition for global optimality is obtained. The method is tested on numerous problem instances of real data sets. In the vast majority of cases we are able to verify that the solutions are optimal, in particular, for small to medium-scale problems.

Robustness analysis of logical networks and its application in infinite systems

: The intent of this program was to investigate how single mode fiber optic technology can support a flexible, redundant and therefore robust (survivable) network. This study focused on the signal processing that should be performed at the optical receiver to properly combine the signals received from various paths and the system performance that could be achieved by such processing. As a result of wideband optical technology it is reasonable to use multiple paths in fiber optic broadcast network to achieve simplicity and robustness. This leads to problems of how to reconcile signals received over multiple paths. The study examined the performance of fiber optics networks with incoherent sources and multiple paths. The networks were modeled as having either a fixed number of equal strength paths or an infinite number of paths with exponentially decreasing strengths.

Simulating dynamic RUL based CBM scheduling. A case study in the railway sector