About: Logical topology is a research topic. Over the lifetime, 4089 publications have been published within this topic receiving 70347 citations.
Papers published on a yearly basis
TL;DR: This paper will discuss how geometry and topology can be applied to make useful contributions to the analysis of various kinds of data, particularly high throughput data from microarray or other sources.
Abstract: An important feature of modern science and engineering is that data of various kinds is being produced at an unprecedented rate This is so in part because of new experimental methods, and in part because of the increase in the availability of high powered computing technology It is also clear that the nature of the data we are obtaining is significantly different For example, it is now often the case that we are given data in the form of very long vectors, where all but a few of the coordinates turn out to be irrelevant to the questions of interest, and further that we don’t necessarily know which coordinates are the interesting ones A related fact is that the data is often very high-dimensional, which severely restricts our ability to visualize it The data obtained is also often much noisier than in the past and has more missing information (missing data) This is particularly so in the case of biological data, particularly high throughput data from microarray or other sources Our ability to analyze this data, both in terms of quantity and the nature of the data, is clearly not keeping pace with the data being produced In this paper, we will discuss how geometry and topology can be applied to make useful contributions to the analysis of various kinds of data Geometry and topology are very natural tools to apply in this direction, since geometry can be regarded as the study of distance functions, and what one often works with are distance functions on large finite sets of data The mathematical formalism which has been developed for incorporating geometric and topological techniques deals with point clouds, ie finite sets of points equipped with a distance function It then adapts tools from the various branches of geometry to the study of point clouds The point clouds are intended to be thought of as finite samples taken from a geometric object, perhaps with noise Here are some of the key points which come up when applying these geometric methods to data analysis • Qualitative information is needed: One important goal of data analysis is to allow the user to obtain knowledge about the data, ie to understand how it is organized on a large scale For example, if we imagine that we are looking at a data set constructed somehow from diabetes patients, it would be important to develop the understanding that there are two types of the disease, namely the juvenile and adult onset forms Once that is established, one of course wants to develop quantitative methods for distinguishing them, but the first insight about the distinct forms of the disease is key
26 Mar 2000
TL;DR: This work considers the problem of adjusting the transmit powers of nodes in a multihop wireless network as a constrained optimization problem with two constraints-connectivity and biconnectivity, and one optimization objective-maximum power used.
Abstract: We consider the problem of adjusting the transmit powers of nodes in a multihop wireless network (also called an ad hoc network) to create a desired topology. We formulate it as a constrained optimization problem with two constraints-connectivity and biconnectivity, and one optimization objective-maximum power used. We present two centralized algorithms for use in static networks, and prove their optimality. For mobile networks, we present two distributed heuristics that adaptively adjust node transmit powers in response to topological changes and attempt to maintain a connected topology using minimum power. We analyze the throughput, delay, and power consumption of our algorithms using a prototype software implementation, an emulation of a power-controllable radio, and a detailed channel model. Our results show that the performance of multihop wireless networks in practice can be substantially increased with topology control.
15 Aug 2001
TL;DR: The goal is to produce a topology generation framework which improves the state of the art and is based on the design principles of representativeness, inclusiveness, and interoperability.
Abstract: Effective engineering of the Internet is predicated upon a detailed understanding of issues such as the large-scale structure of its underlying physical topology, the manner in which it evolves over time, and the way in which its constituent components contribute to its overall function. Unfortunately, developing a deep understanding of these issues has proven to be a challenging task, since it in turn involves solving difficult problems such as mapping the actual topology, characterizing it, and developing models that capture its emergent behavior. Consequently, even though there are a number of topology models, it is an open question as to how representative the generated topologies they generate are of the actual Internet. Our goal is to produce a topology generation framework which improves the state of the art and is based on the design principles of representativeness, inclusiveness, and interoperability. Representativeness leads to synthetic topologies that accurately reflect many aspects of the actual Internet topology (e.g. hierarchical structure, node degree distribution, etc.). Inclusiveness combines the strengths of as many generation models as possible in a single generation tool. Interoperability provides interfaces to widely-used simulation applications such as ns and SSF and visualization tools like otter. We call such a tool a universal topology generator.
TL;DR: This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet.
Abstract: The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet. Two implementations that generate networks whose topology resembles that of typical internetworks are described, together with publicly available source code.
01 Jan 2002
TL;DR: In this article, the authors analyze the topology graph and evaluate generated network traffic of Gnutella and find that the current configuration has the benefits and drawbacks of a power-law structure, and that the Gnutlla virtual network topology does not match well with the underlying Internet topology, hence leading to ineffective use of the physical network infrastructure.
Abstract: Despite recent excitement generated by the peer-to-peer (P2P) paradigm and the surprisingly rapid deployment of some P2P applications, there are few quantitative evaluations of P2P systems behavior. The open architecture, achieved scale, and self-organizing structure of the Gnutella network make it an interesting P2P architecture to study. Like most other P2P applications, Gnutella builds, at the application level, a virtual network with its own routing mechanisms. The topology of this virtual network and the routing mechanisms used have a significant influence on application properties such as performance, reliability, and scalability. We have built a “crawler” to extract the topology of Gnutella’s application level network. In this paper we analyze the topology graph and evaluate generated network traffic. Our two major findings are that: (1) although Gnutella is not a pure power-law network, its current configuration has the benefits and drawbacks of a power-law structure, and (2) the Gnutella virtual network topology does not match well the underlying Internet topology, hence leading to ineffective use of the physical networking infrastructure. These findings guide us to propose changes to the Gnutella protocol and implementations that may bring significant performance and scalability improvements. We believe that our findings as well as our measurement and analysis techniques have broad applicability to P2P systems and provide unique insights into P2P system design tradeoffs.
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