131 research outputs found

    Self-stabilizing network orientation algorithms in arbitrary rooted networks

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    Network orientation is the problem of assigning different labels to the edges at each processor, in a globally consistent manner. A self-stabilizing protocol guarantees that the system will arrive at a legitimate state in finite time, irrespective of the initial state of the system. Two deterministic distributed network orientation protocols on arbitrary rooted, asynchronous networks are proposed in this work. Both protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state in which every processor has a valid node label and every link has a valid edge label. The first protocol assumes an underlying depth-first token circulation protocol; it orients the network as the token is passed among the nodes and stabilizes in O(n) steps after the token circulation stabilizes, where n is the number of processors in the network. The second protocol is designed on an underlying spanning tree protocol and stabilizes in O(h) time, after the spanning tree is constructed, where h is the height of the spanning tree. Although the second protocol assumes the existence of a spanning tree of the rooted network, it orients all edges--both tree and non-tree edges--of the network

    Hearing the Tonality in Microtonality

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    In the late 1970s and 1980s, composer-pianist Easley Blackwood wrote a series of microtonal compositions exploring the tonal and modal behavior of a dozen non–twelve-tone equal temperaments, ranging from 13 to 24 tones per octave. This dissertation investigates a central paradox of Blackwood’s microtonal music: that despite being full of intervals most Western listeners have never heard before, it still seems to “make sense” in nontrivial ways. Much of this has to do with the music’s idiosyncratic approach to tonality, which I define as a regime of culturally conditioned expectations that guides one’s attentional processing of music’s gravitational qualities over time. More specifically, Blackwood configures each tuning’s unfamiliar elements in ways that correspond to certain schematic expectations Western listeners tend to have about how tonal music “works.” This is why it is still possible to hear the forest of tonality in this music, so to speak, despite the odd-sounding trees that comprise it. Because of its paradoxical blend of expectational conformance and expectational noncompliance, Blackwood’s microtonal music makes for a useful tool to snap most Western-enculturated listeners out of their ingrained modes of musical processing and reveal certain things about tonality that are often taken for granted. Accordingly, just as Blackwood writes conventional-sounding music in unconventional tunings, this dissertation rethinks several familiar music-theoretic terms and concepts through the defamiliarizing lens of microtonality. I use Blackwood’s microtonal music as a prism to shine a light on traditional theories of tonality, scale degrees, consonance and dissonance, and harmonic function, arguing that many of these theories rely on assumptions that are tacitly tied to twelve-tone equal temperament and common-practice major/minor music. By unhooking these terms and concepts from any one specific tuning or historical period, I build up a set of analytical tools that can allow one to engage more productively with the many modalities of tonality typically heard on a daily basis today. This dissertation proceeds in six chapters. The four interior chapters each center on one of the terms and concepts mentioned above: scale degrees (Chapter 2), consonance and dissonance (Chapter 3), harmonic function (Chapter 4), and tonality (Chapter 5). In Chapter 2, I propose a system for labeling scale degrees that can provide more nuance and flexibility when reckoning with music in any diatonic mode (and in any tuning). In Chapter 3, I advance an account of consonance and dissonance as expectational phenomena (rather than purely psychoacoustic ones), and I consider the ways that non-pitched elements such as meter and notation can act as “consonating” and/or “dissonating” forces. In Chapter 4, I characterize harmonic function as arising from the interaction of generic scalar position and metrical position, and I devise a system for labeling harmonic functions that is better attuned to affective differences across the diatonic modes. In Chapter 5, I synthesize these building blocks into a conception of fuzzy heptatonic diatonic tonality that links together not only all of Blackwood’s microtonal compositions but also more familiar musics that use a twelve-tone octave, from Euroclassical to popular styles. The outer chapters are less explicitly music-analytical in focus. Chapter 1 introduces readers to Blackwood’s compositional approach and notational system, considers the question of his intended audience, and discusses the ways that enculturation mediates the cognition of microtonality (and of unfamiliar music more generally). Chapter 6 draws upon archival documents to paint a more detailed picture of who Blackwood was as a person and how his idiosyncratic worldview colors his approach to composition, scholarship, and interpersonal interaction. While my nominal focus in these six chapters is Blackwood’s microtonal music, the repertorial purview of my project is far broader. One of my guiding claims throughout is that attending more closely to the paradoxes and contradictions of Blackwood’s microtonality can help one better understand the musics they are accustomed to hearing. For this reason, I frequently compare moments in Blackwood’s microtonal music to ones in more familiar styles to highlight unexpected analogies and point up common concerns. Sharing space with Blackwood in the pages that follow are Anita Baker, Ornette Coleman, Claude Debussy, and Richard Rodgers, among others—not to mention music from Curb Your Enthusiasm, Fortnite, Sesame Street, and Star Wars. Ultimately, this project is a testament to the value of stepping outside of one’s musical comfort zone. For not only can this reveal certain things about that comfort zone that would not be apparent otherwise, but it can also help one think with greater nuance, precision, and (self-)awareness when “stepping back in” to reflect upon the music they know and love

    08431 Abstracts Collection -- Moderately Exponential Time Algorithms

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    From 19/10/200819/10/2008 to 24/10/200824/10/2008, the Dagstuhl Seminar 08431 ``Moderately Exponential Time Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    Multicasting in All-Optical WDM Networks

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    n this dissertation, we study the problem of (i) routing and wavelength assignment, and (ii) traffic grooming for multicast traffic in Wavelength Division Multiplexing (WDM) based all-optical networks. We focus on the 'static' case where the set of multicast traffic requests is assumed to be known in advance. For the routing and wavelength assignment problem, we study the objective of minimizing the number of wavelengths required; and for the traffic grooming problem, we study the objectives of minimizing (i) the number of wavelengths required, and (ii) the number of electronic components required. Both the problems are known to be hard for general fiber network topologies. Hence, it makes sense to study the problems under some restrictions on the network topology. We study the routing and wavelength assignment problem for bidirected trees, and the traffic grooming problem for unidirectional rings. The selected topologies are simple in the sense that the routing for any multicast traffic request is trivially determined, yet complex in the sense that the overall problems still remain hard. A motivation for selecting these topologies is that they are of practical interest since most of the deployed optical networks can be decomposed into these elemental topologies. In the first part of the thesis, we study the the problem of multicast routing and wavelength assignment in all-optical bidirected trees with the objective of minimizing the number of wavelengths required in the network. We give a 5/2-approximation algorithm for the case when the degree of the bidirected tree is at most 3. We give another algorithm with approximation ratio 10/3, 3 and 2 for the case when the degree of the bidirected tree is equal to 4, 3 and 2, respectively. The time complexity analysis for both these algorithms is also presented. Next we prove that the problem is hard even for the two restricted cases when the bidirected tree has (i) depth 2, and (ii) degree 2. Finally, we present another hardness result for a related problem of finding the clique number for a class for intersection graphs. In the second part of the thesis, we study the problem of multicast traffic grooming in all-optical unidirectional rings. For the case when the objective is to minimize the number of wavelengths required in the network, given an 'a'-approximation algorithm for the circular arc coloring problem, we give an algorithm having asymptotic approximation ratio 'a' for the multicast traffic grooming problem. We develop an easy to calculate lower bound on the minimum number of electronic components required to support a given set of multicast traffic requests on a given unidirectional ring network. We use this lower bound to analyze the worst case performance of a pair of simple grooming schemes. We also study the case when no grooming is carried out in order to get an estimate on the maximum number of electronic components that can be saved by applying intelligent grooming. Finally, we present a new grooming scheme and compare its average performance against other grooming schemes via simulations. The time complexity analysis for all the grooming schemes is also presented

    Scheduling algorithms for throughput maximization in data networks

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 215-226).This thesis considers the performance implications of throughput optimal scheduling in physically and computationally constrained data networks. We study optical networks, packet switches, and wireless networks, each of which has an assortment of features and constraints that challenge the design decisions of network architects. In this work, each of these network settings are subsumed under a canonical model and scheduling framework. Tools of queueing analysis are used to evaluate network throughput properties, and demonstrate throughput optimality of scheduling and routing algorithms under stochastic traffic. Techniques of graph theory are used to study network topologies having desirable throughput properties. Combinatorial algorithms are proposed for efficient resource allocation. In the optical network setting, the key enabling technology is wavelength division multiplexing (WDM), which allows each optical fiber link to simultaneously carry a large number of independent data streams at high rate. To take advantage of this high data processing potential, engineers and physicists have developed numerous technologies, including wavelength converters, optical switches, and tunable transceivers.(cont.) While the functionality provided by these devices is of great importance in capitalizing upon the WDM resources, a major challenge exists in determining how to configure these devices to operate efficiently under time-varying data traffic. In the WDM setting, we make two main contributions. First, we develop throughput optimal joint WDM reconfiguration and electronic-layer routing algorithms, based on maxweight scheduling. To mitigate the service disruption associated with WDM reconfiguration, our algorithms make decisions at frame intervals. Second, we develop analytic tools to quantify the maximum throughput achievable in general network settings. Our approach is to characterize several geometric features of the maximum region of arrival rates that can be supported in the network. In the packet switch setting, we observe through numerical simulation the attractive throughput properties of a simple maximal weight scheduler. Subsequently, we consider small switches, and analytically demonstrate the attractive throughput properties achievable using maximal weight scheduling. We demonstrate that such throughput properties may not be sustained in larger switches.(cont.) In the wireless network setting, mesh networking is a promising technology for achieving connectivity in local and metropolitan area networks. Wireless access points and base stations adhering to the IEEE 802.11 wireless networking standard can be bought off the shelf at little cost, and can be configured to access the Internet in minutes. With ubiquitous low-cost Internet access perceived to be of tremendous societal value, such technology is naturally garnering strong interest. Enabling such wireless technology is thus of great importance. An important challenge in enabling mesh networks, and many other wireless network applications, results from the fact that wireless transmission is achieved by broadcasting signals through the air, which has the potential for interfering with other parts of the network. Furthermore, the scarcity of wireless transmission resources implies that link activation and packet routing should be effected using simple distributed algorithms. We make three main contributions in the wireless setting. First, we determine graph classes under which simple, distributed, maximal weight schedulers achieve throughput optimality.(cont.) Second, we use this acquired knowledge of graph classes to develop combinatorial algorithms, based on matroids, for allocating channels to wireless links, such that each channel can achieve maximum throughput using simple distributed schedulers. Third, we determine new conditions under which distributed algorithms for joint link activation and routing achieve throughput optimality.by Andrew Brzezinski.Ph.D

    Subject index volumes 1–92

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