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Broadcasting in Unlabeled Tori
Parallel Processing Letters, 1998We consider broadcasting a message from one node to all other nodes of an asynchronous totally unlabeled torus: neither nodes nor links have a priori assigned labels but they know the topology and the size of the torus. Nodes can send messages of arbitrary size and we are interested in minimizing the total number of messages.
Krzysztof Diks +2 more
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Bulletin of the London Mathematical Society, 1969
In the preprint [2] of Kirby and Siebenmann, it is shown that vanishes for / # 3 and has order at most 2 in that case. It is further shown that isotopy classes of PL structures on a topological manifold of dimension ^ 5 correspond bijectively to reductions from Top to PL of the structure group of its stable tangent bundle.
Hsiang, W.-C., Wall, C. T. C.
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In the preprint [2] of Kirby and Siebenmann, it is shown that vanishes for / # 3 and has order at most 2 in that case. It is further shown that isotopy classes of PL structures on a topological manifold of dimension ^ 5 correspond bijectively to reductions from Top to PL of the structure group of its stable tangent bundle.
Hsiang, W.-C., Wall, C. T. C.
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The Annals of Mathematics, 1961
Introduction ? 0. Notation and conventions ? 1. Arbitrary fields 1.1. Duality 1.2. Splitting fields 1.3. Isogenies 1.4. Raising the field of definition 1.5. A structure theorem 1.6. Differential forms ? 2. Local fields 2.1. Maximal compact groups 2.2. Isogenies 2.3. Reduction modulo p ? 3. Fields of dimension 1 3.1. Adelization 3.2.
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Introduction ? 0. Notation and conventions ? 1. Arbitrary fields 1.1. Duality 1.2. Splitting fields 1.3. Isogenies 1.4. Raising the field of definition 1.5. A structure theorem 1.6. Differential forms ? 2. Local fields 2.1. Maximal compact groups 2.2. Isogenies 2.3. Reduction modulo p ? 3. Fields of dimension 1 3.1. Adelization 3.2.
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IEEE Transactions on Information Theory, 1997
Summary: In this correspondence it is shown how the elements of finite fields when mapped on the surface of a torus can be used for block coding over a three-dimensional signal space. The block codes are useful for data transmission using the recently defined Mannheim distance.
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Summary: In this correspondence it is shown how the elements of finite fields when mapped on the surface of a torus can be used for block coding over a three-dimensional signal space. The block codes are useful for data transmission using the recently defined Mannheim distance.
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2007
We show that face routing, the well-known local routing algorithm for plane graphs introduced by Kranakis and Urrutia, does not in fact succeed for embedded graphs on the torus or higher genus surfaces (contrary to conjecture). We then describe a generalization of face routing, and prove that this algorithm does provide a local routing algorithm for ...
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We show that face routing, the well-known local routing algorithm for plane graphs introduced by Kranakis and Urrutia, does not in fact succeed for embedded graphs on the torus or higher genus surfaces (contrary to conjecture). We then describe a generalization of face routing, and prove that this algorithm does provide a local routing algorithm for ...
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