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Optimal File Sharing in Distributed Networks
, 1991
"... The following le distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a le size k, an arbitrary le w of k bits is to be distributed among all nodes of G. To this end, each node is assigned a memory device such that, by accessing the mem ..."
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The following le distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a le size k, an arbitrary le w of k bits is to be distributed among all nodes of G. To this end, each node is assigned a memory device such that, by accessing the memory of its own and of its adjacent nodes, the node can reconstruct the contents of w. The objective is to minimize the total size of memory in the network. This paper presents a le distribution scheme which realizes this objective for k log G, where G stands for the maximum degree in G: For this range of k, the total memory size required by the suggested scheme approaches an integer programming lower bound on that size. The scheme is also constructive in the sense that, given G and k, the memory size at each node in G, as well as the mapping of any le w into the node memory devices, can be computed in time complexity which is polynomial in k and jV j. Furthermore, each node can reconstruct the contents of such a le w in O(k 2) bit operations. Finally, it is shown that the requirement of k being much larger than log G is necessary in order to have total memory size close to the integer programming lower bound.
New Results in Graph Layout
 School of Computer Science, Carleton Univ
, 2003
"... A track layout of a graph consists of a vertex colouring, an edge colouring, and a total order of each vertex colour class such that between each pair of vertex colour classes, there is no monochromatic pair of crossing edges. This paper studies track layouts and their applications to other models o ..."
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A track layout of a graph consists of a vertex colouring, an edge colouring, and a total order of each vertex colour class such that between each pair of vertex colour classes, there is no monochromatic pair of crossing edges. This paper studies track layouts and their applications to other models of graph layout. In particular, we improve on the results of Enomoto and Miyauchi [SIAM J. Discrete Math., 1999] regarding stack layouts of subdivisions, and give analogous results for queue layouts. We solve open problems due to Felsner, Wismath, and Liotta [Proc. Graph Drawing, 2001] and Pach, Thiele, and Toth [Proc. Graph Drawing, 1997] concerning threedimensional straightline grid drawings. We initiate the study of threedimensional polyline grid drawings and establish volume bounds within a logarithmic factor of optimal.