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Titlebook: WALCOM: Algorithms and Computation; Third International Sandip Das,Ryuhei Uehara Conference proceedings 2009 Springer-Verlag Berlin Heidel

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Minmax Tree Cover in the Euclidean Space balanced tree partitioning problem requires to cover all vertices in . by a set . of . trees of the graph so that the ratio . of . to .(..)/. is minimized, where .. denotes a minimum spanning tree of .. The problem has been used as a core analysis in designing approximation algorithms for several t
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A Separator Theorem for String Graphs and Its Applications bipartite subgraph .. has at most ... edges, where .. is a constant depending only on .. Another application is that, for any . > 0, there is an integer .(.) such that every string graph with . vertices and girth at least .(.) has at most (1 + .). edges.
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Approximating Shortest Paths in Graphsny interesting variations of the original problem..In this article, we trace some of the fundamental developments like spanners and distance oracles, their underlying constructions, as well as their applications to the approximate all-pairs shortest paths.
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