In a seminal STOC'95 paper, Arya et al. conjectured that spanners for low-dimensional Euclidean spaces with constant maximum degree, hop-diameter O(log n) and lightness O(log n) (i.e., weight O(log n) • ω(MST)) can be constructed in O(n log n) time. This conjecture, which became a central open question in this area, was resolved in the affirmative by Elkin and Solomon in STOC'13 (even for doubling metrics). In this work we present a simpler construction of spanners for doubling metrics with the above guarantees. Moreover, our construction extends in a simple and natural way to provide k-fault tolerant spanners with maximum degree O(k~2), hop-diameter O(log n) and lightness O(k~2 log n).
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机译:在STOC'95的开创性论文中,Arya等人。推测可以在O( n log n)时间。这个猜想成为该领域的一个主要公开问题,埃尔金和所罗门(Elkin)和所罗门(Solomon)在STOC'13中肯定地解决了这个问题(即使是将指标加倍)。在这项工作中,我们提出了一种使用上述保证将扳手加倍的更简单的扳手结构。此外,我们的结构以简单自然的方式扩展,可为k容错扳手提供最大度数O(k〜2),跃点直径O(log n)和明度O(k〜2 log n)。
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