Abstract
In a seminal STOC’95 paper, Arya et al. conjectured that spanners for low-dimensional Euclidean spaces with constant maximum degree, hop-diameter O(logn) and lightness O(logn) (i.e., weight \(O(\log n) \cdot w(\textsf{MST}))\) can be constructed in O(n logn) 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(logn) and lightness O(k 2 logn).
This work is supported by the Koshland Center for basic Research.
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Chan, T.H.H., Li, M., Ning, L., Solomon, S. (2013). New Doubling Spanners: Better and Simpler. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_27
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DOI: https://doi.org/10.1007/978-3-642-39206-1_27
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