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Article: New Doubling Spanners: Better and Simpler
Title | New Doubling Spanners: Better and Simpler |
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Authors | |
Keywords | Arya et al. Stoc 1995 conjecture Fault-tolerant doubling spanners Lightness Optimal hop-diameter Small degree |
Issue Date | 2015 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sicomp.php |
Citation | SIAM Journal on Computing, 2015, v. 44 n. 1, p. 37-53 How to Cite? |
Abstract | In a seminal STOC 1995 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 $O(log n) cdot w({MST}))$ 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 2013. In fact, Elkin and Solomon proved that the conjecture of Arya et al. holds even in doubling metrics. However, Elkin and Solomon's spanner construction is complicated. In this work we present a significantly simpler construction of spanners for doubling metrics with the same guarantees as above. Our construction is based on the basic net-tree spanner framework. However, by employing well-known properties of the net-tree spanner in conjunction with numerous new ideas, we managed to get significantly stronger results. First and foremost, 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 $O(k^2 log n)$. This is the first construction of fault-tolerant spanners (even for Euclidean metrics) that achieves good bounds (polylogarithmic in $n$ and polynomial in $k$) on all the involved parameters simultaneously. Second, we show that the lightness bound of our construction can be improved to $O(k^2)$ (with high probability), for random points in $[0,1]^D$, where $2 le D = O(1)$. © 2015, Society for Industrial and Applied Mathematics |
Persistent Identifier | http://hdl.handle.net/10722/215509 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 2.143 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chan, THH | - |
dc.contributor.author | Li, M | - |
dc.contributor.author | Ning, L | - |
dc.contributor.author | Solomon, S | - |
dc.date.accessioned | 2015-08-21T13:28:28Z | - |
dc.date.available | 2015-08-21T13:28:28Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | SIAM Journal on Computing, 2015, v. 44 n. 1, p. 37-53 | - |
dc.identifier.issn | 0097-5397 | - |
dc.identifier.uri | http://hdl.handle.net/10722/215509 | - |
dc.description.abstract | In a seminal STOC 1995 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 $O(log n) cdot w({MST}))$ 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 2013. In fact, Elkin and Solomon proved that the conjecture of Arya et al. holds even in doubling metrics. However, Elkin and Solomon's spanner construction is complicated. In this work we present a significantly simpler construction of spanners for doubling metrics with the same guarantees as above. Our construction is based on the basic net-tree spanner framework. However, by employing well-known properties of the net-tree spanner in conjunction with numerous new ideas, we managed to get significantly stronger results. First and foremost, 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 $O(k^2 log n)$. This is the first construction of fault-tolerant spanners (even for Euclidean metrics) that achieves good bounds (polylogarithmic in $n$ and polynomial in $k$) on all the involved parameters simultaneously. Second, we show that the lightness bound of our construction can be improved to $O(k^2)$ (with high probability), for random points in $[0,1]^D$, where $2 le D = O(1)$. © 2015, Society for Industrial and Applied Mathematics | - |
dc.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sicomp.php | - |
dc.relation.ispartof | SIAM Journal on Computing | - |
dc.rights | © 2015 Society for Industrial and Applied Mathematics. First Published in SIAM Journal on Computing in volume 44, issue 1, published by the Society for Industrial and Applied Mathematics (SIAM). | - |
dc.subject | Arya et al. Stoc 1995 conjecture | - |
dc.subject | Fault-tolerant doubling spanners | - |
dc.subject | Lightness | - |
dc.subject | Optimal hop-diameter | - |
dc.subject | Small degree | - |
dc.title | New Doubling Spanners: Better and Simpler | - |
dc.type | Article | - |
dc.identifier.email | Chan, THH: hubert@cs.hku.hk | - |
dc.identifier.authority | Chan, THH=rp01312 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1137/130930984 | - |
dc.identifier.scopus | eid_2-s2.0-84923767323 | - |
dc.identifier.hkuros | 247361 | - |
dc.identifier.volume | 44 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 37 | - |
dc.identifier.epage | 53 | - |
dc.identifier.isi | WOS:000353967100002 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0097-5397 | - |