New additive spanners

Shiri Chechik

doi:https://doi.org/10.1137/1.9781611973105.36

New additive spanners

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper considers additive and purely additive spanners. We present a new purely additive spanner of size Õ(n^7/5) with additive stretch 4. This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n^3/2) and the other for 6-additive spanner of size O(n ^4/3), and thus answers a main open question in this area. In addition, we present a construction for additive spanners with Õ(n ^1+δ) edges and additive stretch of Õ(n ^1/2-3δ/2) for any 3/17 ≤ δ < 1/3, improving the stretch of the existing constructions from O(n^1-3δ) to Õ(√n^1-3δ). Finally, we show that our (1,n ^1/2-3δ/2)-spanner construction can be tweaked to give a sublinear additive spanner of size Õ(n^1+3/17) with additive stretch O(√distance).

Original language	English
Title of host publication	Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
Pages	498-512
Number of pages	15
DOIs	https://doi.org/10.1137/1.9781611973105.36
State	Published - 2013
Externally published	Yes
Event	24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 - New Orleans, LA, United States Duration: 6 Jan 2013 → 8 Jan 2013

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference	24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
Country/Territory	United States
City	New Orleans, LA
Period	6/01/13 → 8/01/13

All Science Journal Classification (ASJC) codes

Software
General Mathematics

Access to Document

https://doi.org/10.1137/1.9781611973105.36

Cite this

@inproceedings{ace429fd766c4f109c92333dc3cffc34,

title = "New additive spanners",

abstract = "This paper considers additive and purely additive spanners. We present a new purely additive spanner of size {\~O}(n7/5) with additive stretch 4. This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n3/2) and the other for 6-additive spanner of size O(n 4/3), and thus answers a main open question in this area. In addition, we present a construction for additive spanners with {\~O}(n 1+δ) edges and additive stretch of {\~O}(n 1/2-3δ/2) for any 3/17 ≤ δ < 1/3, improving the stretch of the existing constructions from O(n1-3δ) to {\~O}(√n1-3δ). Finally, we show that our (1,n 1/2-3δ/2)-spanner construction can be tweaked to give a sublinear additive spanner of size {\~O}(n1+3/17) with additive stretch O(√distance).",

author = "Shiri Chechik",

year = "2013",

doi = "https://doi.org/10.1137/1.9781611973105.36",

language = "الإنجليزيّة",

isbn = "9781611972511",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

pages = "498--512",

booktitle = "Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013",

note = "24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 ; Conference date: 06-01-2013 Through 08-01-2013",

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AU - Chechik, Shiri

PY - 2013

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N2 - This paper considers additive and purely additive spanners. We present a new purely additive spanner of size Õ(n7/5) with additive stretch 4. This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n3/2) and the other for 6-additive spanner of size O(n 4/3), and thus answers a main open question in this area. In addition, we present a construction for additive spanners with Õ(n 1+δ) edges and additive stretch of Õ(n 1/2-3δ/2) for any 3/17 ≤ δ < 1/3, improving the stretch of the existing constructions from O(n1-3δ) to Õ(√n1-3δ). Finally, we show that our (1,n 1/2-3δ/2)-spanner construction can be tweaked to give a sublinear additive spanner of size Õ(n1+3/17) with additive stretch O(√distance).

AB - This paper considers additive and purely additive spanners. We present a new purely additive spanner of size Õ(n7/5) with additive stretch 4. This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n3/2) and the other for 6-additive spanner of size O(n 4/3), and thus answers a main open question in this area. In addition, we present a construction for additive spanners with Õ(n 1+δ) edges and additive stretch of Õ(n 1/2-3δ/2) for any 3/17 ≤ δ < 1/3, improving the stretch of the existing constructions from O(n1-3δ) to Õ(√n1-3δ). Finally, we show that our (1,n 1/2-3δ/2)-spanner construction can be tweaked to give a sublinear additive spanner of size Õ(n1+3/17) with additive stretch O(√distance).

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U2 - https://doi.org/10.1137/1.9781611973105.36

DO - https://doi.org/10.1137/1.9781611973105.36

M3 - منشور من مؤتمر

SN - 9781611972511

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 498

EP - 512

BT - Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013

T2 - 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013

Y2 - 6 January 2013 through 8 January 2013

ER -

New additive spanners

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