Abstract
In the Steiner point removal problem, we are given a weighted graph G = (V, E) and a set of terminals K \subset V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that distances between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer, and Nguyen [SIAM J. Comput., 44 (2015), pp. 975-995] devised a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Proceedings of the 29th Annual ACM/SIAM Symposium on Discrete Algorithms, 2018, pp. 1353-1360] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We devise a novel and simpler algorithm (called the Relaxed-Voronoi algorithm) which incurs distortion O(log k). This algorithm can be implemented in almost linear time (O(| E| log | V | )).
| Original language | English |
|---|---|
| Pages (from-to) | 249-278 |
| Number of pages | 30 |
| Journal | SIAM Journal on Computing |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 Society for Industrial and Applied Mathematics
Funding
\ast Received by the editors April 30, 2018; accepted for publication January 22, 2019; published electronically March 26, 2019. A preliminary version appeared in Proceedings of SODA'18, 2018. http://www.siam.org/journals/sicomp/48-2/M118440.html Funding: The research was supported in part by ISF grant (1718/18) and BSF grant 2015813. \dagger Department of Computer Science, Ben Gurion University of the Negev, Beer Sheva, 8410501, Israel ([email protected]).
| Funders | Funder number |
|---|---|
| United States-Israel Binational Science Foundation | 2015813 |
| Israel Science Foundation | 1718/18 |
Keywords
- Distortion
- Metric embedding
- Minor graph
- Randomized algorithm
- Steiner point removal (SPR)