# Light Spanner and Monotone Tree

@article{Hung2012LightSA, title={Light Spanner and Monotone Tree}, author={Hao-Hsiang Hung}, journal={ArXiv}, year={2012}, volume={abs/1207.3807} }

In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem) [8] and others [3]. We have developed an efficient algorithm in [9] for light spanners in bounded pathwidth graphs, based on an intermediate data structure called monotone tree. In this paper, we extended the results to include bounded catwidth graphs.

## 4 Citations

### A Light Metric Spanner

- Mathematics2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

This paper shows that doubling spaces admit (1 + ε)-stretch spanners with lightness WD = (ddim /ε)<sup>O(ddim)</sup>.

### Minor-Free Graphs Have Light Spanners

- Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

We show that every H-minor-free graph has a light (1+≥ilon)-spanner, resolving an open problem of Grigni and Sissokho and proving a conjecture of Grigni and Hung \cite{GH12}. Our lightness…

### The Greedy Spanner is Existentially Optimal

- Computer Science, MathematicsPODC
- 2016

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.

### The Greedy Spanner is Existentially Optimal [ Extended

- Computer Science, Mathematics
- 2016

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.

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