# Computing shortest words via shortest loops on hyperbolic surfaces

@article{Yin2011ComputingSW, title={Computing shortest words via shortest loops on hyperbolic surfaces}, author={Xiaotian Yin and Yinghua Li and Wei Han and Feng Luo and Xianfeng Gu and Shing-Tung Yau}, journal={Computer-Aided Design}, year={2011}, volume={43}, pages={1449-1456} }

Given a loop on a surface, its homotopy class can be specified as a word consisting of letters representing the homotopy group generators. One of the interesting problems is how to compute the shortest word for a given loop. This is an NP-hard problem in general. However, for a closed surface that allows a hyperbolic metric and is equipped with a canonical set of fundamental group generators, the shortest word problem can be reduced to finding the shortest loop that is homotopic to the given… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 16 REFERENCES

## SHORTENING CURVES ON SURFACES

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## DEHN’S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Über unendliche diskontinuierliche Gruppen

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Discrete Surface Ricci Flow

VIEW 1 EXCERPT

## Algebraic Topology

VIEW 1 EXCERPT

## Greedy optimal homotopy and homology generators

VIEW 1 EXCERPT

## Optimal System of Loops on an Orientable Surface

VIEW 2 EXCERPTS

## Combinatorial Ricci Flows on Surfaces

VIEW 2 EXCERPTS

## Multiperiodic functions for surface design

VIEW 1 EXCERPT