Stretching Stretch

Understand

We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms.

• The generalization, based on discounting highly stretched edges by taking their $p$-th power for some $0 < p < 1$, is directly related to performances of existing algorithms.
• This discounting of high-stretch edges allows us to treat many classes of edges with coarser granularity.
• It leads to a two-pass approach that combines bottom-up clustering and top-down decompositions to construct these embeddings in $\mathcal{O}(m\log\log{n})$ time.