Tom Kelly

h-index8
2papers
305citations

2 Papers

4.6LGSep 1, 2022
Large-Scale Auto-Regressive Modeling Of Street Networks

Michael Birsak, Tom Kelly, Wamiq Para et al.

We present a novel generative method for the creation of city-scale road layouts. While the output of recent methods is limited in both size of the covered area and diversity, our framework produces large traversable graphs of high quality consisting of vertices and edges representing complete street networks covering 400 square kilometers or more. While our framework can process general 2D embedded graphs, we focus on street networks due to the wide availability of training data. Our generative framework consists of a transformer decoder that is used in a sliding window manner to predict a field of indices, with each index encoding a representation of the local neighborhood. The semantics of each index is determined by a dictionary of context vectors. The index field is then input to a decoder to compute the street graph. Using data from OpenStreetMap, we train our system on whole cities and even across large countries such as the US, and finally compare it to the state of the art.

2.1COMar 17
The independence ratio of 4-cycle-free planar graphs

Tom Kelly, Sid Kolichala, Caleb McFarland et al.

We prove that every $n$-vertex planar graph $G$ with no triangle sharing an edge with a 4-cycle has independence ratio $n/α(G) \leq 4 - \varepsilon$ for $\varepsilon = 1/30$. This result implies that the same bound holds for 4-cycle-free planar graphs and planar graphs with no adjacent triangles and no triangle sharing an edge with a 5-cycle. For the latter case we strengthen the bound to $\varepsilon = 2/9$.