An Exploration of the Geometry of Road Networks Through Embeddings in the Euclidian Plane

Live Poster Session: Zoom Link
Thursday, July 30th 1:15-2:30pm EDT

Miles Aronow
Miles Aronow

I am a rising junior from West Hartford, Connecticut, majoring in Mathematics and Computer Science. In addition to my studies, I compete for Wesleyan as a member of the Cross Country and Track and Field teams. I enjoy trail running, board games, and the State of Connecticut.

Abstract: Half of the global population already lives in cities, and by 2050 two-thirds of the world’s people are expected to live in urban areas. The speed and scale of urbanization brings tremendous challenges in developing sustainable cities. In this project, we seek to understand the road networks of cities through a geometric lens. Specifically, we explore the dimensionality of urban road networks by embedding them in the Euclidean plane. We hypothesize that cities are effectively two dimensional, that is they embed in two dimensions such that the euclidean distance between points in the embedding matches the shortest path between points in the network with little distortion. In this poster we examine the effectiveness of embeddings on different sampling techniques and observe that random samples of nodes from a larger network embed with lower stress and distortion then small subgraphs of similar order. Furthermore, we show that embeddings tend to improve as sample size increases and that cities vary in their ability to be embedded successfully.

MilesAronowFinalPoster

Live Poster Session: Zoom Link
Thursday, July 30th 1:15-2:30pm EDT

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