Almost-Optimal Sublinear Additive Spanners in Graph Theory

Explore a cutting-edge lecture on graph theory and algorithms presented by Zihan Tan from Rutgers University at the Simons Institute. Delve into the concept of sublinear additive spanners, a powerful tool for graph simplification. Learn how these spanners can approximate distances in undirected, unweighted graphs with remarkable efficiency. Discover the latest breakthrough in constructing almost-optimal sublinear additive spanners, achieving a stretch function of d+O(d^{1-1/k}) with O(n^{1+1/(2^{k+1}-1)+o(1)}) edges for any constant integer k≥2. Understand how this result nearly matches the lower bound established by Abboud, Bodwin, and Pettie in 2017. Gain insights into the implications of this work for maintaining distances in graph data structures. The 41-minute talk, based on joint research with Tianyi Zhang, offers a deep dive into advanced graph algorithms and their applications in computer science and network analysis.