no code implementations • 22 Feb 2024 • Mitchell Black, Zhengchao Wan, Gal Mishne, Amir Nayyeri, Yusu Wang
The distinguishing power of graph transformers is closely tied to the choice of positional encoding: features used to augment the base transformer with information about the graph.
1 code implementation • 14 Feb 2023 • Mitchell Black, Zhengchao Wan, Amir Nayyeri, Yusu Wang
We propose to use total effective resistance as a bound of the total amount of oversquashing in a graph and provide theoretical justification for its use.
no code implementations • 14 Mar 2022 • Peyman Afshani, Mark De Berg, Kevin Buchin, Jie Gao, Maarten Loffler, Amir Nayyeri, Benjamin Raichel, Rik Sarkar, Haotian Wang, Hao-Tsung Yang
For the Euclidean version of the problem, for instance, combining our results with known results on Euclidean TSP, yields a PTAS for approximating an optimal cyclic solution, and it yields a $(2(1-1/k)+\varepsilon)$-approximation of the optimal unrestricted solution.
no code implementations • 5 May 2020 • Peyman Afshani, Mark De Berg, Kevin Buchin, Jie Gao, Maarten Loffler, Amir Nayyeri, Benjamin Raichel, Rik Sarkar, Haotian Wang, Hao-Tsung Yang
The problem is NP-hard, as it has the traveling salesman problem as a special case (when $k=1$ and all sites have the same weight).