6 papers
Group Action and Spin Representation Lead to a Holant* Complexity Dichotomy on Domain Size 3
Jin-Yi Cai, Jin Soo Ihm
We prove a complexity dichotomy theorem for problems over complex-valued symmetric constraint functions on domain size . We give a decidable tr…
Pure Nash Equilibria under the Affine Mechanism: A Potential Game of Exaggeration
Jason Jisen Li, Young Wu, Yancheng Zhu +2
The mean mechanism is known to be non-incentive-compatible, namely, rational players are incentivized to misreport their values. Despite this game-theoretic issue, the mean mechani…
New Planar Algorithms and a Full Complexity Classification of the Eight-Vertex Model
Austen Fan, Jin-Yi Cai, Shuai Shao +1
We prove a complete complexity classification theorem for the planar eight-vertex model. For every parameter setting in for the eight-vertex model, the partition func…
Holant* Dichotomy on Domain Size 3: A Geometric Perspective
Jin-Yi Cai, Jin Soo Ihm
Holant problems are a general framework to study the computational complexity of counting problems. It is a more expressive framework than counting constraint satisfaction problems…
The Battling Influencers Game: Nash Equilibria Structure of a Potential Game and Implications to Value Alignment
Young Wu, Yancheng Zhu, Jin-Yi Cai +1
When multiple influencers attempt to compete for a receiver's attention, their influencing strategies must account for the presence of one another. We introduce the Battling Influe…
A Uniformly Random Solution to Algorithmic Redistricting
Jin-Yi Cai, Jacob Kruse, Kenneth Mayer +1
The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that…