The HyperTrac Project: Recent Progress and Future Research Directions on Hypergraph Decompositions

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in…

在超图世界模型中使用最大似然路径的目标不可知规划

Goal Agnostic Planning using Maximum Likelihood Paths in Hypergraph World Models

提出基于超图的目标不可知自动规划引擎，结合机器学习与传统AI优势，证明其能确定最优解并数学界定学习性能，通过三个典型规划问题验证有效性。

Quadratic Decomposable Submodular Function Minimization

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and hypergraphs settings, such as graph-based semi-supervised learning and PageRank. We approach the problem via a new dual strategy and describe an objective that may be optimized via random coordinate descent (RCD) methods and projections onto cones. We also establish the linear convergence rate of the RCD algorithm and develop efficient projection algorithms with p…