平面密度约束下能量最小化的快速多重网格算法

Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs

Given an embedded planar acyclic digraph G, we define the problem of acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM) to be the problem of determining a hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian acyclic digraph. Our results include: 1. We provide a characterization under which a planar st-digraph G is hamiltonian. 2. For an outerplanar st-digraph G, we define the st-polygon decomposition of G and, based on its properties, we develop …

识别2层和外部k-平面图

Recognizing 2-Layer and Outer $k$-Planar Graphs

本文研究2层k-平面图和外部k-平面图的识别问题，提出XP算法并证明其XNLP难性，同时在单层顶点顺序给定情形下给出FPT算法。

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. Th…

High-performance Energy Minimization with Applications to Adiabatic Quantum Computing

Energy minimization of Ising spin-glasses has played a central role in statistical and solid-state physics, facilitating studies of phase transitions and magnetism. Recent proposals suggest using Ising spin-glasses for non-traditional computing as a way to harness the nature's ability to find min-energy configurations, and to take advantage of quantum tunneling to boost combinatorial optimization. Laboratory demonstrations have been unconvincing so far and lack a non-quantum baseline for definitive comparisons. In this work we (i) design and evaluate new computational techniques to simulate na…

量子图绘制

Quantum Graph Drawing

本文研究2-层绘制与书式布局中的量子算法，基于Grover搜索给出相对经典精确算法至少二次加速的框架，并通过D-Wave实验表明量子退火在2-层交叉最小化上具有竞争力。

分层树的同步绘制

Simultaneous Drawing of Layered Trees

本文研究多棵平面嵌入有根树在分层绘制中的交叉最小化问题，分别为两棵树给出多项式时间动态规划，并为三层上任意数量树给出归约至最短路径的 XP 时间算法。