相关论文: On Phases of Unique Sink Orientations

A unique sink orientation (USO) is an orientation of the $n$-dimensional cube graph ($n$-cube) such that every face (subcube) has a unique sink. The number of unique sink orientations is $n^{\Theta(2^n)}$. If a cube orientation is not a…

A unique sink orientation (USO) is an orientation of the hypercube graph with the property that every face has a unique sink. A number of well-studied problems reduce in strongly polynomial time to finding the global sink of a USO; most…

A unique sink orientation (USO) is an orientation of the edges of a hypercube such that each face has a unique sink. Many optimization problems like linear programs reduce to USOs, in the sense that each vertex corresponds to a possible…

A unique sink orientation (USO) is an orientation of the edges of a polytope in which every face contains a unique sink. For a product of simplices $\Delta_{m-1} \times \Delta_{n-1}$, Felsner, G\"artner and Tschirschnitz (2005) characterize…

Unique Sink Orientations (USOs) of cubes can be used to capture the combinatorial structure of many essential algebraic and geometric problems. For various structural and algorithmic questions, including enumeration of USOs and algorithm…

An orientation of a grid is called unique sink orientation (USO) if each of its nonempty subgrids has a unique sink. Particularly, the original grid itself has a unique global sink. In this work we investigate the problem of how to find the…

An acyclic USO on a hypercube is formed by directing its edges in such as way that the digraph is acyclic and each face of the hypercube has a unique sink and a unique source. A path to the global sink of an acyclic USO can be modeled as…

Unique-sink orientations (USOs) are an abstract class of orientations of the n-cube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and…

Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as for instance Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic…

Algorithms for finding the sink in Unique Sink Orientations (USOs) of the hypercube can be used to solve many algebraic and geometric problems, most importantly including the P-Matrix Linear Complementarity Problem and Linear Programming.…

We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…

A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to sample approximately from the uniform…

The complexity classes Unique End of Potential Line (UEOPL) and its promise version PUEOPL were introduced in 2018 by Fearnly et al. UEOPL captures search problems where the instances are promised to have a unique solution. UEOPL captures…

In this paper, we prove that any nontrivial $\mathrm{SO}(k )\times \mathrm{SO}(n+1-k)$-symmetric ancient compact noncollapsed solution of the mean curvature flow agrees up to scaling and rigid motion with the $\mathrm{O}(k)\times…

We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…

The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique…

Faceted interfaces are a key feature in self-resembling morphologies of many microstructures generated from solid state phase transformations. Interpretations, predictions and simulations of the faceted morphologies remain a challenge,…

Orientations of supersingular elliptic curves encode the information of an endomorphism of the curve. Computing the full endomorphism ring is a known hard problem, so one might consider how hard it is to find one such orientation. We prove…

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set;…

We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…