Related papers: A Universal Construction for Unique Sink Orientati…
A unique sink orientation (USO) is an orientation of the $n$-dimensional hypercube graph such that every non-empty face contains a unique sink. Schurr showed that given any $n$-dimensional USO and any dimension $i$, the set of edges $E_i$…
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 $n$-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…
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…
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…
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.…
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…
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…
We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…
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)…
The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…
We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspects of real-world robots. First, modules often do not occupy…
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…
Reverse engineering (RE) of user interfaces (UIs) plays an important role in software evolution. However, the large diversity of UI technologies and the need for UIs to be resizable make this challenging. We propose ReverseORC, a novel RE…
A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them,…
In this work we present a method of decomposition of arbitrary unitary matrix $U\in\mathbf U(2^k)$ into a product of single-qubit negator and controlled-$\sqrt{\mbox{NOT}}$ gates. Since the product results with negator matrix, which can be…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…
A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…