Related papers: Exact Cover with light
The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilising the…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's famous covering problem. Similar numbers can be defined by…
Several alternative possibilities of how to create an electromagnetic device being able to reconstruct near-field distribution of a source with sub-wavelength resolution (so-called perfect lens) are considered. It is shown that there is a…
Frontal photopolymerization (FPP) provides a versatile method for the rapid fabrication of solid polymer network materials by exposing photosensitive molecules to light. Dimensional control of structures created by this process is crucial…
In this paper, an algorithm for determining 3-colorability, i.e. the decision problem (YES/NO), in planar graphs is presented. The algorithm, although not exact (it could produce false positives) has two very important features: (i) it has…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the parameterized complexity of two problems related to arithmetic progressions, called Cover by…
Existing scene understanding systems mainly focus on recognizing the visible parts of a scene, ignoring the intact appearance of physical objects in the real-world. Concurrently, image completion has aimed to create plausible appearance for…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
We introduce the entangled coherent state representation, which provides a powerful technique for efficiently and elegantly describing and analyzing quantum optics sources and detectors while respecting the photon number superselection rule…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
The aim of this note is to provide a reduction of the Exact Matching problem to the Top-$k$ Perfect Matching Problem. Together with earlier work by El Maalouly, this shows that the two problems are polynomial-time equivalent. The Exact…
With the rapid development of fashion market, the customers' demands of customers for fashion recommendation are rising. In this paper, we aim to investigate a practical problem of fashion recommendation by answering the question "which…
In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the…
Image completion is a task that aims to fill in the missing region of a masked image with plausible contents. However, existing image completion methods tend to fill in the missing region with the surrounding texture instead of…