Related papers: Computing Height-Optimal Tangles Faster
Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
The qubit routing problem, also known as the swap minimization problem, is a (classical) combinatorial optimization problem that arises in the design of compilers of quantum programs. We study the qubit routing problem from the viewpoint of…
We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeater's sizes. Based on this, we are able to demonstrate that…
Let $L$ be a finite lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of given $L$ and $f,g \in \mathcal{E}(L)$, finding the greatest lower bound $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ in the…
Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can be quantized into binary codes to give an efficient…
Let $L$ be a set of $n$ lines in the plane. The zone $Z(\ell)$ of a line $\ell$ in the arrangement $\mathcal{A}(L)$ of $L$ is the set of faces of $\mathcal{A}(L)$ whose closure intersects $\ell$. It is known that the combinatorial size of…
The energy efficiency of future networks is becoming a significant and urgent issue, calling for greener network designs. At the same time, rapid development of wireless networks shows a trend of increasing complexity in network structure…
We consider distributed computation of functions of distributed data in random planar networks with noisy wireless links. We present a new algorithm for computation of the maximum value which is order optimal in the number of transmissions…
Long-distance quantum communication in quantum networks faces significant challenges due to the constraints imposed by the no-cloning theorem. Most existing quantum communication protocols rely on the a priori distribution of entanglement…
In this paper, we investigate the transmission range assignment for N wireless nodes located on a line (a linear wireless network) for broadcasting data from one specific node to all the nodes in the network with minimum energy. Our goal is…
We study the limits of bipartite entanglement distribution using a chain of quantum repeaters that have quantum memories. To generate end-to-end entanglement, each node can attempt the generation of an entangled link with a neighbor, or…
A class of counting problems ask for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. We give several efficient algorithms, based on a linear optimization…
Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and…
In the Twin Towers of Hanoi version of the well known Towers of Hanoi Problem there are two coupled sets of pegs. In each move, one chooses a pair of pegs in one of the sets and performs the only possible legal transfer of a disk between…
We present a $O(n^{\frac{3}{2}})$-time algorithm for the \emph{shortest (diagonal) flip path problem} for \emph{lattice} triangulations with $n$ points, improving over previous $O(n^2)$-time algorithms. For a large, natural class of inputs,…
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is…