Related papers: Subquadratic Encodings for Point Configurations
We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. We also present a…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…
Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
We present an $O(n^2\log^4 n)$-time algorithm for computing the center region of a set of $n$ points in the three-dimensional Euclidean space. This improves the previously best known algorithm by Agarwal, Sharir and Welzl, which takes…
For every fixed $d \in \mathbb{N}$, we design a data structure that represents a binary $n \times n$ matrix that is $d$-twin-ordered. The data structure occupies $O_d(n)$ bits, which is the least one could hope for, and can be queried for…
An algorithm is demonstrated that finds an ordinary intersection in an arrangement of $n$ lines in $\mathbb{R}^2$, not all parallel and not all passing through a common point, in time $O(n \log{n})$. The algorithm is then extended to find…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g.,…
We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called $C_{ab}$ curves, as well as algorithms for inverting the encoding map, which we call "unencoding". Some $C_{ab}$ curves have…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
We propose a new succinct representation of labeled trees which represents a tree T using |T|H_k(T) number of bits (plus some smaller order terms), where |T|H_k(T) denotes the k-th order (tree label) entropy, as defined by Ferragina at al.…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
Variational quantum algorithms have attracted attention for their potential to solve combinatorial optimization problems. We study how the choice of encoding affects the resource requirements and optimization behavior of a variational…
In this paper, we investigate the homothetic point enclosure problem: given a set $S$ of $n$ triangles with sides parallel to three fixed directions, find a data structure for $S$ that can report all the triangles of $S$ that contain a…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
Network reconstruction consists in determining the unobserved pairwise couplings between $N$ nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent…