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We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…

Computational Geometry · Computer Science 2012-08-14 Luc Habert , Michel Pocchiola

We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.

Quantum Algebra · Mathematics 2008-09-19 Clark Alexander

For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of, seed, by broadening the notion of generator. This new concept allows us to explore the semigroup tree in an alternative…

Combinatorics · Mathematics 2017-12-27 Maria Bras-Amorós , Julio Fernández-González

Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…

Computational Complexity · Computer Science 2015-06-19 Wei Wei , Renquan Zhang , Baolong Niu , Binghui Guo , Zhiming Zheng

We present in this work, if a set of well organized suboracles is available, an algorithm for multiobject search with certainty in an unsorted database of $N$ items. Depending on the number of the objects, the technique of phase tunning is…

Quantum Physics · Physics 2007-05-23 Jin-Yuan Hsieh , Che-Ming Li , Der-San Chuu

We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…

Combinatorics · Mathematics 2023-06-22 János Balogh , Cosmin Bonchiş , Diana Diniş , Gabriel Istrate , Ioan Todinca

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…

Quantum Physics · Physics 2007-05-23 Andrew M. Childs , Andrew J. Landahl , Pablo A. Parrilo

An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…

High Energy Physics - Theory · Physics 2009-11-11 Antonio Accioly , Marco Dias

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…

Algebraic Geometry · Mathematics 2016-05-26 Jonathan D. Hauenstein , Jose Israel Rodriguez , Frank Sottile

Set partitions are arrangements of distinct objects into groups. The problem of listing all set partitions arises in a variety of settings, in particular in combinatorial optimization tasks. After a brief review, we give practical…

Data Structures and Algorithms · Computer Science 2026-02-03 Arnav Khinvasara , Alexander Pikovski

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…

Discrete Mathematics · Computer Science 2021-01-19 Dariusz Dereniowski , Wieslaw Kubiak

An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…

Computational Complexity · Computer Science 2015-03-20 Philon Nguyen

Given any algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to inexact first-order information. This is…

Optimization and Control · Mathematics 2024-06-04 Phillip Kerger , Marco Molinaro , Hongyi Jiang , Amitabh Basu

Let $\mathrm{R}$ be a real closed field and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\'e characteristic of real algebraic as well as semi-algebraic…

Algebraic Geometry · Mathematics 2017-07-13 Saugata Basu , Cordian Riener

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

Logic in Computer Science · Computer Science 2025-04-18 Zhibo Chen , Frank Pfenning

Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…

Soft Condensed Matter · Physics 2010-12-22 Aaron S. Keys , Christopher R. Iacovella , Sharon C. Glotzer

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

Algebraic Topology · Mathematics 2016-12-14 Nicolás Cianci , Miguel Ottina

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Representation Theory · Mathematics 2019-06-05 Vladimir V Kornyak

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…

Machine Learning · Computer Science 2021-06-17 Rahman Salim Zengin , Volkan Sezer

Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete…

Cryptography and Security · Computer Science 2024-06-11 Martin Ekerå , Joel Gärtner