23 papers · ranked by Valyu relevance
Robin Eßmann, Tobias Nipkow, Simon Robillard, Ujkan Sulejmani
Approximation algorithms for NP-complete problems [Vaz03] are a rich area of research untouched by automated verification. We present the first formal verifications of five classical and one lesser known approximation algorithm. Three of these algorithms had been verified on paper by program verification experts [BM03…
Barış Can Esmer, Ariel Kulik, Dániel Marx, Daniel Neuen + 1 more
'Roohani Sharma'] We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection between parameterized approximation and exponentialtime approximation algorithms for monotone subset minimization problems. In a monotone subset minimization problem…
Jingyang Zhao, Zimo Sheng, Mingyu Xiao
TSP is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is wellknown that TSP admits a constant approximation ratio on metric graphs but becomes NP-hard to approximate within any computable function f(n) on general graphs. This…
Antonios Antoniadis, Marek Eliáš, Adam Polak, Moritz Venzin
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask to select a feasible subset of input items of minimal (or maximal) total weight.…
Barış Can Esmer, Ariel Kulik, Dániel Marx, Daniel Neuen + 1 more
In a recent work, Esmer et al. describe a simple method - approximate monotone local search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more generally, parameterized approximation algorithms. In this work, we generalize…
Klairton L. Brito, Andre R. Oliveira, Alexsandro O. Alexandrino, Ulisses Dias + 1 more
'Ulisses Dias' 'Zanoni Dias'] Background In the comparative genomics field, one of the goals is to estimate a sequence of genetic changes capable of transforming a genome into another. Genome rearrangement events are mutations that can alter the genetic content or the arrangement of elements from the genome. Reversal…
Yuki Amano
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum b-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In this paper, we consider the problem under the local oracle model to investigate the…
Yael Kirkpatrick, Liam Roditty, Richard Qi, Virginia Vassilevska Williams
Computing the diameter of a graph is a problem of great interest both in general algorithms research and specifically within fine-grained complexity, where it is a cornerstone hard problem. Recent work has achieved a full conditional lower bound tradeoff curve for both directed and undirected graphs. However, the best…
Donghoon Shin, Sunghee Choi, Praveen Kumar Donta
We present improved algorithms for the Steiner tree problem with the minimum number of Steiner points and bounded edge length. Given n terminal points in a 2D Euclidean plane and an edge length bound, the problem asks to construct a spanning tree of n terminal points with minimal Steiner points such that every edge…
Michal Dory, Mohsen Ghaffari, Saeed Ilchi
We describe a simple deterministic $O \varepsilon ^{-1}\log \Delta $ round distributed algorithm for $2\alpha +11 + \varepsilon $ approximation of minimum weighted dominating set on graphs with arboricity at most $\alpha$. Here $\Delta$ denotes the maximum degree. We also show a lower bound proving that this round…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Yossi Azar, Danny Vainstein
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a binary tree (i.e., Hierarchical Clustering). Points which are close in the metric…
Paritosh Garg, Linus Jordan, Ola Svensson
While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of 2 for the unweighted matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted instances. Their approach is based on the versatile local ratio technique and also applies…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…
Pier Paolo Poir, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Authors not listed
Chemical reactions are regarded as transformations of chemical structures, and the question of which atoms in the reactants correspond to which atoms in the products has attracted chemists for a long time. Atom-to-atom mapping (AAM) is a procedure that establishes such correspondence(s) between the atoms of reactants…
Lars Arvestad
Distance-based methods for inferring evolutionary trees are important subroutines in computational biology, sometimes as a first step in a statistically more robust phylogenetic method. The most popular method is Neighbor Joining, mainly to to its relatively good accuracy, but Neighbor Joining has a cubic time…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Changin Oh, Kathleen P. Wilkie
We present the Toroidal Search Algorithm (TSA), a novel population-based metaheuristic optimization method inspired by the topology of a torus. Conventional metaheuristics frequently suffer from boundary stagnation, a phenomenon that severely degrades performance in bounded and high-dimensional search spaces. TSA…
Lionel Zoubritzky, François-Xavier Coudert
We present here an open-source Julia library for the topological identification of crystalline materials, with algorithmic and computational improvements over the previously available software in the field, resulting in a speed increase of one order of magnitude. This new algorithm and implementation can therefore be…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Zimei Chen, Yi Ren, Eryn Sale, Ying Nian Wu + 1 more
Accumulating evidence suggests the canonical cortical circuit, consisting of excitatory (E) and diverse classes of inhibitory (I) interneurons, implement sampling-based Bayesian inference to compute stimulus posteriors. However, most of the identified sampling algorithms in the circuit are still simpler than the…
Remco Bouckaert, Lena Collienne, Alex Gavryushkin
There are a growing number of areas, e.g. epidemiology and within-organism cancer evolution, where re-analysing all available data from scratch every time new data becomes available or old data is refined is no longer feasible. All these and related areas can benefit from online phylogenetic inference that can booster…