Modification of the algorithm for beat tracking of a musical melody

A new efficient modification of the known heuristic algorithm for real-time beat tracking is proposed. An improved formula for updating the relative frequencies of time intervals between adjacent onsets is used in the modification. The algorithm has shown good performance on the MIREX Beat Tracking test base. © 2013 Pleiades Publishing, Ltd

The computational complexity and approximability of a series of geometric covering problems

We consider a series of geometric problems of covering finite subsets of finite-dimensional numerical spaces by minimal families of hyperplanes. We prove that the problems are hard and Max-SNP-hard. © 2013 Pleiades Publishing, Ltd

Discriminative power for ensembles of linear decision rules

A novel class of ensembles of linear decision rules is introduced which includes majority voting-based ensembles as a particular case. Based on this general framework, new results are given that state the ability of a subclass to discriminate between two infinite subsets A and B in R n, thus generalizing Mazurov's theorem for two finite sets. © 2013 Pleiades Publishing, Ltd

Minimal Committee Problem for Inconsistent Systems of Linear Inequalities on the Plane

A representation of an arbitrary system of strict linear inequalities in R^n as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a committee solution of an inconsistent plane system of linear inequalities is given. A solution of two problems on minimal committee of a plane system is proposed. The obtained solutions to these problems can be found by means of the proposed algorithm.Comment: 29 pages, 2 figure

Аппроксимационная схема Хаймовича - Ринноя Кана для CVRP в метрических пространствах фиксированной размерности удвоения

The Capacitated Vehicle Routing Problem (CVRP) is a classical extremal combinatorial routing problem with numerous applications in operations research. Although the CVRP is strongly NP-hard both in the general case and in the Euclidean plane, it admits quasipolynomial- and even polynomial-time approximation schemes (QPTAS and PTAS) in Euclidean spaces of fixed dimension. At the same time, the metric setting of the problem is APX-complete even for an arbitrary fixed capacity q ≥ 3. In this paper, we show that the classical Haimovich-Rinnooy Kan algorithm implements a PTAS and an Efficient Polynomial-Time Approximation Scheme (EPTAS) in an arbitrary metric space of fixed doubling dimension for q = o(log log n) and for an arbitrary constant capacity, respectively. © 2019 Krasovskii Institute of Mathematics and Mechanics. All right reserved

Relaxation of pursuit-evasion differential game and program absorption operator

We consider some natural relaxation of pursuit-evasion differential game. For two closed sets, which are parameters, similar guidance problem for ε-neighborhoods is being solved. We are interested in finding a minimal size of such neighborhoods, which allows player I successfully solve his guidance problem in the class of generalized non-anticipating strategies. To resolve above-mentioned differential game, a modification of Program Iterations Method is implemented. Size of the neighborhoods is found as a position function and it's defined by application of special iterative procedure further below. As a corollary, it is shown that desired function is a fixed point of the open-loop operator, which defines the procedure. © 2020 Udmurt State University. All rights reserved.Russian Foundation for Basic Research, RFBR: 19–01–000573 A.Funding. The study was funded by RFBR, project number 19–01–000573 A

A Problem-Specific Branch-and-Bound Algorithm for the Protected Shortest Simple Path Problem with Must-Pass Nodes

An instance of the Protected Shortest Simple Path Problem with Must-Pass Nodes (PSSPP-MPN) is specified by an edge-weighted directed graph with dedicated source, destination, and additional must-pass nodes. The goal is to find two vertex-disjoint paths, such that the former one is simple, visits all the must-pass nodes, and has the minimum transportation cost. In this paper, we show that the PSSPP-MPN is strongly NP-hard even for subsets of must-pass nodes of arbitrary fixed size and propose a novel problem-specific branch-and-bound algorithm for this problem. Results of competitive numerical evaluation against the public dataset'Rome99' from the 9th DIMACS Implementation Challenge show that the proposed algorithm notably outperforms the state-of-the-art MIP-optimizer Gurobi both by accuracy and execution time. © 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)Ural Mathematical CenterMinistry of Education and Science of the Russian Federation, Minobrnauka, (075-02-2022-874)Yuri Ogorodnikovfl Roman Rudakovfl and Michael Khachay were supported by Ural Mathematical Center and the Ministry of Science and Higher Education of the Russian Federation (Agreement no. 075-02-2022-874)