Related papers: Computational Complexity of Arranging Music
There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework…
Choreographies are global descriptions of interactions among concurrent components, most notably used in the settings of verification and synthesis of correct-by-construction software. They require a top-down approach: programmers first…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm…
Arranging music for a different set of instruments that it was originally written for is traditionally a tedious and time-consuming process, performed by experts with intricate knowledge of the specific instruments and involving significant…
Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic…
Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…
We explore the chaotic dynamics and complexity of a neuro-system with respect to variable synaptic weights in both noise free and noisy conditions. The chaotic dynamics of the system is investigated by bifurcation analysis and 0-1 test. A…
We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.
We present a statistical-modelling method for piano reduction, i.e. converting an ensemble score into piano scores, that can control performance difficulty. While previous studies have focused on describing the condition for playable piano…
Structure is one of the most essential aspects of music, and music structure is commonly indicated through repetition. However, the nature of repetition and structure in music is still not well understood, especially in the context of music…
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…
Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…