scholarly journals Computational Complexity of Arranging Music

2017 ◽  
Author(s):  
Erik D. Demaine ◽  
William S. Moses
Keyword(s):  
Artificial Intelligence ◽  
Dynamic Programming ◽  
Computational Complexity ◽  
Data Structures ◽  
Music Theory ◽  
Algorithms And Data Structures ◽  
Rock Band ◽  
Computer Scientists ◽  
Np Complete ◽  
Single Instrument

Music has long been a subject of analysis for mathematicians and has led to interesting questions in music theory and other fields. For the most part, computer scientists have looked into applying artificial intelligence to music and finding algorithms and data structures to solve various musical problems. These problems tend to be solvable in polynomial time using dynamic programming and have various applications. This chapter takes an additional step in this direction, asking what sorts of problems in music cannot be efficiently computed. Specifically, it asks how various constraints affect the computational complexity of arranging music originally written for one set of instruments for a single instrument instead. It then applies these results to other domains, including musical choreography (such as ice skating and ballet) as well as to creating levels for rhythm games (such as Rock Band). It proves that all of the problems are NP-complete.

Computational Complexity and Statistical Physics

2005 ◽  
Keyword(s):  
Phase Transitions ◽  
Computational Complexity ◽  
Computer Science ◽  
Statistical Physics ◽  
Combinatorial Problems ◽  
Complete Problems ◽  
Computer Scientists ◽  
Background Material ◽  
Np Complete ◽  
Exciting Area

Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them. Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.

Humanism and Music

2020 ◽  
Author(s):  
Christopher M. Driscoll
Keyword(s):  
Artificial Intelligence ◽  
Popular Culture ◽  
Popular Music ◽  
Case Studies ◽  
Contemporary Music ◽  
Theoretical Relationship ◽  
Rock Band ◽  
Historical Developments ◽  
The Relationship

This chapter explores the relationship between humanism and music, giving attention to important theoretical and historical developments, before focusing on four brief case studies rooted in popular culture. The first turns to rock band Modest Mouse as an example of music as a space of humanist expression. Next, the chapter explores Austin-based Rock band Quiet Company and Westcoast rapper Ras Kass and their use of music to critique religion. Last, the chapter discusses contemporary popular music created by artificial intelligence and considers what non-human production of music suggests about the category of the human and, resultantly, humanism. These case studies give attention to the historical and theoretical relationship between humanism and music, and they offer examples of that relationship as it plays out in contemporary music.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

scholarly journals Representations, Affordances, and Interactive Systems

2021 ◽  
Vol 5 (5) ◽  
pp. 23
Author(s):  
Robert Rowe
Keyword(s):  
Artificial Intelligence ◽  
Cognitive Science ◽  
Data Structures ◽  
Digital Computer ◽  
Mental Representations ◽  
Interactive Systems ◽  
Algorithmic Composition ◽  
The World ◽  
History Of

The history of algorithmic composition using a digital computer has undergone many representations—data structures that encode some aspects of the outside world, or processes and entities within the program itself. Parallel histories in cognitive science and artificial intelligence have (of necessity) confronted their own notions of representations, including the ecological perception view of J.J. Gibson, who claims that mental representations are redundant to the affordances apparent in the world, its objects, and their relations. This review tracks these parallel histories and how the orientations and designs of multimodal interactive systems give rise to their own affordances: the representations and models used expose parameters and controls to a creator that determine how a system can be used and, thus, what it can mean.

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