Related papers: Computational Complexity of Arranging Music
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…
We consider several computational problems related to conjugacy between subshifts of finite type, restricted to $k$-block codes: verifying a proposed $k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and reducing the…
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…
Music segmentation refers to the dual problem of identifying boundaries between, and labeling, distinct music segments, e.g., the chorus, verse, bridge etc. in popular music. The performance of a range of music segmentation algorithms has…
We answer the following question posed by Lechuga: Given a simply-connected space $X$ with both $H_*(X,\qq)$ and $\pi_*(X)\otimes \qq$ being finite-dimensional, what is the computational complexity of an algorithm computing the cup-length…
Out of the scope of the usual positions of computing in the field of music and musicology, one notices the emergence of human-computer systems that do exist by breaking off. Though these singular systems take effect in the usual fields of…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition…
Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. In this paper, we solve various open problems concerning the computational complexity of stable partitions in additively…
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…
Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings…
In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
We consider a specific scenario of text aggregation, in the realm of musical harmonization. Musical harmonization shares similarities with text aggregation, however the language of harmony is more structured than general text. Concretely,…
Aesthetics, among other criteria, can be statistically examined in terms of the complexity required for creating and decrypting a work of art. We propose three laws of aesthetic complexity. According to the first law of aesthetic…