An Optimal Algorithm To Recognize Robinsonian Dissimilarities

International audienceA dissimilarity D on a finite set S is said to be Robinsonian if S can be totally ordered in such a way that, for every $i < j < k, D(i, j) ≤ D(i, k)$ and $D(j, k) ≤ D(i, k)$. Intuitively, D is Robinsonian if S can be represented by points on a line. Recognizing Robinsonian dissimilarities has many applications in se-riation and classification. In this paper, we present an optimal $O(n 2)$ algorithm to recognize Robinsonian dissimilarities, where n is the cardinal of S. Our result improves the already known algorithms

An Optimal Algorithm To Recognize Robinsonian Dissimilarities

International audienceA dissimilarity D on a finite set S is said to be Robinsonian if S can be totally ordered in such a way that, for every $i < j < k, D(i, j) ≤ D(i, k)$ and $D(j, k) ≤ D(i, k)$. Intuitively, D is Robinsonian if S can be represented by points on a line. Recognizing Robinsonian dissimilarities has many applications in se-riation and classification. In this paper, we present an optimal $O(n 2)$ algorithm to recognize Robinsonian dissimilarities, where n is the cardinal of S. Our result improves the already known algorithms

Digital Approaches to Troubadour Song

Thesis (Ph.D.) - Indiana University, Jacobs School of Music, 2020The troubadours were poet-composers who flourished in Occitania (today southern France) and surrounding areas during the twelfth and thirteenth centuries. Their lyric poems survive in chansonniers (songbooks) which usually contain only the texts. A fraction of the melodies that accompanied these poems were written down; fewer than 350 melodies survive for a lyric corpus of over 2,600 songs which appear over 13,000 times in all extant sources. This dissertation is part of a larger project whose aim is twofold: to create an openaccess, electronic, searchable archive of these melodies and to apply computational methods of analysis to identify the musical characteristics of the melodies, find patterns and relationships, and track trends in style both over time and within the works of individual authors. In this study, I first illustrate the methodology I followed to assess and encode the corpus of troubadour melodies and give an overview of the types of tools used to analyze the encoded melodies. In the subsequent chapters, I present five case studies which investigate musical features of the repertory through computational and statistical approaches, where I confirm, revise, or expand on existing knowledge of the repertory. The first case study identifies the extent and features of Guiraut Riquier’s melismatic writing by applying analytical techniques typically used to analyze textual corpora. The second case study applies a different technique borrowed from computational linguistics, Latent Semantic Analysis (LSA), to track the similarity of melodies with versions extant in multiple sources and to compare the phrases of melodies in one manuscript which have notation for more than one stanza. The three case studies in Chapter III adopt other analytical approaches to investigate and compare the pitch and interval content of the melodies. These studies help identify patterns in pitch organization in the entire repertory, point out stylistic trends of specific troubadours, and compare selected musical features by source. Overall, this study demonstrates the possibilities of computational approaches to contribute to existing scholarship on this repertory. Furthermore, the digital archive created for this project aims to empower additional research on the music of the troubadours, including the study of corpus-wide characteristics, the analysis of stylistic traits in specific authors or sources, and changes in style over the course of the tradition