The question is related to applications of interval graphs in music: https://music.stackexchange.com/questions/124648/are-there-applications-of-interval-graphs-in-musical-analysis

For each voice v_j we have notes n_ji (not rests) which are played at times s_ji and end at time e_ji. Now let us collect all intervals of time where the notes of all voices are played: I_1 = [a_1,b_1],...,I_n = [a_n,b_n]. We can construct an undirected graph, which matches what can be heard: I is connected to J iff I intersects J is not empty. Hence two notes are connected if they share some time interval when they are played together. Hence the listeners experience of listening some notes overlapped at the same time, is translated in graph theoretical terms to the interval graph for further analysis.

My question is: Is there an algorithm which will construct the interval graph fast, taking into consideration that intervals of the same voice should not overlap?

Thanks for your help.



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